Circular plates are important structural elements in modern engineering structures. In this paper a computationally efficient and accurate numerical model is presented for the study of free vibration and bending behavior of thick circular plates based on Mindlin plate theory. The approach developed is based on the discrete singular convolution method and the use of regularized Shannon's delta kernel. Frequency parameters, deflections and bending moments are obtained for different geometric parameters of the circular plate. Comparisons are made with existing numerical and analytical solutions in the literature. It is found that the DSC method yields accurate results for the free vibration and bending problems of thick circular plates. Copyright © 2008 John Wiley & Sons, Ltd.

Free vibration and bending analysis of circular Mindlin plates using singular convolution method

The intense vibration of a roadheader rotary table damages the cutting system of the roadheader and reduces the efficiency. This paper analyzes the vibration of a rotary table by combining the finite element model with tested data from an underground coalmine. First, the force of the rotary table during the cutting procedure was analyzed, and the finite element model was built using Pro/E and ADAMS. The tested data were then imported into the model after selection, procession, and combination were conducted. Next, the six lowest-order parameters of the rotary table were calculated. A vibration analysis of the rotary table under certain working conditions was conducted, and the results were compared with those from a modal experiment using a single-point excitation method. According to the comparison between the simulation result and experiments, it is clear that this method is both reasonable and feasible. And it could supplement the theoretical foundation of the analysis of other roadheader components, providing reference for the improvement of the structure and dynamic properties of a roadheader. In addition, other vibration components of a roadheader such as the cutting head and the cutting arm could also be analyzed through the proposed method, with very reliable precision.

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Analysis of Vibration of Roadheader Rotary Table Based on Finite Element Method and Data from Underground Coalmine

Free, transverse vibrations of thin plates with discontinuous boundary conditions

Two cases of a rectangular plate having moment singularities at the ends of a partial internal line support are analytically investigated. The bending of the plate by uniform loading is formulated in terms of dual-series equations. Application of the finite Hankel integral transform reduces the dual-series equations to a Fredholm integral equation of the second kind that can be solved by standard techniques. Numerical results are given for the deflections and bending moments along the line outside of an internal line support and the change in strain energy due to the presence of a partial support.

Inverse square root moment singularities in rectangular plates containing an internal line support

The natural vibration of a circular membrane with a discontinuity at the fixed boundary is investigated by an analytical method and the finite element analysis. A new analytical method is developed to consider the mixed boundary value problem using the orthogonality of the Fourier series. The finite element analysis has been done using ANSYS. The results from both simulations agree well as the problem is linear elastic problem. The mode shapes of the cracked membrane show that the vibration of the ligament dominates the vibration of smaller natural frequencies as the angle of the crack become larger because the flexibility of the free part in the ligament provide lower vibration modes. Introduction A membrane is a thin structure which is a two dimensional system similar to a string. It cannot bear bending resistance and the restoring force is due only to the tension in the structure. Its importance grows as the applications are broadened. The eardrum is always modeled as a membrane and the joints with the soft tissues such as ligaments and tendons can be considered as mixed boundary condition on the membrane [1]. The dynamic characteristics are important in design of a stencil mask [2]. Rossi and Laura commented on the vibration of a circular plate with mixed boundary as ‘there is practically no information in the technical literature for the mixed boundary combination: clamped – free and simply supported – free’ [3] and it is same for membrane vibration. Also the dynamic characteristics of a cell membrane are important to understand the behavior of cell under dynamic stimulation [4]. These are motivations of this study. Equations The governing equation of the natural vibration of a membrane is

P.A.A. Laura

Papers

Transverse Vibrations of a Thin, Elastic Circular Plate with Mixed Boundary Conditions