Forced vibration analysis of inhomogeneous quasicrystal coating in a thermal environment

Abstract

The tremendous attention of researchers has been attracted to the unusual properties of quasicrystals in coatings. In this paper, the exact solutions of the functionally graded multilayered two-dimensional quasicrystal coating structures in a thermal environment are derived for advanced boundary-value problems with mixed boundary conditions. The state space method is formulated to the thermal coupling with quasicrystal linear elastic theory that derives the state equations for functionally graded quasicrystal coating structures along the thickness direction. The mixed supported boundary conditions in the x-direction and the simply supported boundary conditions in the y-direction are subjected to time-harmonic temperature loadings, which are represented by means of the differential quadrature technique and Fourier series expansions, respectively. Traction on both the bottom and top surfaces is free, and perfect thermal and mechanical contacts between constituents are incorporated at the internal interfaces. A global propagator matrix, which connects the field variables at the top interface to those at the bottom interface for the whole coating structure, is further completed by joint coupling matrices to overcome the numerical instabilities. Finally, three application examples are proposed to throw light on various effects of the power law index, frequency, and different boundary conditions on the field variables in three-layer coating structures. The present solution can serve as a benchmark for the modeling of functionally graded quasicrystal coating structures based on various numerical methods.