Calvi Liege 2010 Students

8/13/2019 Calvi Liege 2010 Students

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Spacecraft Structural Dynamics & Loads - A. Calvi 1

This presentation is distributed to the students of the University of LiegeSatell ite Engineering Class November 29, 2010)

This presentation is not for further distribution

Spacecraft Structural Dynamics & Loads

An Overview

Adriano Calvi, PhDESA / ESTEC, Noordwijk, The Netherlands


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ForewordForeword

This half-day course on Structural Dynamics and Loads intends topresent the subject within the broad context of the development ofspacecraft structures.

Basic notions as well as some advanced

concepts are explained with minimum mathematics

The content is the result of the authors experience acquiredthrough his involvement with research and industrial activitiesmainly at the European Space Agency and Alenia Spazio

The course is specifically tailored for university students


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Specific Objectives of the Presentation

To provide a short overview about structural dynamics and its

importance in the development of the spacecraft structures (design,analysis & test)

To introduce the students to the logic and criteria

as regards

dynamics and loads

To point out the importance of some topics such as modaleffective mass, dynamic testing

and model validation

often notaddressed in the University Courses

To show results of some applications (satellites, launchers, etc.)

To testify the importance of structural dynamics analysis (andspecifically of some numerical methods)


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Spacecraft Structural Dynamics & Loads (1)

Introduction

Preliminary concepts: the launch mechanical environment

Requirements for spacecraft structures

The role of structural dynamics in a space project

Dynamic analysis types

Real eigenvalue

Frequency response

Transient response

Shock response

Random vibration

The effective mass concept

Preliminary design, design load cycles & verification loads cycle


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Payload-launcher Coupled Loads Analysis (CLA)

Mechanical tests

Modal survey test

Sinusoidal vibration test

Acoustic noise test

Shock test

Random vibration test

Overtesting, notching

and sine vibration testing

Mathematical model updating and validation

Summary and conclusive remarks

Bibliography


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Preliminary concepts (1)Preliminary concepts (1)

Structural dynamics is the study of structures subjected to amechanical environment which depends on time and leading to amovement

Excitation transmission types (mechanical & acoustic)

Type of time functions (sinusoidal, transient, random)

Type of frequencies involved (low frequency, broadband)

Domain of analysis (time domain, frequency domain)

Structure representation with a mathematical model (continuous ordiscrete)


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Preliminary concepts (2)Preliminary concepts (2)

The parameter most commonly used (in the industry) to define the motionof a mechanical system

is the acceleration

Typical ranges of acceleration of concern in aerospace structures are from0.01 g to 10,000 g.

Frequency (Hz or rad/s) and octave

Vibroacoustics, pressure (N/m 2) and Sound Pressure Level (dB)

Random vibration and (acceleration) Power Spectral Density (g 2/Hz)

Shock Response Spectrum

Root mean square (rms) = square root of the mean of the sum of all thesquares

Note 1: the decibel is a tenth of a bel, the logarithm (base 10)

of a power ratio (itis accepted that power is proportional to the square of the rms

of acceleration,velocity, pressure, etc.)

Note 2: it must be emphasized that dB in acoustics is not an unit of acousticpressure but simply a power ratio with respect to a reference pressure whichmust be stated or clearly implicit


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Example of satellite structural design conceptExample of satellite structural design concept


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Accelerations Accelerations some remarkssome remarks

The parameter most commonly used (in the industry) to define themotion of a mechanical system is the acceleration

Good reasons: accelerations are directly related to forces/stresses andeasy

to specify and measure

Some hidden

assumptions

Criteria for equivalent structural damage (e.g. shock response spectra)Note: failures usually happen in the largest stress areas, regardless if theyare the largest acceleration areas!

Rigid or static determinate junction (e.g. quasi-static loads)

Important consequences

Need for considering the actual

(e.g. test

or

flight) boundary conditions

(e.g. for the purpose of notching)

Need for a valid

F.E. model (e.g. to be used for force and stress recovery)


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Mechanical loads are caused by:Mechanical loads are caused by:

Transportation

Rocket Motor Ignition Overpressure

Lift-off Loads

Engine/Motor Generated Acoustic Loads

Engine/Motor Generated Structure-borne Vibration Loads

Engine/Motor Thrust Transients

Pogo Instability, Solid Motor Pressure Oscillations

Wind and Turbulence, Aerodynamic Sources

Liquid Sloshing in Tanks

Stage and Fairing Separation Loads

Pyrotechnic Induced Loads

Manoeuvring Loads

Flight Operations, Onboard Equipment Operation


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Launch mechanical environmentLaunch mechanical environment

Steady state accelerations

Low frequency vibrations

Broad band vibrations

Random vibrations

Acoustic loads

Shocks

Loads (vibrations) are transmitted to the payload (e.g. satellite)

through its mechanical interface

Acoustic loads also directly excite payload surfaces


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SteadySteady --statestate and lowand low --frequency transient accelerationsfrequency transient accelerations


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Acoustic Loads Acoustic Loads

During the lift off and the early phases ofthe launch an extremely high level ofacoustic noise surrounds the payload

The principal sources of noise are:

Engine functioning

Aerodynamic turbulence

Acoustic noise (as pressure waves)impinging on light weight panel-likestructures produce high response


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Broadband and high frequency vibrationsBroadband and high frequency vibrations

Broad band random vibrations are produce by:

Engines functioning

Structural response to broad-band acoustic loads

Aerodynamic turbulent boundary layer


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ShocksShocks

Mainly caused by the actuation of pyrotechnic devices:

Release mechanisms for stage and satellite separation

Deployable mechanisms for solar arrays etc.


