An inverse non-linear force vibration problem of estimating the external forces in a damped system with time-dependent system parameters

An inverse non-linear force vibration problem based on the iterative regularization method, i.e., the conjugate gradient method (CGM), is used to estimate the unknown time-dependent external forces in a damped system having time-dependent system parameters by using the measured system displacement. It is assumed that no prior information is available on the functional form of the unknown external forces in the present study, thus, it is classified as the function estimation in inverse calculation. The accuracy of the inverse analysis is examined by using the simulated exact and inexact measurements. The numerical simulations are performed to test the validity of present algorithm by using different types of external forces and measurements. Results show that an excellent estimation on the external forces can be obtained with any arbitrary initial guesses within a couple of seconds of CPU time at Pentium II-300 MHz PC.