Generalized reverberation matrix (GRM) formulation is presented to investigate elastic wave propagation in a complex multilayered solid by the combination of reverberation-ray matrix (RRM) method and stiffness matrix (SM) method. RRM method formulates a reverberation matrix, which reflects the reflection or refraction of the elastic waves in the multilayered solid. However, the dimension of RRM increases as the sublayer number increases, which may result in lower calculation efficiency of the generalized rays. SM formulation yields a system matrix of the constant dimension to promise higher calculation efficiency, but it is difficult to identify the generalized rays. In order to calculate the generalized rays in the complex multi-layered solid efficiently, the RRM formulation is applied to the interested sublayer for the evaluation of the generalized rays and SM formulation to the other sublayers, to construct a generalized reverberation matrix of the constant dimension, which is independent of the sublayer number. Numerical examples show that GRM formulation has higher calculation efficiency for the generalized rays in the complex multilayered-solid configuration compared with RRM formulation.
elastic waves multilayered medium generalized reverberation matrix stiffness matrix
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