Free vibration analysis of parallelogram laminated thin plates under multi-points supported elastic boundary conditions

Abstract

Free vibration characteristics of parallelogram laminated thin plates under multi-points supported elastic boundary conditions are studied by improved Fourier series method (IFSM) in this paper. The parallelogram thin plate region is first transformed into the unit square region. Artificial virtual springs are introduced to simulate various boundary constraints. In the study, to remove the jumps or discontinuities problem on the boundary, an IFSM is used to express all allowable displacement functions of parallelogram laminated thin plates. All energy equations of thin plates are established by the classical thin plate elasticity theory. Then the Rayleigh-Ritz method is used to solve the problem. The innovation of this paper lies in the combination of non-uniform boundary constraints and coordinate transformation. By comparing a large number of numerical results with the finite element method, the results show that the method has high stability, accuracy, and rapid convergence. Moreover, the parametric research of vibration characteristics of the parallelogram laminated thin plate is also studied. The method can easily obtain the free vibration peculiarities of parallelogram laminated thin plates under multi-points supported elastic boundary constraints, including its natural frequencies and modal shapes.