包括激发和衰减的粘弹性Ⅱ型破裂过程的研究

Research of Visco-Elastic Type Ⅱ Rupture with Exciting and Attenuation Process

摘要: 用非线性Rayleigh阻尼公式描述初始破裂时有激发而加速,至一定高速时有衰减而止裂。视介质为匀质各向同性的Voigt线性粘弹性体,用小参数摄动法把滑开型(Ⅱ型)破裂定义的非线性偏微分方程组线性化,得出各次逼近解所定义的线性方程组,再用动坐标表示的广义Fourier级数把问题简化为非齐次的Mathieu方程,用WKBJ法给出问题在稳定区域的渐近解。

Abstract: With non-linear Rayleigh damping formula we describe the exciting process when the rupture velocity is low and the attenuation process w hen the rupture velocity reaches a certain high value, Assuming the medium of the earth crust is homogeneous and isotropic linear Voigt visco-elastic 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 generalized Fourier series with moving coordinates as its variables,thus we transform them into non-homogeneous Mathieu equations. At last Mathieu equations are solved by WKBJ method.

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