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Abstract This paper presents a new solution techniques—Modified Stiffness Matrix Method for the dynamic response under concentrated load embedded in three-dimensional viscoelastic layered half space, combined with the Hankel integral transform approach. Based on the potential function theory, this kind of three-dimensional problem can be broken down to two two-dimensional problem of in-plane response (P-SV waves) and anti-plane response( SH waves) respectively. Similar to principle of the displacement method in structural mechanics, the up and bottom surfaces of the force layer are fixed firstly, and the reaction forces at two fixed ends can be obtained by superposition of particular and homogeneous solution of the wave equation. Then loosen the two “fixed end constraint”, using direct stiffness method to get the displacement of each layer surface. In the layer imposed by the load, the Green’s function is decomposed of the particular solution, the homogeneous solution and the reaction solution, in which the particular solution can be impaled by the analytical solution in the whole space. With this method, the convergence problem of improper integral can be solved with Sources and receivers at close or same depths. Finally, this method is proved to be efficient and accurate for both low frequency and high frequency dynamic problems by numerical examples.
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Received: 13 August 2012
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2013, Vol. 34 