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Static and dynamic environment specification (typical ranges)Static and dynamic environment specification (typical ranges)


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QuasiQuasi --Static Loads (accelerations)Static Loads (accelerations)

Loads independent of time or which vary slowly, so that the dynamicresponse of the structure is not significant

(ECSS-E-ST-32). Note: this is

the definition of a quasi-static event!

Combination of static and low frequency loads into an equivalent

static

load specified for design purposes as C.o.G. acceleration

(e.g. NASA RP- 1403, NASA-HDBK-7004). Note: this definition is fully adequate for the

design of the spacecraft primary structure. For the design of componentsthe contribution of the high frequency loads, if relevant, is included as well!

CONCLUSION: quasi static loading means under steady-stateaccelerations

(unchanging applied force balanced by inertia loads). For

design purposes (e.g. derivation of design limit loads, selection of thefasteners, etc.), the quasi-static loads are normally calculated bycombining both static and dynamic load contributions. In this context thequasi static loads are equivalent to (or interpreted by the designer

as)

static loads , typically expressed as equivalent accelerations at the C.o.G.


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Typical Requirements for Spacecraft Structures

Strength

Structural life

Structural response

Stiffness

Damping

Mass Properties

Dynamic Envelope

Positional Stability

Mechanical Interface

Basic requirement : the structure shall support the payload andspacecraft subsystems with enough strength and stiffness topreclude any failure (rupture, collapse, or detrimental deformation)that may keep them from working successfully.


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Requirements evolutionRequirements evolution


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Design requirements and verificationDesign requirements and verification


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Examples of (Mechanical) Requirements (1)

The satellite shall be compatible with 2 launchers (potential candidates:VEGA, Soyuz in CSG, Rockot, Dnepr)...

The satellite and all its units shall withstand applied loads due to themechanical environments to which they are exposed during the service-life

Design Loads shall be derived by multiplication of the Limit Loads by a designfactor equal to 1.25 (i.e. DL= 1.25 x LL)

The structure shall withstand the worst design loads without failing orexhibiting permanent deformations.

Buckling is not allowed.

The natural frequencies of the structure shall be within adequate bandwidthsto prevent dynamic coupling with major excitation frequencies

The spacecraft structure shall provide the mounting interface to

the launchvehicle and comply with the launcher interface requirements.


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Examples of (Mechanical) Requirements (2)

All the Finite Element Models (FEM) prepared to support the mechanicalverification activities at subsystem and satellite level shall be delivered in

NASTRAN format

The FEM of the spacecraft in its launch configuration shall be detailed enough toensure an appropriate derivation and verification of the design loads and of themodal response of the various structural elements of the satellite up to 140 Hz

A reduced FEM of the entire spacecraft correlated with the detailed FEM shall bedelivered for the Launcher Coupled Loads Analysis (CLA)

The satellite FEMs

shall be correlated against the results of modal survey testscarried out at complete spacecraft level, and at component level

for units above

50 kg

The structural model of the satellite shall pass successfully qualification sinevibration Test.

The flight satellite shall pass successfully acceptance sine vibration test.


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Spacecraft stiffness requirements for different launchersSpacecraft stiffness requirements for different launchers

Launch vehicle manuals specify minimum values for the payload natural(fundamental) frequency of vibration in order to avoid dynamic coupling betweenlow frequency dynamics of the launch vehicle and payload modes


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The Role of Structural Dynamics in a Space ProjectThe Role of Structural Dynamics in a Space Project

Mechanical environment definition (structural response and loads

identification by analysis and test)

Launcher/Payload coupled loads analysis

Random vibration and vibroacoustic analyses

Jitter analysis

Test predictions (e.g. sine test by frequency response analysis)

Test evaluations (sine, acoustic noise)

Input to structural life analysis (e.g. generation of the loading spectrum)

Structural identification (by analysis and test)

Modal analysis

Modal survey test and experimental modal analysis


Design qualification and flight product acceptance

Qualification and Acceptance tests (sine, random, acoustic noise, shock)


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Introduction





Real eigenvalue

Frequency response

Transient response

Shock response

Random vibration




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Dynamic analysis typesDynamic analysis types

Real eigenvalue analysis (undamped free vibrations)

Modal parameter identification, etc.

Linear frequency response analysis (steady-state response oflinear structures to loads that vary as a function of frequency)

Sine test prediction, transfer functions calculation, LV/SC CLA etc.

Linear transient response analysis (response of linear structures toloads that vary as a function of time).

LV/SC CLA, base drive analysis, jitter analysis, etc.

Shock response spectrum analysis

Specification of equivalent environments (e.g. equivalent sine input),

Shock test specifications, etc.

Vibro-acoustics (FEM/BEM, SEA) & Random vibration analysis

Vibro-acoustic test prediction & random vibration environment definition

Loads analysis for base-driven random vibration


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Reasons to compute normal modes (real eigenvalue analysis)Reasons to compute normal modes (real eigenvalue analysis)

To verify stiffness requirements

To assess the dynamic interaction between a component and itssupporting structure

To guide experiments (e.g. modal survey test)

To validate computational models (e.g. test/analysis correlation)

As pre-requisite for subsequent dynamic analyses

To evaluate design changes

Mathematical model quality check (model verification)

Numerical methods: Lanczos,


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Real eigenvalue analysisReal eigenvalue analysis

Note: mode shape normalizationScaling is arbitrary

Convention: Mass, Max or Point


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Mode shapesMode shapes

Cantilever beam

Simply supported beam


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Satellite Normal Modes Analysis

Mode 1: 16.2 Hz Mode 2: 18.3 Hz

INTEGRAL Satellite (FEM size 120000 DOFs)


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Frequency Response AnalysisFrequency Response Analysis

Used to compute structural response to steady-state harmonicexcitation

The excitation is explicitly defined in the frequency domain

Forces can be in the form of applied forces and/or enforcedmotions

Two different numerical methods: direct and modal

Damped forced vibration equation of motion with harmonicexcitation:


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Frequency response considerationsFrequency response considerations

If the maximum excitation frequency is much less than the lowest resonant frequency of the system, a static analysis is probably

sufficient

Undamped or very lightly damped structures exhibit large dynamic

responses for excitation frequencies near natural frequencies(resonant frequencies)

Use a fine enough frequency step size ( f) to adequately predictpeak response.

