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Deriving analytical solution to 3D nonlinear elastic wave equation

Sundaraelangovan selvam's picture

Dear Researchers,

I work as a Ph.D. researcher at TU-Delft, Netherlands and I am modeling nonlinear propagation of 3D elastic waves (Compressional and Shear waves) in the nonlinear elastic medium using the INCS method (please check the attached image showing equations). The ultimate aim of this model is to simulate the 3D compressional and shear displacements, evaluate the displacement fields, the nonlinear force terms (appears in RHS of nonlinear elastic wave equation) and capture the generation of higher harmonics by iteratively solving integral equations for wavefield. We have some preliminary numerical results and we are looking for the possible options to validate our 3D numerical model.

I need some idea on how to derive the analytical solution for the above case and I am wondering if there are any 3D- analytical solutions available?. 

Any suggestions/ideas would be much appreciable. Thanks in advance.

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