Harmonic response of multilayered one-dimensional quasicrystal plates subjected to patch loading

Abstract

Dynamic analyses of a multilayered one-dimensional quasicrystal plate subjected to a patch harmonic loading with simply supported lateral boundary conditions are presented. The pseudo-Stroh formulation and propagator matrix method are used to obtain the exact three-dimensional response of the plate. In order to avoid resonance, the frequency of the patch loading is chosen away from the natural frequencies by introducing a small imaginary part. The patch loading is expressed in the form of a double Fourier series expansion. Comprehensive numerical results are shown for a sandwich plate with two different stacking sequences. The results reveal the influence of layering, loading area, phonon–phason coupling coefficient and input frequency. This work is the first step towards understanding quasicrystals under intricate loading conditions such as indentation and impact, and the exact closed-form solution can serve as a reference in convergence studies of other numerical methods and for verification of existing or future plate theories.