Modelling of 3 D Steady-State Oscillations of Anisotropic Multilayered Structures Applying the Green ’ s Functions

Two innovative numerical procedures are suggested for calculating of spatial steady-state oscillations of a infinite layered plate with arbitrary elastic anisotropy of each layer. The procedures are based on the algorithm of construction of the Green’s matrix in Fourier domain for a multilayered structure. This algorithm does not require the inversion of linear systems of large order and allows one to do calculations in the domain of large wave numbers and frequencies. The inverse Fourier transform is defined as a repeated integral in polar coordinates in wave 426 A. Karmazin, E. Kirillova, W. Seemann, P. Syromyatnikov numbers domain. At first, the inverse Fourier transform is computed by using a contour of integration which deviates from the real axis and encloses the real poles of the transform of the Green’s matrix. To speed up the calculation of a repeated integral, the asymptotic properties of the symbol of the Green’s matrix are used. The second numerical procedure developed is based on the introduction of a complex frequency with small imaginary part, which provides an opportunity to integrate along the real axis. As examples, the complex amplitudes of the displacement on the surface of three different composites for various types of surface loads are computed.