Modeling and experimental study on free vibration of plates with curved edges

Abstract

This paper reports a modeling and experimental study on the free vibration characteristics of plates with curved edges. The model is established by the first-order shear deformation theory (FSDT) and Chebyshev differential quadrature method (CDQM). The one-to-one coordinate transformation technique is introduced into the CDQM to map the plate with curved edges into a square plate. The admissible displacement functions of the square plate are expanded by two-dimensional Chebyshev polynomials and discretized by Gauss-Lobatto sampling points. The boundary conditions are applied to the plate according to the projection matrix method. Experimental studies of six aluminum plates with different shapes are carried out to investigate the vibration characteristics and verify the validity of the proposed CDQM. Furthermore, the results of the present CDQM are also compared with those of the finite element method (FEM) and existing numerical approaches to examine its efficiency and accuracy. The results show that the current CDQM can rapidly and accurately compute the vibration characteristics of plates with curved edges under different boundary conditions.