A generalized inverse force vibration problem for simultaneously estimating the time-dependent external forces

The conjugate gradient method (CGM) with adjoint equations was applied to a generalized inverse force vibration problem to simultaneously estimate the unknown time-dependent external forces in a multiple-degree-of-freedom damped system with time-dependent system parameters by using the simulated measured system displacement. The accuracy of the inverse analysis for a two-degree-of-freedom problem is examined by using the simulated exact and inexact displacement measurements in the numerical experiments. Results have shown that the excellent estimations on the external forces can be obtained with any arbitrary initial guesses within a very short CPU time on a Pentium III-500 MHz PC.