Critical Temperatures for Vibrations and Buckling of Magneto-Electro-Elastic Nonlocal Strain Gradient Plates

Abstract

An analytical method is presented in this work for the linear vibrations and buckling of nano-plates in a hygro-thermal environment. Nonlinear von Kármán terms are included in the plate kinematics in order to consider the instability phenomena. Strain gradient nonlocal theory is considered for its simplicity and applicability with respect to other nonlocal formulations which require more parameters in their analysis. Present nano-plates have a coupled magneto-electro-elastic constitutive equation in a hygro-thermal environment. Nano-scale effects on the vibrations and buckling behavior of magneto-electro-elastic plates is presented and hygro-thermal load outcomes are considered as well. In addition, critical temperatures for vibrations and buckling problems are analyzed and given for several nano-plate configurations.

On the mapping procedure based on higher‐order Hermite polynomials for laminated thin plates with arbitrary domains in gradient elasticity

“…This limitation has been recently overcome in some works that aimed at studying the mechanical behavior in gradient elasticity of laminated composite thin plates. The papers by Cornacchia et al 40,41 and Tocci Monaco et al [42][43][44][45] should be mentioned as examples of thin laminates in gradient elasticity, studied by means of the Navier's analytical technique. It should be recalled that the membrane and bending behaviors of plates is coupled for particular lamination sequences.…”

Investigation of the effect of viscosity and fluid flow on buckling behaviour of non‐local nanoplate with surface energy

“…Tocci Monaco et al. [18] examined non‐local strain gradient plates’ linear buckling in a hygro‐thermal medium. The dynamic buckling of a sandwich nanoplate (SNP) was investigated using non‐local elasticity theory.…”

“…Naderi and Saidi [17] proposed a novel non-local Mindlin plate theory in order to assess the stability of nanoplates under uniaxial and biaxial loads. Tocci Monaco et al [18] examined non-local strain gradient plates' linear buckling in a hygro-thermal medium. The dynamic buckling of a sandwich nanoplate (SNP) was investigated using non-local elasticity theory.…”

Radial Point Interpolation Method for Isotropic Nanoplates in Bending Using Strain Gradient Theory

“…These kind of structures, in fact, have proven to be extremely versatile, finding wide applications in Micro-Electro-Mechanical-Systems (MEMS) and Nano-Electro-Mechanical-Systems (NEMS) which require the employment of nanorods, nanobeams and nanoplates [Mariano and Trovalusci (1999); Barretta et al (2018); Mahmure et al (2021); ; Akgöz and Civalek (2015a); ; Numanglu et al (2018); ]. Nonlocal theories have been widely applied in the study of these structural components to investigate nonlocal effects in both static [Trovalusci and Augusti (1998); Tuna et al (2019); ; Tocci Monaco et al (2021b); Barretta and Marotti de Sciarra (2013)] and dynamic [Avey et al (2021); Deniz et al (2021); Tocci Monaco et al (2021a); Numanglu et al (2018); Barretta et al (2019); ] analysis.…”