Curvature Effects on the Vibration Characteristics of Doubly Curved Shallow Shells with General Elastic Edge Restraints

Hui Shi,Zhigang Liu,Tianhang Yang ,W L Li,Shiliang Jiang

doi:10.1155/2015/435903

Abstract

Effects of curvature upon the vibration characteristics of doubly curved shallow shells are assessed in this paper. Boundary conditions of the shell are generally specified in terms of distributed elastic restraints along the edges. The classical homogeneous boundary supports can be easily simulated by setting the stiffnesses of restraining springs to either zero or infinite. Vibration problems of the shell are solved by a modified Fourier series method that each of the displacements is invariably expressed as a simple trigonometric series which converges uniformly and acceleratedly over the solution domain. All the unknown expansion coefficients are treated equally as a set of independent generalized coordinates and solved using the Rayleigh-Ritz technique. The current method provides a unified solution to the vibration problems of curved shallow shells involving different geometric properties and boundary conditions with no need of modifying the formulations and solution procedures. Extensive tabular and graphical results are presented to show the curvature effects on the natural frequencies of the shell with various boundary conditions.

Highlights

Vibration problems of shell structures have long been of considerable attention by the researchers and engineers because they are widely used in structural, mechanical, and aerospace engineering applications
They investigated the dynamic characteristics of shallow shell structures using the conforming triangular shaped shell elements [7, 8]
The finite element method has been widely used in solving various shell vibration problems, it is sometimes less desired as compared with an analytical solution because the parameters of concern are all digitized and their significance can be lost in the numerical or discretization process

Summary

Introduction

Vibration problems of shell structures have long been of considerable attention by the researchers and engineers because they are widely used in structural, mechanical, and aerospace engineering applications. Olson and Lindberg [6] studied the vibratory behaviors of a cantilevered curved fan blade. From practical point of view, when a shell is elastically restrained, the springs will have to be manually created in a finite element model, which can become an overwhelming task, especially when spring rates vary along an edge. This concern will become more remarked when a stochastic process or field will have to be taken into account

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