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Ding Zhou

Bio: Ding Zhou is an academic researcher from Nanjing Tech University. The author has contributed to research in topics: Boundary value problem & Beam (structure). The author has an hindex of 29, co-authored 148 publications receiving 2580 citations. Previous affiliations of Ding Zhou include Nanjing University of Science and Technology & University of Manchester.


Papers
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Journal ArticleDOI
TL;DR: In this paper, a method for free vibration analysis of rectangular plates with any thicknesses, which range from thin, moderately thick to very thick plates, is described. And the analysis is based on a linear, small-strain, three-dimensional elasticity theory.

148 citations

Journal ArticleDOI
TL;DR: In this paper, a three-dimensional free vibration analysis of circular and annular plates via the Chebyshev-Ritz method is presented, which is based on the linear, small strain, 3D elasticity theory.

122 citations

Journal ArticleDOI
TL;DR: In this article, the free-vibration characteristics of rectangular thick plates resting on elastic foundations have been studied, based on the three-dimensional, linear and small strain elasticity theory.
Abstract: The free-vibration characteristics of rectangular thick plates resting on elastic foundations have been studied, based on the three-dimensional, linear and small strain elasticity theory. The foundation is described by the Pasternak (two-parameter) model. The Ritz method is used to derive the eigenvalue equation of the rectangular plate by augmenting the strain energy of the plate with the potential energy of the elastic foundation. The Chebyshev polynomials multiplied by a boundary function are selected as the admissible functions of the displacement functions in each direction. The approach is suitable for rectangular plates with arbitrary boundary conditions. Convergence and comparison studies have been performed on square plates on elastic foundations with different boundary conditions. It is shown that the present method has a rapid convergent rate, stable numerical operation and very high accuracy. Parametric investigations on the dynamic behaviour of clamped square thick plates on elastic foundations have been carried out in detail, with respect to different thickness-span ratios and foundation parameters. Some results found for the first time have been given and some important conclusions have been drawn.

98 citations

Journal ArticleDOI
TL;DR: In this paper, the vibratory characteristics of a rectangular plate in contact with water on one side are studied, and an analytical-Ritz method is developed to analyse the interaction of the plate-water system.
Abstract: In this paper, the vibratory characteristics of a rectangular plate in contact with water on one side are studied. The elastic plate is considered to be a part of a vertical rectangular rigid wall in contact with water, the edges of which are elastically restrained and parallel to those of the rigid wall. The location and size of the plate on the rigid wall may vary arbitrarily. The water with a free surface is in a rectangular domain infinite in the length direction. The effects of free surface waves, compressibility of the water and the hydrostatic water pressure are neglected in the analysis. An analytical-Ritz method is developed to analyse the interaction of the plate–water system. First of all, by using the method of separation of variables and the method of Fourier series expansion, the exact expression of the motion of water is derived in the form of integral equations including the dynamic deformation of the plate. Then the Rayleigh–Ritz approach is used to derive the eigenfrequency equation of the system via the variational principle of energy. By selecting beam vibrating functions as the admissible functions of the plate, the added virtual mass incremental (AVMI) matrices for plate vibration are obtained. The convergency studies are carried out. The effects of some parameters such as the depth and width of water, the support stiffnesses, location and aspect ratio of the plate and the plate–water size and density ratios on the eigenfrequencies of the plate–water system are investigated. Several numerical examples are given. The validity of AVMI factor approach is also confirmed by comparing the AVMI factor solutions with the analytical-Ritz solutions. The results show that the approach presented here can also be used as excellent approximate solutions for rectangular plates in contact with water of infinite width and/or infinite depth. Copyright © 2000 John Wiley & Sons, Ltd.

91 citations

Journal ArticleDOI
TL;DR: In this paper, a general approach for solving the free vibration of solid and hollow circular cylinders is presented, which is based on the small-strain, linear and exact elasticity theory.

90 citations


Cited by
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Book
19 May 2005
TL;DR: In this article, the authors present a detailed review of liquid sloshing dynamics in rigid containers, including linear forced and non-linear interaction under external and parametric excitations.
Abstract: Preface Introduction 1. Fluid field equations and modal analysis in rigid containers 2. Linear forced sloshing 3. Viscous damping and sloshing suppression devices 4. Weakly nonlinear lateral sloshing 5. Equivalent mechanical models 6. Parametric sloshing (Faraday's waves) 7. Dynamics of liquid sloshing impact 8. Linear interaction of liquid sloshing with elastic containers 9. Nonlinear interaction under external and parametric excitations 10. Interactions with support structures and tuned sloshing absorbers 11. Dynamics of rotating fluids 12. Microgravity sloshing dynamics Bibliography Index.

920 citations

Journal ArticleDOI
TL;DR: In this article, a hyperbolic shear deformation theory applicable to bending and free vibration analysis of isotropic, functionally graded, sandwich and laminated composite plates is presented.

451 citations

Journal ArticleDOI
TL;DR: In this article, the fundamental frequency analysis of functionally graded (FG) beams having different boundary conditions is analyzed within the framework of the classical, the first-order and different higher-order shear deformation beam theories.

373 citations

Journal ArticleDOI
TL;DR: A comprehensive review of various theories for the modeling and analysis of functionally graded plates and shells is presented in this paper, where a thorough review of the literature related to the development of three-dimensional elasticity solutions and a unified formulation is also presented.

346 citations

Journal ArticleDOI
TL;DR: In this paper, the effect of shear deformations using the first-order shear deformation theory is derived and solved exactly for various combinations of boundary conditions by using the exact element method.

299 citations