Estimation of interfacial forces in time domain for linear systems

Abstract

A structural path rank ordering process under transient excitations requires a good knowledge of the interfacial path forces, which are difficult to directly measure. Four time domain methods to estimate the interfacial forces are proposed and comparatively evaluated with application to linear time-invariant, proportionally damped discrete systems. First, the transient response is derived by modal analysis and a direct time domain technique to calculate the interfacial forces is outlined. Next, the frequency domain estimation methods, based on the sub-system concept are reviewed, and an inverse Fourier transform scheme is introduced. An indirect method of estimating interfacial force in transient state is then developed through an inverse procedure of modal analysis. The sub-system approach is employed to obtain the interfacial forces based on the forced vibration response of the original system and modal data of the sub-system. Finally, an approximate time domain scheme is suggested that could be used only if the system properties are known or precisely estimated. Although the proposed indirect methods are designed for eventual experimental applications, this article provides numerical feasibility studies via a simple source–path–receiver system (with parallel vibration paths) that has five translational degrees of freedom. The proposed methods are compared under ideal impulse force excitation input and a periodic sawtooth load (without and with Gaussian noise) to observe the starting transients as well as subsequent motions and interfacial forces. Preliminary comparisons with a laboratory experiment are very promising.