8/11/2019 Sem.org IMAC XVI 16th Int 162702 Correlation FE Models Base Excitation Tests

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Correlation of FE Models to Base Excitation Tests

Mark Donley

Structural Dynamics Research Corporation

2000 Eastman Drive

Milford, Ohio 45150, USA

mark.donley@sdrc.com

BSTR CT

Validation of F models

is

typically performed in the context

of a modal test. The early automated correlation methods were

modal based and used the measured modal frequencies

as

targets

for updating the F

model. More recent response based

methods use the frequency response functions measured in

the

modal test as

the correlation targets. While modal testing gives

valuable information about a system s dynamic properties, the

loads are not representative of the operational loads the system

will experience. For this reason, systems that will be subject

to dynamic excitation from base motion are often tested in a

shake table test. An F model correlated with the base

excitation test data

is

useful in terms

of

certifying the design,

but most model updating methods do not address data from a

base excitation test. In this paper, an FRF response based

correlation method is extended to more general response

correlation and specifically to base excitation response

correlation. The method is demonstrated with

an

example.

NOMENCL TURE

{X} - FE model response vector

{X ltest - Measured response vector

Xhase - Base acceleration

{F - Applied force vector

[D]

[Lill]

[ ~ j ]

[H]

{Hj}

[M]

[K]

[ ]

[G]

a

1

- Dynamic stiffness matrix

- Difference in dynamic stiffness matrix

- Change to [D] for ith design variable

- Dynamic flexibility matrix

- jth column

of

dynamic flexibility matrix

FE model mass matrix

- FE model stiffness matrix

- FE model viscous damping matrix

- FE model hysteretic damping matrix

- Update factor for ith design variable

Nctv - Number of design variables

- Circular frequency ( rad/sec )

Y 1

INTRODUCTION

Correlation

of

finite element models is usually conducted in

the context of a modal test. Indeed, the early automated

correlation methods were modal based and used the measured

modal frequencies

as

targets for updating the F model[ 1], [2].

The more recently developed response based methods use the

raw frequency response functions (FRFs) measured in the

modal test as the correlation targets[3], [4].

F models are correlated to modal test data to validate that the

predictions made with the models are accurate. Modal test data

is particularly useful for dynamic correlation because the test is

performed to excite the important modes of the system.

Typically the test involves exciting the system with either an

impact hammer or a shaker. The location and magnitude of the

loads are selected such that enough energy can be input to the

system to excite the modes of interest.

In many situations though, the information needed from a test

is not the identification

of

the modes, but the verification

of

the response to operational loads. Simulated operational tests

are performed for this reason.

In

these tests, loads similar to

the operational loads in frequency content, magnitude, and

direction are applied to the test article.

Many simulated operational tests involve the application of

base motion excitation. In this type of test the system is

fixtured to a shake table or to displacement driven actuators and

subjected

to

controlled motions. Many aerospace components

are tested in this manner to evaluate the system s dynamic

response to launch, or flight vibrations. Automotive systems

are also tested in this manner to evaluate the response to road

input.

Although the base motion test by itself is a validation of the

system, FE models correlated with the base excitation test data

provide additional validation of the design and any subsequent

design modifications.

t

is also likely that validation of the FE

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model with base motion test is more appropriate than with

modal test data. This is because the relatively light loading of a

modal test may not exercise any nonl inear effect that occurs in

operation

or

may not overcome friction forces that are not

present

in operation.

Modal data

in

that case

can

give

misleading stiffness results.

It

is believed that in the current state

of

practice, only a cursory

degree

of FE model correlation

is

performed

for a

base

excitation test. In part, this may

be because

most of

the

developed model updating methods

do

not specifically address

this type of correlation.

The

response based updating methods

however, would seem particularly suited for this application

because the responses are similar to FRFs. An investigation

was

performed to evaluate extension

of

response based

correlation to base motion tests. It was found that by using the

large mass modeling procedure for performing base excitation

simulations, the response based methods can be used.

The

procedure is described in this paper and is demonstrated in an

example.

It is noted that this method deals specifically with a data from a

frequency sweep base motion test. Other types

of

applied base

motions such as from shock or random events are not addressed

by this method.

TH ORY

In the frequency domain, the response of a linear dynamic

system, {X(w)} due to an applied force, {F(w)} is computed as

{ X(w) } = [

H w))

{ F(w) }

I)

where

l H w)]

is the dynamic flexibility,

or

receptance, for the

system.

Note

that the dependency on frequency henceforth

should be understood and will not be explicitly written.

For a linear structural system the dynamic flexibility matrix is

equivalent to the inverse of the dynamic stiffness and hence is

related to the mass, damping, and stiffness of the system by

the following equation

[H

= [D f

1

2)

=

[-

w

2

[M) + iw[C] + [K] + i [G]r

1

Letting [D) represent the dynamic stiffness

of

an

FE

model and

[Dltest represent the dynamic stiffness

of the corresponding test

article, any difference between the model response

{X}

and the

measured response, {Xltest is caused by a difference in dynamic

stiffness.

Designating the dynamic stiffness difference as [ ~ D , the goal

of response based updating methods is to determine the set of

model changes that gives a

change of

[ ~ D to the

FE

model's

dynamic stiffness. A common assumption in updating a model

is that the change in dynamic stiffness can be represented as the

combined

effect

of

dynamic stiffness changes from a set

of

design variables. This is expressed as

Nctv

[ ~ D Xi [ ~ D i

4)

i=l

Here

[ ~ D i l

is the

change

in

dynamic

stiffness

due

to a

prescribed change to the ith design variable.

