粘弹性拉张型地震破裂过程的解析解

ANALYTICAL SOLUTION FOR VISCOELASTIC TENSILE RUPTURE OF THE CRUST

本文应用包括地壳破裂发震过程中具有激发及衰减的非线性Rayleigh阻尼,用Voigt粘弹性模型表示地壳,它能更全面地反映地壳介质分子之间的内摩擦造成的粘滞性阻尼,在数学方法上,用解非线性问题解析法的摄动理论结合动坐标的富氏级数,把问题的非线性控制方程组化为各阶线性化的控制方程组后,再简化为标准的Mathieu方程构成的耦连方程组,再用WKBJ方法,给出其在稳定区域的近似解,从而得出了问题的解析解。

In this paper, the nonlinear Rayleigh damping that describes exciting as well as decaying processes during an earthquake motion is adopted. The Voigt viscoelaslic model is used to present the erustal medium so as to reflect the important viscous damping caused by the internal friction between molecules of the crust. For mathematical approach, the perturbation theory is applied to deduced the nonlinear partial differential governing equations into linear asymptotic governing equations for each order of the small parameter, i . e . the dimensionless parameter of the nonlinear term. Fourier series in moving coordinates is then applied to deduce the linear partial differential governing into two coupled Mathieu equations. Finally, the WKBJ method is used to get the approximate solution.