Smaller frequency spacing should be used in regions near resonantfrequencies, and larger frequency step sizes should be used inregions away from resonant frequencies


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Harmonic forced response with dampingHarmonic forced response with damping


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Transient Response AnalysisTransient Response Analysis

Purpose is to compute the behaviour of a structure subjected to time- varying excitation

The transient excitation is explicitly defined in the time domain

Forces can be in the form of applied forces and/or enforced motions

The important results obtained from a transient analysis are typically

displacements, velocities, and accelerations of grid points, and forces and stresses in elements

Two different numerical methods: direct

(e.g. Newmark) and modal

(e.g. Lanczos

+ Duhamels integral or Newmark)

Dynamic equation of motion:


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Modal Transient Response AnalysisModal Transient Response Analysis


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Transient response considerationsTransient response considerations

The integration time step must be small enough to represent accuratelythe variation in the loading

The integration time step must also be small enough to represent

themaximum frequency of interest (cut-off frequency)

The cost of integration is directly proportional to the number of time steps

Very sharp spikes in a loading function induce a high-frequency transientresponse. If the high-frequency transient response is of primaryimportance in an analysis, a very small integration time step must be

used

The loading function must accurately describe the spatial and temporaldistribution of the dynamic load


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ShockShock response spectrum (and analysis)response spectrum (and analysis)

Response spectrum analysis is an approximate method ofcomputing the peak response of a transient excitation

applied to a

structure or component

There are two parts to response spectrum analysis: (1) generationof the spectrum and (2) use of the spectrum for dynamic response

such as stress analysis

Note 1: the part (2)

of the response spectrum analysis has alimited use in structural dynamics of spacecraft (e.g. preliminarydesign) since the accuracy of the method may be questionable

Note 2: the term shock

can be misleading (not always a physicalshock, i.e. an environment of a short duration, is involved. Itwould be better to use response spectrum)


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Generation of a response spectrum (1)Generation of a response spectrum (1)


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Generation of a response spectrum (2)Generation of a response spectrum (2)

the peak response for one oscillator does not necessarily occur at thesame time as the peak response for another oscillator

there is no phase information since only the magnitude of peak response iscomputed

It is assumed in this process that each oscillator mass is very small relativeto the base structural mass so that the oscillator does not influence the

dynamic behaviour of the base structure


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Shock Response Spectrum. Some remarksShock Response Spectrum. Some remarks

The 1-DOF system is used as reference structure (since thesimplest) for the characterization of environments (i.e.

quantification of the severity equivalent environments can bespecified)

In practice, the criterion used for the severity is the maximumresponse which occurs on the structure

(note: another criterion

relates to the concept of fatigue damage)

A risk in comparing two excitations of different nature is in theinfluence of damping on the results (e.g. maxima are proportionalto Q for sine excitation and variable for transient excitation!)

The absolute acceleration spectrum is used, which providesinformation about the maximum internal forces and stresses

The shock spectrum is a transformation of the time history which

is

not reversible (contrary to Fourier transform)


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Shock Response SpectrumShock Response Spectrum

(A) is the shock spectrumof a terminal peaksawtooth (B) of 500 Gpeak amplitude and 0.4millisecond duration


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Random vibration (analysis)Random vibration (analysis)

Random vibration is vibration that can be described only in astatistical sense

The instantaneous magnitude is not known at any given time;rather, the magnitude is expressed in terms of its statisticalproperties (such as mean value, standard deviation, and probabilityof exceeding a certain value)

Examples of random vibration include earthquake ground motion,wind pressure fluctuations on aircraft, and acoustic excitation dueto rocket and jet engine noise

These random excitations are usually described in terms of a

power spectral density (PSD) function

Note: in structural dynamics of spacecraft, the random vibrationanalysis is often performed with simplified techniques (e.g. basedon Miles

equation

+ effective modal mass models)


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Random noise with normal amplitude distributionRandom noise with normal amplitude distribution


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Power Spectral Density (conceptual model)Power Spectral Density (conceptual model)


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Sound Pressure Level (conceptual model)Sound Pressure Level (conceptual model)


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Modal effective mass (1)Modal effective mass (1)

It may be defined as the mass terms in a modal expansion of thedrive point apparent mass of a kinematically

supported system

Note: driving-point FRF: the DOF response is the same as the excitation

This concept applies to structure with base excitation

Important particular case: rigid or statically determinate junction

It provides an estimate of the participation of a vibration mode, interms of the load it will cause in the structure, when excited

Note: avoid using: it is the mass which participates to the mode!