The

coefficients

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based on equation (5) is needed in these cases. The general

application must encompass forces applied at several locations

and the magnitude/phase of the forces varying with frequency.

An extension to the general application of equation (5) is

relatively minor enhancement to make to a method already

based on equation (7). When implemented, its application to

base excitation correlation requires the use

of

a modeling

technique called the large mass method. This method,

commonly used for base excitation simulation, is needed

because equation (5) is based on applied forces, rather than

enforced motions. The large mass method essentially casts the

base excitation simulation in terms

of

an applied force

analysis.

Figure 1 illustrates the large mass modeling concept. Instead

of

restraining the FE model of the structure at ground points it is

connected to a point with large mass. The large mass

represents the base for which the motion is to be specified. As

a general rule

of

thumb, the large mass should be about 1E3 to

IE6 times larger than the mass

of

the structure.

Application

of

a force to the unrestrained large mass causes a

base acceleration which is a function

of

the inertance

of

the

system. The system inertance is dominated by the mass

of

the

base so that the base acceleration is proportional to the applied

force

as

Xbase

= base

Mbase

8)

Thus, specification

of

a base motion is obtained indirectly by

applying a force that is proportional to the acceleration. The

resulting motion

of

the structure is the sum of the base motion

plus the flexible response due to the motion. It is noted the

although the method is described for a single enforced base

motion, the concept can be generalized to multiple input

motions.

\

tructure

r-

';

1

l

Mbase >>

Mstructure

\

Base

Jr .

Fbase

Figure I. Base Excitation Simulation with Large Mass

To evaluate the feasibility of the described method for base

excitation correlation, the SDRC FRFCORR response-based

correlation software was enhanced to use the general form of

equation (5).

It

was used

in

the following example correlation

of

a satellite component.

EXAMPLE APPLICATION

Often in aerospace applications, components must be flight

certified by subjecting them to a base excitation test to

simulate the effects

of

launch vibrations. Figure 2 shows a

model

of

a hypothetical structure representing a panel section

from a satellite. It is assumed that the panel was fixtured to a

shake table and a frequency sweep base motion test was

performed in each of the three translational directions.

nstrument

Figure

2.

Satellite Panel Model

The panel system consists

of

a ribbed aluminum panel that

supports two objects. One is called an instrument and the other

a receiver. Both objects are modeled as lumped masses. The

instrument connects to the panel by bushings modeled

as

linear

springs. The receiver connects to the panel by a four legged

space frame modeled with beams. The opening in the panel

between the instrument and the receiver is braced with beam

elements.

I t is assumed that the panel is tested with a portion

of

the

frame that holds the panel and makes up the superstructure of

the satellite. This frame is modeled with beam elements that

connect to the panel. The frame is assumed to mount to the

shake table at four comers. The mounting connection is rigid

in the translational directions but springs are used to give

flexibility in two rotational directions.

Simulated test data was obtained by altering properties of the

FE model by a known amount and generating responses for the

applied base motions. Figure 3 shows the spectrum of the

assumed base acceleration in G's applied

in

each of the three

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tests. The peak base acceleration is 5 G between 100 and 200

Hz.

c

0

Q

/

0

/

r e q e n

y

Hz)

Figure

3.

Base Motion Acceleration

The following model properties were altered in the FE model

to give the simulated test data.

Material modulus of receiver support beams (CMOD)

Instrument bushing X - stiffness (I_BSH_KX)

Instrument bushing Y - stiffness (I_BSH_KY)

Instrument bushing Z - stiffness (I_BSH_KZ)

Frame to table

RX

stiffness (FR_TBL_RX)

Frame to table

RZ

stiffness (FR_TBL_RZ)

Frame cross-sectional area (FRAME_A)

Frame II bending inertia (FRAME_Il)

Frame

I2

bending inertia (FRAME_I2)

Frame torsional inertia (FRAME_J)

Interior brace bending inertia (BRACE_Il)

Instrument X-X mass moment of inertia (INST_IXX)

Instrument

Y

Y mass moment of inertia (INST _IYY)

Instrument Z-Z mass moment

of

inertia (INST _IZZ)

Receiver mass (RECV _M)

Receiver X-X mass moment of inertia (RECV_lXX)

Receiver

Y

Y mass moment of inertia (RECV_IYY)

Receiver Z-Z mass moment

of

inertia (RECV _IZZ)

The factors

by

which these

18

properties were altered to give

the simulated test data are listed in Table 1 under the column

heading titled Exact Correction . The factor is the multiplier

applied to the

FE

model property to give the test model

property. For example, a factor of 2 means that the property

was doubled. By this convention, all stiffness properties were

doubled,

all

inertia properties were reduced by 25%, and the one

mass property was not changed at all. Response measurements

were obtained for 66 translational DOF for a frequency range of

50 to I 000 Hz.

Progress of the model updating was focused on the correlation

of

the receiver motion. Initial comparisons

of

the receiver

response from the simulated test and the FE model are shown

in

Figures 4 and 5. The solid line indicates the test data and the

dashed line is the FE model prediction. Figure 4 shows the X

response of the receiver for an X-direction base motion. Figure

5 shows the Z response for a Z-direction base motion. As

expected by the model alterations, most of the test modes have

higher frequencies than the FE model modes.

c

0

e

c

.Q

Q