Free Transverse Vibration of Rectangular Orthotropic Plates with Two Opposite Edges Rotationally Restrained and Remaining Others Free

Yuan Zhang,Sigong Zhang

doi:10.3390/app9010022

Abstract

Many types of engineering structures can be effectively modelled as orthotropic plates with opposite free edges such as bridge decks. The other two edges, however, are usually treated as simply supported or fully clamped in current design practice, although the practical boundary conditions are intermediate between these two limiting cases. Frequent applications of orthotropic plates in structures have generated the need for a better understanding of the dynamic behaviour of orthotropic plates with non-classical boundary conditions. In the present study, the transverse vibration of rectangular orthotropic plates with two opposite edges rotationally restrained with the remaining others free was studied by applying the method of finite integral transforms. A new alternative formulation was developed for vibration analysis, which provides much easier solutions. Exact series solutions were derived, and the excellent accuracy and efficiency of the method are demonstrated through considerable numerical studies and comparisons with existing results. Some new results have been presented. In addition, the effect of different degrees of rotational restraints on the mode shapes was also demonstrated. The present analytical method is straightforward and systematic, and the derived characteristic equation for eigenvalues can be easily adapted for broad applications.

Highlights

In Civil Engineering, many types of bridge decks and floor systems can be effectively modeled as orthotropic plates with opposite free edges
A considerable amount of literature has been published on analytical solutions for vibration of orthotropic plates with classical boundary conditions such as supported, clamped, Appl
It should be noted that the series solutions obtained by the present method are theoretically convergent to the exact values when N → ∞ while solutions with desired accuracy can be determined by finite terms

Summary

Introduction

In Civil Engineering, many types of bridge decks and floor systems can be effectively modeled as orthotropic plates with opposite free edges. A considerable amount of literature has been published on analytical solutions for vibration of orthotropic plates with classical boundary conditions such as supported, clamped, Appl. Limited research has been conducted to study orthotropic plates with elastically restrained and free edges. Liu and Huang [16] directly extended the semi-analytical finite difference method reported in [8] to free vibrations of orthotropic plates with elastically restrained and free edges. An analytical method of finite integral transforms has been extensively applied to obtained the exact series solutions of bending of plates [17,18,19,20]. An alternative formulation of the finite integral transform method was developed for the free vibration of R–F–R–F rectangular orthotropic plates. The mode shapes of an orthotropic plate having different degrees of rotational restraints along the opposite edges were illustrated

Formulation and Methodology

Numerical Results

Results

Conclusions