The effect of multidimensional temperature distribution on the vibrational characteristics of a size-dependent thick bi-directional functionally graded microplate

Abstract

This article develops the modified couple stress theory to study the free vibration of bi-directional functionally graded microplates subjected to multidimensional temperature distribution. Third-order shear deformation and classical theories of plates are adapted for free vibration analysis of thick and thin microplates, respectively. Employing the third-order shear deformation theory, both normal and shear deformations are considered without the need for shear correction factor. Material of the bi-directional functionally graded microplate is graded smoothly through the length and thickness of the microplate. Gradient of the material is assumed to obey from the power law in terms of the volume fraction of the constituents. Assuming the uniform and nonuniform temperature distributions, the effect of thermal environment on dynamic behavior of the microplate is discussed in detail. Applying the Ritz method, the displacement field is expanded by admissible functions which satisfy the essential boundary conditions, and Hamilton principle is employed to determine the natural frequencies of the microplate. Developed model has been applied to determine the natural frequencies in problems of thin/thick, one-directional/bi-directional functionally graded, and homogeneous/nonhomogeneous microplates. Effects of parameters such as the thermal environment, power law indexes [Formula: see text] and length scale parameter on free vibration of these problems are studied in detail. The results show that higher values of length scale parameter and temperature rise decrease the natural frequency of the bi-directional functionally graded microplate. According to results obtained by classical and third-order shear deformation theories, the third-order shear deformation theory is proposed for vibration analysis of microplates with thickness-to-length ratio less than five.

Natural vibrations of double bi-directional functionally graded Euler–Bernoulli beams connected by a variable Winkler elastic layer

“…The moment Lyapunov exponent and perturbation methods were applied to analyze the stability of the double nanobeam. Other researchers studied several BDFG structures [22][23][24][25][26][27][28][29][30][31][32] and double-beam systems. [33][34][35][36] Based on the above discussion, it is noted that no efforts have been dedicated to carry out the free vibrations of bidirectional functionally graded (BDFG) double Euler-Bernoulli beams connected by a variable Winkler elastic layer, as they can represent applications as double-beam cranes, double-beam spectrometers, and double-beam interferometers.…”

A comprehensive study on the size-dependent analysis of strain gradient multi-directional functionally graded microplates via finite element model

“…Farzam and Hassani [68] proposed an IGA-RPT for linear analysis of in-plane FG porous microplates. Bakhsheshy and Mahbadi [69] derived Navier solution to study vibration of 2D FG microplates subjected to temperature distribution using the TSDT. It is clear that there is a gap related to the size-dependent behaviour of the multi-directional FG microplates using a quasi-3D shear deformation theory via the MSGT and finite element model (FEM), which are the main contributions of this paper.…”