Vibration Analysis of Orthotropic Triangular Nanoplates Using Nonlocal Elasticity Theory and Galerkin Method

Subject Areas : Engineering

A.R Shahidi ¹ , S.H Shahidi ² , A Anjomshoae ³ , E Raeisi Estabragh ^{4 *}

1 - Department of Mechanical Engineering, Isfahan University of Technology
2 - Department of Mechanical Engineering, Isfahan University of Technology
3 - Department of Mechanical Engineering, Isfahan University of Technology
4 - Department of Mechanical Engineering, University of Jiroft

Received: 2016-06-29 Accepted : 2016-08-30 Published : 2016-09-20

Keywords: Galerkin Method, Small scale effect, Vibration analysis, Nonlocal elasticity, Triangular nanoplate,

Abstract :

In this article, classical plate theory (CPT) is reformulated using the nonlocal differential constitutive relations of Eringen to develop an equivalent continuum model for orthotropic triangular nanoplates. The equations of motion are derived and the Galerkin’s approach in conjunction with the area coordinates is used as a basis for the solution. Nonlocal theories are employed to bring out the effect of the small scale on natural frequencies of nano scaled plates. Effect of nonlocal parameter, lengths of the nanoplate, aspect ratio, mode number, material properties, boundary condition and in-plane loads on the natural frequencies are investigated. It is shown that the natural frequencies depend highly on the non-locality of the nanoplate, especially at the very small dimensions, higher mode numbers and stiffer edge condition.