Nonlocal strain gradient free vibration analysis of sandwich functionally graded porous nanoshell integrated with piezoelectric surface layers taking into account flexoelectric effect

Abstract

In addition to accounting for non-gradient nonlocal elastic stress, a nonlocal strain gradient theory (NSGT) also considers the nonlocality of higher-order strain gradients; thus, it is applicable to small-scale structures and can account for both hardening and softening effects. An analytical model is constructed in this research endeavor to depict the free vibration characteristics of sandwich functionally graded porous (FGP) doubly-curved nanoshell integrated with piezoelectric surface layers consists of three distinct layers, taking into account flexoelectrici effect based on NSGT and novel refined high-order shear deformation hypothesis. The novelty of this study is that the two nonlocal coefficients and material length scale of the core layer are variable along thickness, like other material characteristics. The equilibrium equation of motion of the doubly-curved nanoshell is derived from Hamilton’s principle, then the Galerkin method is applied to derive the natural vibration frequency values of the doubly-curved nanoshell with different boundary conditions (BCs). The influence of parameters such as flexoelectric effect, nonlocal and length scale factors, elastic medium stiffness factor, porosity factor, and BCs on the free vibration esponse of the nanoshell is detected and comprehensively studied. This paper is claimed to provide a theoretical predicition on the impact of the size-small dependent and flexoelectric effect upon the oscillation of FGP nanoshell integrated with piezoelectric surface layers, thus sheding light on understanding the underlying physics of electromechanical coupling at the nanoshell to some extent.

Graphical abstract

Keywords

analytical solution / flexoelectric effect / piezoelectric / free vibration / nonlocal strain gradient theory

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