Abstract: With non-linear Rayleigh damping formulate describe the exciting process when the rupture velocity is low and the attenuation process when the rupture velocity re ache s a certain high value. Assuming the medium of the earth crust is homogeneous and isotropic linear Voigt viscoelastic body, with small parameter perturbation method to deduce the non-linear governing partial differential equations into a system of asymptotic linear ones, we solve them by means of generalizedfourier series with moving coordinates as its variables, thus transform them into non-homogeneous mathieu equations. At last Matkieu equations are solved by WK3J method.

Key words: sampled-data feedback, transition system, control