Dynamic amplification factor

Modal reaction forces

Base (junction) excitation


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The effective mass matrix can be calculated either by the modalparticipation factors

or by using the modal interface forces

Normally only the values on the leading diagonal of the modaleffective mass matrix are considered and expressed in percentage

of the structure rigid body properties (total mass and secondmoments of inertia)

The effective mass characterises the mode and it is independentfrom the eigenvector normalisation

Gen. mass

Resultant of modal interface forces

i-th mode Rigid body modes

Modal participation factorsEffective mass

Eigenvector max value


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For the complete set of modes the summation of the modaleffective mass is equal to the rigid body mass

Contributions of each individual mode to the total effective masscan be used as a criterion to classify the modes

(global or local)

and an indicator of the importance of that mode, i.e. an indication ofthe magnitude of participation in the loads analysis

It can be used to construct a list of important modes for thetest/analysis correlation and it is a significant correlation parameter

It can be used to create simplified mathematical models (equivalentmodels with respect to the junction)


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Example of Effective Mass table(MPLM test and FE model)


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Introduction





Real eigenvalue

Frequency response

Transient response

Shock response

Random vibration




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A5 Typical Sequence of events A5 Typical Sequence of events


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A5 Typical Longitudinal Static Acceleration A5 Typical Longitudinal Static Acceleration


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Sources of Structural Loadings (Launch)Sources of Structural Loadings (Launch)

Axial-Acceleration Profile for the Rockot Launch Vehicle

g8

7

6

5

43

2

1

0t,150 200 250 300100500

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-20

-10

0

10

20

30

40

50

60

70

80

a c c e

l e r a t i o n

[ m / s

2 ]

t [s]


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Axial Acceleration at Launcher/Satellite Interface (Engines Cut-off)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-20

-10

0

10

20

30

40

50

60

70

80

a c c e l e r a t

i o n

[ m / s

2 ]

t [s]


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Load Factors for Preliminary Design (Ariane 5)Load Factors for Preliminary Design (Ariane 5)


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QuasiQuasi --static loads for different launchersstatic loads for different launchers


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QuasiQuasi --Static Flight Limit loads for Dnepr and SoyuzStatic Flight Limit loads for Dnepr and Soyuz


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Example of Physical (and Modal) Mass Acceleration Curvefor preliminary design of payload hardware or equipment items

100

10

11 10 100 1000

Physical

Modal

Effective Mass, kg

D y n a m

i c R e s p o n s e

A c c e

l e r a

t i o n ,

g


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Load Combination Criteria for Components(International Space Station Program)


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Loads and Factors

Expendable launch vehicles,pressurized hardware andmanned system Test Logic

Common Design LogicSatellitesTest Logic

Limit Loads - LL

Design Limit LoadsDLL

x Coef. A

DYL

x Coef. B

DUL

x Coef. C

x KQ x KA

QL AL

x KQ x KA

QL

AL

I n c r e a s

i n g

L o a

d

L e v e

l

ECSS E-ST-32-10


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Some definitionsSome definitions

Design:

The process used to generate the set information describing the

essential characteristics of a product (ECSS-P-001A)

Design means developing requirements, identifying options, doing analyses and trade studies, and defining a product in enough detail so

it can be built (T. P. Sarafin)

Verification:

Confirmation by examination and provision of objective evidence thatspecified requirements have been fulfilled (ISO 8402:1994)

Verification means providing confidence through disciplined steps thata product will do what it is supposed to do (T. P. Sarafin)

Note: we can prove

that the spacecraft satisfies the measurable criteriawe have defined, but we cannot prove

a space mission will be successful


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Design Loads CyclesDesign Loads Cycles A load cycle is the process of:

Generating and combining math models for a proposed design

Assembling and developing forcing functions, load factors, etc. tosimulate the critical loading environment

Calculating design loads and displacements for all significantground, launch and mission events

Assessing the results to identify design modifications or risks

Then, if necessary, modifying the design accordingly or choosing

to

accept the risk


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Design loads cycle processDesign loads cycle process


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Final VerificationFinal Verification

Consist of:

Making sure all requirements are satisfied ( compliance )

Validating the methods and assumptions used to satisfyrequirements

Assessing risks


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Final Verification (crucial points)Final Verification (crucial points)

To perform a Verification Loads Cycle for structures designedand tested to predicted loads

Finite element models correlation with the results of modal andstatic testing

Loads prediction with the current forcing functions

Compliance with analysis criteria (e.g. MOS>0)

To make sure the random-vibration environments used toqualify components were high enough (based on datacollected during the spacecraft acoustic test)

Note: in the verification loads cycle instead of identifying requireddesign changes (design loads cycle) the adequacy of the structurethat has already been built and tested is assessed


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Criteria for Assessing Verification Loads (strength)Criteria for Assessing Verification Loads (strength)

Analysis: margins of safety must me greater that or equal to zero

Test: Structures qualified by static or sinusoidal testing

Test loads or stresses as predicted

(test-verified math model and test

conditions) are compared with the total predicted loads during themission

(including flying transients, acoustics, random vibration,

pressure, thermal effects and preloads)

Test: Structures qualified by acoustic or random vibration testing

Test environments are compared with random-vibration environmentsderived from system-level acoustic testing


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Mechanical tests

Modal survey test


Acoustic noise test

Shock test






Bibliography


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UPPERCOMPOSITE


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Ariane-5 Dynamic Mathematical ModelPAYLOAD

EAP+EAP-

EPC

Dynamic effects up to about 100 Hz

3D FE models of EPC, EAP, UC

Dynamic Reduction using Craig-Bampton

formulation

Incompressible or compressible fluids models for liquidpropellants

Structure/fluid interaction

Nearly incompressible SRB solid propellant modeling

Pressure and stress effects on launcher stiffness

SRB propellant and DIAS structural damping

Non-linear launch table effects


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Sizing flight events (CLA with VEGA Launcher)Sizing flight events (CLA with VEGA Launcher)

