On the wave dispersion in functionally graded porous Timoshenko-Ehrenfest nanobeams based on the higher-order nonlocal gradient elasticity

Abstract

Dispersion characteristics of flexural waves in a functionally graded (FG) porous nanobeam are analytically examined. Kinematics of the nano-sized beam is assumed to be consistent with the Timoshenko-Ehrenfest beam model. Material behavior of the FG porous beam is considered to vary symmetrically along the beam thickness while appropriate symmetric porosity models are applied to account for two diverse distributions of porosity with variable volume of voids. For the first time, size-dependent response of the symmetric FG porous nanobeam is realized within the framework of the higher-order nonlocal gradient elasticity theory. The integro-differential constitutive laws of the stress resultant fields are established and reinstated with the equivalent differential relations equipped with non-standard boundary conditions. The closed-form solution of the phase velocity of flexural waves is analytically determined. The ensuing numerical results of the flexural wave dispersion detect new benchmarks for numerical analysis and can be effectively exploited in design and optimization of composite nano-structural elements of advanced nano-electro-mechanical systems.