Modeling and Simulation of Transverse Free Vibration Analysis of a Rectangular Plate with Cutouts Using Energy Principles

Abstract

A modeling method is proposed for the vibration characteristics of rectangular plates with cutouts having variable size. Different from the existing modeling method by considering the cutout as an extremely thin part of the plate, the energy principles in conjunction with Rayleigh-Ritz solution technique are employed for the modeling of the structure. Under this theoretical framework, the effect of the cutout is taken into account by subtracting the energies of the cutout domains from the total energies of the whole plate with arbitrary boundary conditions. The displacement of the rectangular plate with nonuniform physic parameters is expressed as the combination of a two-dimensional trigonometric cosine series and supplementary terms introduced to ensure the uniform convergence of the solution over the entire solution domain including the cutouts boundary. The effectiveness and reliability of the eigenmodes of the rectangular plate with cutouts are checked against the results obtained by the finite element method (FEM). The cutout number, position, and size are varied to illustrate the effect of the cutouts on the vibration characteristics of the rectangular plate with cutouts.

Vibration Analysis of Driving-Point System with Uncertainties Using Polynomial Chaos Expansion

“…Rectangular plates are widely used in our daily life; all kinds of modeling method have been proposed for the vibration characteristics of rectangular plates with system certainty [31]. In this paper, a rectangular plate is fixed at its left boundary and supported by springs at its right boundary.…”

Free Vibration Analysis of Rectangular Plate with Cutouts under Elastic Boundary Conditions in Independent Coordinate Coupling Method

“…Currently, research has mainly focused on three aspects: the region segmentation, the equivalent substitution, and the separation of cutouts and plate domains. Then, to examine the vibration characteristics of the rectangular plate with cutouts, semi-analytical methods generally used are the Rayleigh-Ritz methods (RRM) [2,13,14], the multi-term extended Kantorovich method (MEKM) [15], the extension of Hencky bar-net method [16], Chebyshev-Lagrangian method [17], the Green function method [18], the superposition method, the assumed mode method [19,20], the improved Fourier series method [21,22], the Dynamic Stiffness Method (DSM) [23], and the Spectro-Geometric Method (SGM) [24].…”

“…The influence of various factors on the vibration characteristics of a rectangular plate with cutouts has been under investigation in the literature. Many researchers discussed the position of cutouts [4,15,17,21] as a central hole, corner hole and edge hole, and analyzed the applicability and accuracy of their methods. The opening ratio and number are directly related to the mass and stiffness of plate structure, which in turn naturally affects the vibration characteristics and stability of structure.…”

“…Cho et al [19,20] and Nie et al [43] analyzed rectangular plates with multiple openings by the assumed mode method. Wang et al [28], Liu et al [22] and Shi et al [21] discussed rectangular plate with inner cutouts or edge cutouts by the improved Fourier series method. Wang et al [24] adopted the Spector-Geometric method to rectangular plate with triangular and rectangular holes.…”

In‐Plane Vibration Analysis of Square Plate with Multiple Cutouts

“…In the existing methods, the cutouts within the structure are considered as a kind of structure with zero thickness. To behave the physical characteristics of the cutouts within the structure, the influence of cutouts on the vibration characteristic of the structure is considered in terms of energy [21]. e energy principle combined with the Rayleigh-Ritz solution is adopted to determine the vibration characteristics of the structures with cutouts.…”