1. Lift-off (P80 Ignition and Blastwave)

2. Mach1/QMAX Gust

3. P80 Pressure Oscill ations

4. Z23 Igni tion

5. Z23 Pressure Oscillations

6. Z9 Ignition


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CLA OutputCLA Output

LV-SC interface accelerations

Equivalent sine spectrum

LV-SC interface forces

Equivalent accelerations at CoG

Internal responses

Accelerations,

Displacements

Forces

Stresses


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Payload / STS CLAPayload / STS CLA

Lift-off Force Resultant in X [lbf]

Lift-off Main Fitting

I/F ForceX Dir. [N]

Lift-off Main Fitting

I/F Force

Z Dir. [N]

Lift-off Keel Fitting

I/F ForceY Dir. [N]


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Mechanical tests

Modal survey test


Acoustic noise test

Shock test






Bibliography


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Testing techniquesTesting techniques Introduction (1)Introduction (1)

Without testing, an analysis can give completely incorrect results

Without the analysis, the tests can represent only a very limited reality

Two types of tests according to the objectives to be reached:

Simulation tests for structure qualification or acceptance

Identification tests (a.k.a. analysis-validation tests) for structureidentification (the objective is to determine the dynamic characteristics ofthe tested structure in order to update

the mathematical model)

Note: identification and simulation tests are generally completelydissociated. In certain cases (e.g. spacecraft sine test) it is technicallypossible to perform them using the same test facility


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Testing techniquesTesting techniques Introduction (2)Introduction (2)

Generation of mechanical environment

Small shakers (with flexible rod; electrodynamic)

Large shakers (generally used to impose motion at the base)

Electrodynamic shaker

Hydraulic jack shaker

Shock machines (pyrotechnic generators and impact machines)

Noise generators + reverberant acoustic chamber (homogeneous and

diffuse field)

Measurements

Force sensors, calibrated strain gauges

Accelerometers, velocity or displacement sensors


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Classes of tests used to verify requirements (purposes)Classes of tests used to verify requirements (purposes)

Development test

Demonstrate design concepts and acquire necessary information fordesign

Qualification test

Show a design

is adequate by testing a single article

Acceptance test

Show a product

is adequate (test each flight article)

Analysis validation test

Provide data which enable to confirm critical analyses or to change(update/validate) mathematical models and redo analyses


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Tests for verifying mechanical requirements (purposes)Tests for verifying mechanical requirements (purposes)

Acoustic test

Verify strength and structural life by introducing random vibration

through acoustic pressure (vibrating air molecules)

Note: acoustic tests at spacecraft level are used to verify adequacy ofelectrical connections and validate the random vibration environmentsused to qualify components

(Pyrotechnic) shock test

Verify resistance to high-frequency shock waves caused by separationexplosives (introduction of high-energy vibration up to 10,000 Hz)

System-level tests are used to verify levels used for component testing


Verify strength and structural life by introducing random vibrationthrough the mechanical interface (typically up to 2000 Hz )


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RockotRockot Dynamic SpecificationDynamic Specification

Marketed by: Eurockot

Actually flight qualified

Manufactured by: Khrunichev

Capability: 950 kg @ 500 km

Launch site: Plesetsk

Environment Level

Sine vibrationLongitudinal = 1 g on [5-10] Hz 1.5 g at 20 Hz

1 g on [40-100] HzLateral = 0.625 g on [5-100] Hz

Acoustic

31.5 Hz = 130.5 dB63 Hz = 133.5 dB125 Hz = 135.5 dB250 Hz = 135.7 dB

500 Hz = 130.8 dB1000 Hz = 126.4 dB

2000 Hz = 120.3 dB

Shock100 Hz = 50 g700 Hz = 800 g1000 Hz 1500 Hz = 2000 g

4000 Hz 5000 Hz = 4000 g10000 Hz = 2000 g


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Modal survey test (identification test)Modal survey test (identification test)Purpose : provide data for dynamic mathematical model validationNote: the normal modes are the most appropriate dynamiccharacteristics for the identification of the structure

Usually performed on structural models (SM or STM) in flightrepresentative configurations

Modal parameters (natural frequencies, mode shapes, damping,effective masses) can be determined in two ways:

by a method with appropriation of modes, sometimes called phaseresonance, which consists of successively isolating each mode by anappropriate excitation and measuring its parameters directly

by a method without appropriation of modes, sometimes called phaseseparation, which consists of exciting a group of modes whoseparameters are then determined by processing the measurements


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Different ways to get modal data from testsDifferent ways to get modal data from tests

Hammer test

Vibration test data analysis

Dedicated FRF measurement & modal analysis

Full scale modal survey with mode tuning I n c r e a s i n g e

f f o r t

D a

t a c o n s i s t e n c y


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Modal Survey Test vs. Modal Data extracted from the Sine Vibration Test

Modal Survey :

requires more effort (financial and time)

provides results with higher quality

Modal Data from Sine Vibration :

easy access / no additional test necessary

less quality due to negative effects from vibration

fixtures / facility tables not indefinitely stiff

higher sweep rate (brings along effects like beating or control instabilities)


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Ariane 5 Ariane 5 -- Sine excitation at spacecraft base (Sine excitation at spacecraft base (sine-equivalent dynamics)


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Sine vibration for different launchers (longitudinal)Sine vibration for different launchers (longitudinal)


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Sine vibration for different launchers (lateral)Sine vibration for different launchers (lateral)


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Herschel on Hydra

( b )( b )


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Acoustic test (objectives) Acoustic test (objectives)

Demonstrate the ability of a specimen towithstand the acoustic environment duringlaunch

