An analytical model for dynamic analysis of inhomogeneous sandwich plate

Sandwich plates are widely used in the engineering domain and are extensively studied by researchers for their special performances. Among them, the sandwich plate with coordinate-dependent material parameters has excellent vibration isolation performance. However, there are few effective and convenient analytical methods for solving the dynamic response of this type of sandwich plate. To solve this problem, an equivalent spring-based model for the dynamic analysis of the sandwich plate is proposed in this paper. Assuming that the sandwich plate is a linear elastic structure, and considering the core plate as equivalent springs, whose stiffness coefficients are derived based on the classical elasticity theory and Kirchhoff hypothesis. Besides, displacement solutions of base and constrained plates of the sandwich plate in the x, y and z directions are expressed as a two-dimensional Fourier series supplemented with several one-dimensional Fourier series, respectively. Then, according to the orthogonality of trigonometric functions and selectivity of Dirac functions, the displacements of the sandwich plate are solved accurately. By comparing with available analytical and numerical results, the proposed method is proven to have excellent performance in dealing with the sandwich plate with coordinate-dependent material parameters. Finally, the dynamic characteristics and vibration isolation performance of the inhomogeneous sandwich plate are discussed. The results show that the proposed method can be used to design the inhomogeneous sandwich plate and improve their vibration isolation performance significantly.