Modal Test Problem & Solution

Ideally, a modal test on a structure would be performed with completely free boundary conditions.  This configuration can be approximated by mounting the structure on compliant air cushions, or by suspending it with elastic cords, so that the mounted natural frequency is much smaller that the structure’s fundamental frequency.

Other choices would be to test the structure with one boundary fixed, or in its final installation configuration.

But there may be certain cases where a structure can only be tested at its “next higher level of assembly.”  NASA is facing this issue for a launch vehicle which can only be tested on its launch platform and tower assembly due to cost and schedule reasons.

The modal test results will thus be for the complete system rather than the vehicle by itself.  But the need is for the vehicle’s modal parameters, which can then be used to calibrate the stiffness in a finite element model.  This would be for the case immediately after liftoff when the vehicle boundary conditions are free-free.  The vehicle natural frequencies and mode shapes are needed to check control stability, structural stresses, etc.

Here is paper which offers a potential solution by extracting the subsystem stiffness matrix from system level modal test results with a known mass matrix.  A simple three-degree-of-freedom system is used.  The parameters are conceptual only and do not represent those of the launch vehicle and its platform.

Note the reduction method in this paper may be similar to System Equivalent Reduction Expansion Process (SEREP) which is used in the automotive industry.

See also:

Receptance Decoupling for Two Rigidly Connected Subsystems

Determination of the Fixed-Base Natural Frequencies for a Two-degree-of-freedom System via Modal Test Receptance

– Tom Irvine

Some NASA Vibration Videos

This video shows the vibration of consoles in the Mobile Launch Platform underneath the Space Shuttle for the liftoff event.

MLP Field Verification Video

This video shows the “tennis shoe” method for exciting a rocket vehicle.

Saturn V Apollo SA-500F Shake Test at VAB 1966 NASA color 1min

More…

Dynamic Model for Vibration Studies of the Saturn Launch Vehicle

– Tom Irvine

Modal Testing Frequency Response Functions

Here is a Matlab script which calculates the H1 & H2 frequency response functions for a force and response time history pair.

modal_frf.zip

It is best suited for the case of random force excitation. It uses ensemble averaging.

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Here is a Matlab script which is suitable for the case of an impulse force and response pair:

frf_from_th.zip

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See also:

Modal Test Webpage

Half-Power Bandwidth Method

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– Tom Irvine

Model Correlation

This week I participated in an NESC conference in Los Angeles. One of my colleagues brought up the following point.

Finite element models are created to represent physical models for analysis purposes. The finite element model natural frequencies can then be compared to data from a modal test of the actual hardware. At this point, the finite element model can then be “calibrated” so that its fundamental frequency agrees with the test results. This can be done, for example, by scaling the elastic modulus in the analytical model.

There are two problems with this approach:

1. The analytical model no longer “matches the drawing” of the hardware, (although this is an inherent flaw in all models to some extent).
2. Changing the elastic modulus will throw off any dynamic stress calculations.

This dilemma deserves further thought…