Validation of analytical models

System level tests verify equipmentqualification loads

Acceptance test for S/C flight models


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Ariane 5 Ariane 5 Acoustic noise spectrum under the fairing Acoustic noise spectrum under the fairing

A i f diff l hA i f diff l h


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Acoustic spectra for different launchers Acoustic spectra for different launchers

Sh k t t Obj ti d kSh k t t Obj ti d k


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Shock test. Objectives and remarksShock test. Objectives and remarks

Demonstrate the ability of a specimen towithstand the shock loads during launchand operation

Verify equipment qualification loadsduring system level tests

System level shock tests are generallyperformed with the actual shockgenerating equipment (e.g. clamp bandrelease)

or by using of a sophisticated pyro- shock generating system (SHOGUN for

ARIANE 5 payloads)

Shock response spectra for different launchers (spacecraft separShock response spectra for different launchers (spacecraft separ ation)ation)


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Shock response spectra for different launchers (spacecraft separ Shock response spectra for different launchers (spacecraft separ ation)ation)

Note: for a consistentcomparison, data

should refer tothe same adapter.

Shock machine (metalShock machine (metal metal pendulum impact machine)metal pendulum impact machine)


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Shock machine (metalShock machine (metal --metal pendulum impact machine)metal pendulum impact machine)


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Random vibration test with slide tableRandom vibration test with slide table


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Random vibration test with slide tableRandom vibration test with slide table

Random vibration test: dataRandom vibration test: data processing bandwidthprocessing bandwidth


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Random vibration test: dataRandom vibration test: data --processing bandwidthprocessing bandwidth

The figures show how the data-processing bandwidth can affect acalculated power spectral density. Whether a PSD satisfies criteriafor level and tolerance depends on the frequency bandwidth usedto process the measured acceleration time history.



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Mechanical tests

Modal survey test


Acoustic noise test

Shock test






Bibliography

Overtesting:Overtesting:di d i


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Overtesting:Overtesting:an introductionan introduction(vibration absorber effect)(vibration absorber effect)

Introduction to overtesting and notching


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Introduction to overtesting and notching

The qualification of the satellite to lowfrequency transient is normallyachieved by a base-shake test

The input spectrum specifies theacceleration input that should excitethe satellite, for each axis

This input is definitively different fromthe mission loads, which are transient

Notching: Reduction of accelerationinput spectrum in narrow frequencybands, usually where test item hasresonances

(NASA-HDBK-7004)


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GOCE on ESTEC Large Slip Table Herschel on ESTEC Large Slip Table


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Shock Response Spectrum and Equivalent Sine Input


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S oc espo se Spect u a d qu va e t S e put

A shock response spectrum is aplot of maximum response

(e.g.

displacement, stress, acceleration)of single degree-of-freedom(SDOF) systems to a given input

versus some system parameter,generally the undamped naturalfrequency.


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ESI for Spacecraft


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CLA (Coupled Load Analysis)

0 10 20 30 40 50 60 70 800

50

100

150

200

250

S R S [ m

/ s 2 ]

frequency [Hz]

SRSQ

SRS ESI

ESI

12

Q

SRS ESI

SRS

Difference is negligible for small damping ratios

/[ sm 2.412DOF2DOF

]/[ sm01.0

Hz23frequencynatural

SDOFSDOF


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][ s

[ Hz

]/[ sm 2.46

][s

[ Hz

Hz23frequencynatural 1.97 01.0

]/[ sm

Transient responseTransient response

Frequency response at ESI levelFrequency response at ESI level

The effects of the sine sweep rate on the structural response


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The acceleration enforced by the shakeris a swept frequency function

The sweep is amplitude modulated

Acceleration transient response can besignificantly lower that the steady-statefrequency response

2 oct/min

0 10 20 30 40 50 60-5

0

5

time [s]

a c c e

l a r a

t i o n

[ m / s

2 ] 4 oct/min

Effect of sweep rateEffect of sweep rate on isolated peak for increasing and decreasingon isolated peak for increasing and decreasing

frequency sweepsfrequency sweeps


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The sweep rate V

has 3effects:

a variation (sign of V ) ofthe frequency of the peak: f

A decrease of the peakamplitude: A

An increase of the peakwidth (with loss ofsymmetry):


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Notching

ESI(equivalent sine)


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SineSine --burst load testburst load test The sine burst test is used to apply a quasi static load to a test item in


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The sine-burst test is used to apply a quasi-static load to a test item inorder to strength qualify the item and its design for flight

A secondary objective is to minimize potential fatigue damage to

thetest item

For components and subsystems, the fixture used for vibration testingoften can also be used for sine-burst strength testing. For this reason,

strength qualification and random vibration qualification can often beperformed during the same test session which saves time and money

Since the test is intended to impart a quasi-static load to the test item,the test frequency must be

(in principle) below the fundamental

resonant frequency of the test item

The sine-burst test is a cost effective alternative to either static loadsor to centrifuge testing

(Sine) quasi static load test(Sine) quasi static load test (sine burst)(sine burst)


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Random vibration test: notching of test specificationRandom vibration test: notching of test specification


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Illustration of notching of random vibration test specification,at the frequencies of strong test item resonances

Spacecraft Structural Dynamics & Loads (2) Payload launcher Coupled Loads Analysis (CLA)


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Mechanical tests

Modal survey test


Acoustic noise test

Shock test






Bibliography

Validation of Finite Element Models

(with emphasis on Structural Dynamics)


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Everyone believes the test data except for theexperimentalist, and no one believes the finiteelement model except for the analyst

All models are wrong, but some are still useful

Verification and Validation Definitions(ASME Standards Committee: V & V in Computational Solid Mechanics )

