A non-linear inverse vibration problem of estimating the time-dependent stiffness coefficients by conjugate gradient method

An iterative regularization method, i.e. the conjugate gradient method (CGM) is applied to an inverse non-linear force vibration problem to estimate the unknown time-dependent sti ness coe cients (or spring constants) in a damped system by using the measured system displacement. It is assumed that no prior information is available on the functional form of the unknown sti ness coe cients in the present study, thus, it is classi ed as the function estimation in inverse calculation. The accuracy of the inverse analysis is examined by using the simulated exact and inexact displacement measurements. The numerical simulations are performed to test the validity of the present algorithm by using di erent types of sti ness coe cients and measurement errors. Results show that an excellent estimation on the time-dependent spring constants can be obtained with any arbitrary initial guesses within a couple of seconds of CPU time at Pentium III-500 MHz PC.