Vibration Analysis of Plate with Irregular Cracks by Differential Quadrature Finite Element Method

Zhongyuan Xu,Wei Chen

doi:10.1155/2017/2073453

Abstract

A universal method combining the differential quadrature finite element method with the virtual spring technique for analyzing the free vibration of thin plate with irregular cracks is proposed. Translational and rotational springs are introduced to restrain the vertical displacement and orientation of the plate. The mass matrix and stiffness matrix for each element are deduced involving the effects of the virtual springs. The connection relationships between elements can be modified by setting the stiffness of the virtual springs. The vibration of two rectangular plates with three irregular shaped cracks and different boundary conditions are presented. The results are compared with those obtained by ANSYS, where the good agreement between the results validates the accuracy and efficiency of the present method.

Highlights

Cracks occurring in the plate cause the changes of the natural frequencies and the dynamic response behavior under loads
Hosseini-Hashemi et al [9] firstly proposed a set of exact closed-form characteristic equations incorporating the shear deformation and rotary inertia to analyze the free vibration of moderately thick rectangular plates with multiple all-over part-through cracks
The vibration results of two rectangular plates with different shaped cracks are presented

Summary

Introduction

Cracks occurring in the plate cause the changes of the natural frequencies and the dynamic response behavior under loads. An extended finite element method is proposed by Bachene et al [4] to study the vibration of cracked plates. Natarajan et al [10] studied the vibration of functionally graded material plates with a through center crack using an 8-noded shear flexible element. Heydari et al [14] proposed a continuous model for flexural vibration of Timoshenko beams with vertical edge crack, where the effects of shear deformation and rotary inertia are considered. The DQFEM has been widely used to model plate structures with complex geometries [25,26,27,28,29,30], which has been proved to be an efficient method using less element numbers and obtaining high accurate results.

Theory and Formulations

Numerical Examples

Conclusions