FREE VIBRATION OF A BINARY COMPOSITE PLATE: A SEMI-ANALYTICAL APPROACH

Binary composite plate is one of the common elements in metamaterial plate structure. A semi-analytical model of the free vibration of the structure is proposed for the binary composite plate composed of a matrix and an embedded body with different material parameters, and its vibration characteristics are studied. The plate is decomposed into two sub-regions based on the domain decomposition method and the distribution of binary materials. The non-smoothness of the local displacement and strain caused by the sudden change of stiffness in the composite plate is described by adding a local trial function to the mode shape function. Based on the essential boundary conditions of the binary composite plate and the condition of compatibility for the displacement at the joint of the two sub-regions, a new mode shape function is constructed. Based on the classical thin plate theory, the Ritz method with special trial functions is used to calculate the natural frequencies and modes of the binary material plate under different geometric configurations. The influence of the size and location of the embedded body on the vibration characteristics of the structure is investigated. The accuracy of this method is verified by the convergence analysis and the finite element simulation results. The results show that the classical global trial function will lead to inaccurate results when analyzing the modes with vibration localization, while the additional local trial function can significantly improve the convergence speed of the Ritz method and the accuracy of the results; the effect of the embedded body position on the low-order natural frequencies is not obvious, but it can significantly change the distribution of the low-order mode shape nodal lines and the region where vibration localization occurs.