Application of n onlocal e lasticity t heory on the w ave p ropagation of f lexoelectric f unctionally g raded (FG) t imoshenko n ano b eams c onsidering s urface e ffects and residual surface stress

Abstract

This research deals with wave propagation of the functionally graded (FG) nano beams based on the nonlocal elasticity theory considering surface and flexoelectric effects. The FG nano beam is resting in Winkler Pasternak foundation. It is assumed that the material properties of the nano beam changes continuously along the thickness direction according to simple power law form. In order to include coupling of strain gradients and electrical polarizations in governing equations of motion, the nonlocal non classical nano beam model containg flexoelectric effect is used. Also, the effect s of surface elasticity, di electricity and piezoelectricity as well as bulk flexoelectricity are all taken into consideration. The governing equations o f motion are derived using Hamilton principle based on first shear deformation beam theory (FSDBT) and also considering residual surface stresses. The analytical method is used to calculate phase velocity of wave propagation in FG nano beam as well as cut off frequency. After verification with validated reference, comprehensive numerical results are present ed to investigate the influence of important parameters such as flexoelectric coefficients of the surface, bulk and residual surface stresses, Wink ler and shear coefficients of foundation, power gradient index of FG material, and geometric dimensions on th e wave propagation characteristics of FG nano beam. The numerical results indicate that considering surface effects/flexoelectric property caused phase velocity increases/decreases in low wave number range, respectively. The influences of aforementioned pa rameters on the occurrence cut off frequency point are very small