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

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