Fixed Base FRF Using Boundary Measurements as References: Analytical Derivation

Abstract

Modal parameters extracted from test articles with known boundary conditions are useful for model correlation and updating but are often not obtained because of the time and cost associated with moving and installing the test article on a rigid or isolated seismic mass and performing a separate modal test. It would be advantageous if frequency response functions from known boundary conditions, such as fixed base frequency response functions, could be obtained while the structure undergoes testing on fixtures that contain compliance or dynamics in the frequency range of interest, such as base shake tables.

This paper proposes a method that uses response measurements at the structure’s boundary to mathematically constrain the test article to produce equivalent fixed base frequency response functions. Fixed base frequency response functions are obtained by using the boundary measurements as additional references to mathematically constrain these degrees of freedom in the frequency range of interest.

This paper provides analytical justification for using the proposed methodology, discusses assumptions associated with boundary deformation, and finally presents an analytical example using a lumped parameter system.