Theoretical and experimental investigations on free vibration characteristics of arbitrary spatially closed-coupled plates

Abstract

A semi-analytical method and related experiments are present in this paper to investigate the free vibration characteristics of the closed-coupled plates with arbitrary spatial coupling angles and curved edges, which are the widely used structural form but researched for the first time. By combining the penalty function method with flexible setting virtual spring stiffness functions and the comprehensive relative motion relation matrices along the edges of the plates system, various types of boundary and spatial coupling connection conditions in practical engineering can be constructed. The semi-analytical solution formulas for the entire vibration model are established by using the first-order shear deformation theory (FSDT) and the two-dimensional Jacobian differential quadrature method (JDQM). To fulfill the requirements of integral operations for displacement approximation functions, the irregular domain mapping technique is employed to transform the irregular solving domain into the regular basic domain. The accuracy and applicability of the present method in predicting eigenfrequencies and mode shapes are proved by hammer modal tests concerning four pyramid/frustum-like built-up plates, comparisons with results from the open literature, as well as the finite element method (FEM) simulations of several specially designed cases. Moreover, many meaningful conclusions are drawn regarding the effects of spatial geometric parameters on the free vibration characteristics of spatially closed-coupled plates with curved edges.