Wave propagation in a porous functionally graded curved viscoelastic nano-size beam
Davood Shahsavari, Behrouz Karami, Abdelouahed Tounsi
Abstract
In this paper, wave propagation analysis of a viscoelastic system of curved nanobeams made of porous functionally graded materials (P-FGM) is studied, for the first time. The displacement fields for the curved nanobeam are obtained via a higher-order shear deformation beam theory which contains curvilinear axial, rotation, transverse, and thickness stretching effects, while size effects are considered using nonlocal strain gradient theory. The effective material properties for P-FGMs are expressed by modified model of power-law variation which is connected with cosine functions to estimate the effect of porosity and Kelvin–Voigt viscoelastic model for estimating viscoelastic behavior on mechanics of nanostructures. The Hamilton’s principle is applied to find governing equations of motion of the viscoelastic curved nanobeam. The state space method and a set of mathematical series are developed to find response. The Influence of porosity value and types of distributions, viscosity coefficient, power-law index, geometry, and opening angle (related to curvature radius) on phase velocity of curved viscoelastic nanobeams is investigated.