Hygro-thermal vibration study of nanobeams on size-dependent visco-Pasternak foundation via stress-driven nonlocal theory in conjunction with two-variable shear deformation assumption

Abstract

This article presents a hygro-thermal-damping vibration analysis of two-variable shear deformation beams supported by a visco-Pasternak foundation. In contrast to the majority of the literature on this subject, the hygro-thermal load, and external foundation are simultaneously presented as nonlocal, by employing the well-posed stress-driven local/nonlocal mixture formulation with a set of constitutive constraints. The Generalized Differential Quadrature Method (GDQM) is adopted to solve the complex eigenvalue problem at hand. In the numerical simulation section, we first conduct comparison studies to validate the accuracy of the present formulation and results. Then, a series of benchmark results for the vibration frequency of different bounded higher-order shear deformation beams supported by the elastic foundation are presented. Subsequently, the effects of simultaneously applying stress-driven nonlocal assumptions on the foundation and hygro-thermal load in the undamped and damping vibration of the shear deformation beams are examined.