Bending Analysis of Isotropic Rectangular Kirchhoff Plates Subjected to Non-Uniform Heating Using the Fourier Transform Method

The object of this paper is the bending analysis of isotropic rectangular Kirchhoff plates subjected to non-uniform heating (NUH) using the Fourier transform method. The bottom and top surfaces of the plate are assumed to have different changes in temperature, whereas the change in temperature of the mid-surface is zero. According to classical plate theory, the governing equation of the plate contains second derivatives of the NUH; these derivatives are zero by constant value of the NUH, which leads to its absence in the governing equation. This paper presented an approach by which Fourier sine transform was utilized to describe the NUH, while the double trigonometric series of Navier and the simple trigonometric series of Lévy were utilized to describe the deflection curve. Thus, the NUH appeared in the governing equation, which simplified the analysis. Rectangular plates simply supported along all edges were analyzed, bending moments, twisting moments, and deflections being determined. In addition, rectangular plates simply supported along two opposite edges were analyzed; the other edges having various support conditions (free, simply supported, and fixed).

Optimal Placement of Viscoelastic Vibration Dampers for Kirchhoff Plates Based on PSO Method

The main subject of this study is to determine the optimal position of a fixed number of viscoelastic dampers on the surface of a thin (Kirchhoff-Love) plate. It is assumed that the dampers are described according to the generalized Maxwell model. In order to determine the optimal position of the dampers, a metaheuristic optimization method is used, called the particle swarm optimization method. The non-dimensional damping ratio of the first mode of the plate vibrations is assumed as an objective function in the task. The dynamic characteristics of the plate with dampers are determined by solving the non-linear eigenproblem using the continuation method. The finite element method is used to determine the stiffness matrix and the mass matrix occurring in the considered eigenproblem. The results of exemplary numerical calculations are also presented, where the final optimal arrangement of dampers on the surface of sample plates with different boundary conditions is shown graphically.

Bending Analysis of Isotropic Rectangular Kirchhoff Plates Subjected to a Thermal Gradient Using the Fourier Transform Method

The object of this paper is the bending analysis of isotropic rectangular Kirchhoff plates subjected to a thermal gradient (TG) using the Fourier transform method. The bottom and top surfaces of the plate are assumed to have different changes in temperature, whereas the change in temperature of the mid-surface is zero. According to classical plate theory, the governing equation of the plate contains second derivatives of the TG; these derivatives are zero by constant value of the TG, which leads to the absence of the TG in the governing equation. This paper presented an approach by which Fourier sine transform was utilized to describe the TG, while the double trigonometric series of Navier and the simple trigonometric series of Lévy were utilized to describe the deflection. Thus, the TG appeared in the governing equation, which simplified the analysis. Rectangular plates simply supported along all edges were analyzed, bending moments, twisting moments, and deflections being determined. In addition, rectangular plates simply supported along two opposite edges were analyzed, the other edges having various support conditions (free, simply supported, and fixed).