V ifi i ( f d l l i ) P f d i i h


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Verification (of codes, calculations) : Process of determining that amodel implementation accurately represents the developers

conceptual description of the model and the solution to the model

Math issue: Solving the equations right

Validation: Process of determining the degree to which a model isan accurate representation of the real world from the perspective ofthe intended uses of the model

Physics issue: Solving the right equations

Note: objective of the validation is to maximise confidence inthe predictive capability of the model

Terminology: Correlation, Updating and Validation Correlation:


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the process of quantifying the degree of similarity and dissimilarity betweentwo models (e.g. FE analysis vs. test)

Error Localization:

the process of determining which areas of the model need to be modified

Updating:

mathematical model improvement using data obtained from an associatedexperimental model (it can be consistent or inconsistent )

Valid model :

model which predicts the required dynamic behaviour of the subjectstructure with an acceptable degree of accuracy, or correctness

Some remarks on the validation of critical analyses

Loads analysis is probably the single most influential task in


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y p y g

designing a space structure

Loads analysis is doubly important because it is the basis for statictest loads as well as the basis for identifying the target responsesand notching criteria

in sine tests

A single mistake in the loads analysis can mean that we design andtest the structure to the wrong loads

We must be very confident in our loads analysis, which means wemust check the sensitivity of our assumptions and validate theloads analysis that will be the basis of strength analysis and statictesting

Note: Vibro-acoustic, random and shock analyses are usually notcritical

in the sense that we normally use environmental tests to

verify mechanical requirements

ASME V&V Guide ASME V&V Guide vs.vs. Validation of FEM for CLAValidation of FEM for CLA

Reality of interest : satellite / low frequency transient environment


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y q y

Intended use of the model : launcher/satelli te CLA (to predict systembehaviour for cases that will not be tested)

Response features of interest : CLA loads (forces, accelerations, etc.)

Validation testing : modal survey test or base-drive sine test

Experimental data : accelerations (and forces) (time histories)

Experimental features of interest : natural frequencies, mode shapes

Metrics : relative errors (e.g. natural frequencies), MAC, etc.

Accuracy requirements : e.g. ECSS-E-ST-32-11

Computational model : NASTRAN F.E. model (eigenmodes analysis)

Validation documentation : ECSS-E-ST-32 (DRD Test/analysiscorrelation)

Targets of the correlation(features of interest for quantitative comparison)


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Characteristics that most affect the structure response to applied forces

Natural frequencies

Mode shapes

Modal effective masses

Modal damping

Total mass, mass distribution

Centre of Gravity, inertia

Static stiffness

Interface forces

Correlation of mode shapesCorrelation of mode shapes


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Spacehab FEM coupled to the test rig model & Silhouette

GOCE modal analysis and survey testGOCE modal analysis and survey test


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CrossCross --Orthogonality Check (COC) and Modal Assurance Criterion (MAC)Orthogonality Check (COC) and Modal Assurance Criterion (MAC)

The cross-orthogonality between the analysis and test mode


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shapes with respect to the mass matrix is given by:

The MAC between a measured mode and an analytical mode isdefined as:

aT m MC

as

T

asmr

T

mr

asT mr

rs MAC

2

Note: COC and MAC do not give a useful measure of the error!

Columbus: Cross-Orthogonality Check up to 35 Hz (target modes) TEST

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

FEM Err.% [Hz] 13.78 15.80 17.20 23.81 24.23 24.65 25.36 25.59 26.59 27.19 27.53 28.87 30.19 30.55 32.73 33.15 33.86 34.57 35.21 36.16


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1 -2.94 13.37 1.00

2 -0.95 15.65 1.00

3 -1.73 16.90 0.99

4 -3.26 23.03 0.93 0.35

5 -1.16 23.95 0.34 0.93

6 -2.00 24.16 0.95

7 -1.98 24.86 0.95 0.27

8 -0.12 25.56 0.86

9 -0.95 26.34 0.22 0.90

10 -2.65 26.47 0.95

11 -0.40 27.42 0.26 0.96

12 -3.65 27.82 0.82 0.27

13 -6.00 28.38 0.46 0.89

15 1.19 30.91 0.26 0.95

17 1.63 33.26 0.94 0.21 0.32

18 - 33.71 0.64 0.34 0.62

19 -4.72 34.45 0.95

20 1.21 34.99 0.57 0.81


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MPLM Modal CorrelationMPLM Modal Correlation

MPLMMPLMModalModalEffectiveEffective


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EffectiveEffectiveMassesMasses(Final Correlation)(Final Correlation)

Soho SVM Cross-Orthogonality CheckF.E.M.

1 2 3 4 8 9 10 15 21 26 29 30 31TEST Err. % Freq. Hz 34.83 37.24 44.07 45.19 51.51 52.68 55.46 62.18 70.92 77.99 81.53 82.25 84.42


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1 2.87 35.86 0.87 0.462 0.00 37.24 0.47 0.873 4.17 45.99 0.874 4.78 47.46 0.77 0.24

5 -3.39 49.82 -0.33 0.766 0.96 53.19 0.75 0.227 2.10 56.65 0.79 0.218 58.67 -0.28 -0.35 -0.229 60.24 -0.30 -0.22 0.46 0.46

10 3.30 64.30 0.6111 66.40 0.21 0.3212 67.50 0.45 -0.43

13 68.73 -0.38

14 69.6815 71.6916 72.71 0.37 -0.3317 3.30 73.34 0.21 0.8518 74.7819 75.6320 78.77 -0.2421 82.1222 7.72 84.51 0.7623 5.54 86.31 0.87 -0.2324 7.21 88.64 0.6425 5.45 89.29 -0.33 0.6326 94.4427 97.1528 99.56

GOCEGOCE -- MAC and Effective MassMAC and Effective Mass


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Aeolus STM: comparison of transfer functions Aeolus STM: comparison of transfer functions


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Sine test response , FEM predicted response and post-test (updated FEM) response

Lack of Matching between F.E. Model and Test

Modelling uncertainties and errors (model is not completely physicallyrepresentative)


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representative)

Approximation of boundary conditions

Inadequate modelling of joints and couplings

Lack or inappropriate damping

representation

The linear assumption of the model versus test non-linearities

Mistakes

(input errors, oversights, etc.)

