A unified local-nonlocal integral formulation for dynamic stability of FG porous viscoelastic Timoshenko beams resting on nonlocal Winkler-Pasternak foundation

Abstract

We present a study on the nonlocal dynamic stability of functionally graded (FG) porous viscoelastic Timoshenko beams resting on a Winkler-Pasternak foundation. The porosity distributions are assumed to be symmetric or antisymmetric about the mid-plane of the beams, and the Kelvin-Voigt viscoelastic model is considered to depict the beams’ viscoelastic properties. Unlike most studies on this topic, we consider both the beam’s bending deformation and the foundation reaction as nonlocal, simultaneously, by uniting the equivalently differential forms of two well-posed local-nonlocal integral models (i.e., strain-driven (ε-D) and stress-driven (σ-D) strategies) which are strictly equipped with a set of constitutive constraint conditions, through which both the softening and hardening effects on the stiffness of structures due to size reduction can be addressed. The generalized differential quadrature method (GDQM) is utilized for discretizing variables presented in the differential problem formulation, from which the numerical solution of the dynamic instability region (DIR) of different bounded beams can be obtained. After conducting comparative studies to validate the proposed model, the effects of nonlocal parameters, static force factor, porosity distribution and viscoelastic property on the DIR are investigated. Moreover, the influence of incorporating the nonlocality of the foundation is also presented.