Analytical solutions of bending and free vibration of moderately thick micro-plate via two-variable strain gradient theory

Abstract

In this paper, the strain gradient theory (SGT) and two-variable refined plate theory are implemented simultaneously to analyze bending and free vibration of micro-plate. The proposed theory is called two-variable strain gradient theory (TV-SGT). The TV-SGT, which can be used for both thin and moderately thick micro-plates, predicts parabolic variation of transverse shear stresses across the plate thickness and does not need the shear correction factor. The governing equations are obtained using a variational approach and solved analytically to find the deflection of simply supported micro-plate under uniformly distributed loading and natural frequency of this plate. Thereby, the effects of length scale parameters and dimensions on the bending deflection and natural frequency of the micro-plate are investigated. Results show that, strengthen micro-plate has higher shear rigidity. Moreover, it is inferred that TV-SGT is well defined to analyze the micro-plate.

The correct derivation of the buckling equations of the shear-deformable FGM plates for the extended Kantorovich method

“…ξ (z) gets transferred to the transverse shear strains and stresses through the kinematic relations. There are numerous versions of the traditional refined plate theory, e.g., [24,2,32,6]; they normally differ in the adopted shear distribution function, ξ (z) . Note that RPT herein refers to the form of the theory ξ (z) is general function.…”

Design of Longitudinal-Bending Coupled Horn of a Giant Magnetostriction Transducer

“…Moreover, they intend to study the thick homogeneous plate, wherever the rotating wheel in the L-BCH is the variable thickness disk. Later, based on the dualvariable strain gradient theory, Farahmand et al [20] analyzed the bending free vibration of medium-thick micro-plates, and studied the influence of size parameters of the plates on the bending deflection and natural frequency of micro-plates; the research objects are microthin plates and medium-thick micro-plates, but the rotating wheel was not a micro-plate. Usarov et al [21] studied the anisotropic free vibration considering internal force, bending moment, and double bending moment via establishing a six-equation system model to describe the motion of the thick plate, thus determining the natural frequency of isotropic and anisotropic thick fixed plate in the lateral vibration situation.…”