| Summary: | 碩士 === 國立聯合大學 === 土木與防災工程學系碩士班 === 100 === When the waves propagate in the formation will be affected by the damping effects, but general studies of anisotropic media did not consider the effect of damping, thus can not reflect actual energy attenuation phenomenon of the wave propagation. Our study therefore derives transient SH wave fundamental and general solutions of the displacement in transversely isotropic layered media containing the hysteretic damping, and explore its effect. Firstly, the variable transformation method is employed to solve the transformed integral of the displacement in an infinite space of damped transversely isotropic medium, and then the boundary conditions and the displacement and stress continuity conditions at the interface between two parallel media are used to derive the reflection and transmission coefficients. The integral imposed with the series product of the coefficients is referred to as a generalized ray integral. Finally the displacements in such layers can be obtained by applying the Cagniard’s method to solve the inverse Laplace transform of each ray integral. Meanwhile two fundamental solutions are derived from two sources’ time functions of the Dirac delta function and the step function. Finally the responses of the general source time function can be obtained from the fundamental solutions. The damped solutions compared with the undamped solutions mainly different in vertical and horizontal shear modulus c44, c66 and their corresponding shear wave velocities are complex numbers, but undamped counterparts are reals. From numerical analyses of some such typical media, the results showed that the hysteretic damping can simulate the energy attenuation phenomenon of actual seismic wave propagation, which the greater the damping, the greater the distance, the more obvious energy attenuation but the faster ray arrival time.
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