Scatter in manufacturing

Uncertainties in physical properties

(geometry, tolerances, material properties)

Uncertainties and errors in testing

Measured data

or parameters contain levels of errors

Uncertainties in the test set-up, input loads, boundary conditions

etc.

Mistakes

(oversights, cabling errors, etc.)

Test-Analysis Correlation CriteriaThe degree of similarity or dissimilarity establishing that the correlationbetween measured and predicted values is acceptable


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ECSS-E-ST-32-11 Proposed Test / Analysis Correlation Criteria

Model Updating Using Design Sensitivity and Optimisation(traditional basic assumptions)


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Some appropriate objective functions, within design optimisationcodes, can be used to drive a F.E.M. to behave in the samemanner as the real structure portrayed by a set of numerical test

results

The test results accurately depict the true behaviour of the structure


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Model updating: example of objective functionsNatural Frequency:

e

eaf f

f f d


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Mode Shape:e

ead ( : modal scale factor)

Effective Transmissibilities:e

eaT~

T~

T~

T~

d

Effective Masses: eea

M~

M~

M~

M~

d

Objective Function

bW bF T with

M~T~

f

d

d

d d

b and

M~

T~

f

w

w

ww

W

Location of Modelling Errors and Selection of the Design

Variables Based on Sensitivity AnalysisCriterion (selection of design variables):


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The design variables should be selected for those elements or element groupswhich have an influence on the eigenfrequencies

and mode shapes which are

targeted during the correlation/updating process (in addition to analysts knowledgeof uncertain modelled regions of the structure and/or results of

other error

localisation analyses)

Two basic approaches are poss ible:

Initial model sensitivities (e.g. initial derivative approach)

A Posteriori

Approach (at the end of a preliminary optimisation process)

Criterion (error localisation):

To determine how effective certain physical properties changes might be in reducingthe difference between measured and calculated data (however high sensitivity isnot generally a sufficient reason for the selection of a candidate parameter!)

Limitations of the sensitivity and optimisation approach

Largest changes can be in the most sensitive parameters ratherthan those in error ( inconsistent updating and misleading error


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localization)

Errors of insensitive regions cannot be detected

The success of the updating procedure can strongly depend on the selection of the design parameters to be updated (it could be

necessary to consider several sets of design parameters to detecterroneous regions of the structure)

The approach could be short-sighted

(possible convergence tolocal minima)

ExerciseExercise

Calculate natural frequencies and modeshapes of the 2-DOF satellite represented


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p pin the figure

Consider a perturbed model, representingthe real (tested) structure, having

k1

= 60 E5 N/m

k

2

= 130 E5 N/m

Calculate natural frequencies and modeshapes for the perturbed (test) model

Correlate the 2 models, i.e. calculate:

Natural frequency deviations

Mode shapes cross-orthogonality

check

Solutions of the exerciseSolutions of the exercise


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Summary and Conclusive Remarks



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Design load cycles & verification loads cycle

Payload-launcher Coupled Loads Analysis

Mechanical tests

Overtesting

& notching


BibliographyBibliography

Sarafin T.P. Spacecraft Structures and Mechanisms, Kluwer, 1995 Craig R.R., Structural Dynamics An introduction to computer methods, J. Wiley


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and Sons, 1981

Clough R.W., Penzien

J., Dynamics of Structures, McGraw-Hill, 1993

Ewins

D.J., Modal Testing

Theory, practice and applications, Research Studies

Press, Second Edition, 2000

Wijker

J., Mechanical Vibrations in Spacecraft Design, Springer, 2004

Girard A., Roy N., Structural Dynamics in Industry, J. Wiley and

Sons, 2008

Steinberg D.S., Vibration Analysis for Electronic Equipment, J. Wiley and Sons,2000

Friswell

M.I., Mottershead

J.E., Finite Element Model Updating in StructuralDynamics, Kluwer

1995

Ariane

5 Users Manual, Arianespace, http://www.arianespace.com/

BibliographyBibliography -- ECSS DocumentsECSS Documents

ECSS-E-ST-32 Space Project Engineering - Structural


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ECSS-E-ST-32-03 Structural finite element models

ECSS-E-ST-32-10 Structural factors of safety for spaceflight

hardware

ECSS-E-ST-32-02 Structural design and verification of

pressurized hardware

ECSS-E-ST-32-11 Modal survey assessment

ECSS-E-ST-32-01 Fracture control

ECSS-E-10-02 Space Engineering - Verification

ECSS-E-10-03 Space Engineering - Test ing

THE END!


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Acknowledgements:

ALENIA SPAZIO, Italy, for the data concerning the projects GOCE, COLUMBUS,MPLM and SOHO

EADS ASTRIUM, UK, for the data concerning the project AEOLUS andEarthCARE

ESA/ESTEC, Structures Section, NL, for the data concerning ARIANE 5 FEmodel and LV/SC CLA

Calvi Liege 2010 Students

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