Free Vibration and Buckling Analysis of Thin Rectangular Plates with Classical Boundary Conditions Under Unilateral In-plane Loads PDF Download
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Languages : en
Pages :
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Languages : en
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Author: David J. Michelussi
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
Interest in the free vibration of thin rectangular plates has emerged due to the rapid growth in computer technology. Delicate electronic components mounted on circuit boards may be placed in environments under dynamic loadings. The designer may need to control the natural frequency or mode shape of a specific board if a known excitation is causing reliability problems in the hardware. Fortunately, constant in-plane loads can be applied to the plate, affecting its stiffness, and hence dynamic characteristics. This method of control is convenient since the circuit board does not need to be redesigned. The method of superposition is used to obtain analytical-type solutions for the free vibration of thin rectangular plates under constant in-plane loads in this thesis. A total of nine plate configurations are examined, each of which possess at least one free edge. Eight building blocks are derived and used to solve the plates under consideration. Each building block solution is of the Levy-type and is analytically exact. Since plate buckling is a limiting case of plate vibration, the solutions obtained can also be used to solve plate buckling problems. Results are calculated for nine plate aspect ratios. Buckling loads, frequencies, and mode shapes are shown. Excellent agreement is found in comparisons with other solution methods.
Author: Daniel J Gorman
Publisher: World Scientific
ISBN: 9814495468
Category : Technology & Engineering
Languages : en
Pages : 383
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Book Description
The elegance and logic of the superposition method have made it a highly attractive analytical procedure for obtaining accurate mathematical solutions to plate vibration problems. Its applicability to vast families of these problems, ranging from the dynamic behaviour of isotropic and orthotropic plates to laminated plate behaviour, is well demonstrated in the technical literature.Now, at last, a comprehensive book is made available to those who wish to use this powerful analytical technique. Beginning with a thorough and lucid introduction to the superposition method as it applies to free vibration of thin isotropic rectangular plates, with all combinations of classical boundary conditions, the book describes procedures for handling vast families of realistic practical plate vibration problems. These include orthotropic plates, point-supported plates, plates resting on elastic edge supports, plates with in-plane forces, buckling of plates, etc. The reader is subsequently introduced to utilization of the superposition method for the analysis of thick Mindlin plates as well as transverse-shear-deformable laminated plates. Particular emphasis is placed on plate free vibration analysis, with a list of pertinent publications attached to each chapter.The superposition method is unique in that all solutions obtained satisfy the governing differential equations exactly throughout the entire domain of the plate. The boundary conditions are satisfied to any desired degree of accuracy.Despite the attractive features of this analytical method, many researchers and designers have access only to published papers related to particular problems. With this new book, they have for the first time a comprehensive, illustrated description of the means of exploiting the superposition method. They will be able to prepare their own computer schemes and analyse any plate vibration problem of interest.
Author: Hari Kishan Koduru
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Rectangular plates are found in most structures of modern industry. Their two-dimensional structural action results in lighter structures and therefore offers numerous economic advantages. Recently interest in rectangular plates increased due to rapid growth in electronic technology where electronic circuit boards in the form of thin rectangular plates are employed. It is well known that while a clamped boundary condition along the edge of thin rectangular plates is easy to formulate mathematically, it is difficult to achieve, even under laboratory conditions. This is due in part to the fact that some rotational elasticity is likely to be found in such supports, whether it is introduced intentionally or inadvertently. In this study, the effects of such elasticity on the free vibration and buckling of plates subjected to uniform in-plane loading are examined. Loading is applied in a direction perpendicular to a pair of opposite edges where lateral displacement is forbidden and edge rotation is opposed by a moment proportional to the degree of edge rotation. The edges running parallel to the in-plane loading are free. Highly accurate solutions are obtained by the method of superposition. Two plates are analysed; one with rotational elastic support at one edge, the other edge being simply supported and, a second plate with rotational elastic support at the pair of opposite edges. Free vibration eigenvalues and buckling loads are computed for various plate geometries, dimensionless rotational stiffnesses with various in-plane loads. It is observed that in limiting cases, eigenvalues and buckling loads agree well in comparison with those of classical cases such as pinned and clamped boundary conditions. It is also found that the edges can be given any desired value of the rotational stiffness.
Author: T.K Varadan
Publisher: ALPHA SCIENCE INTERNATIONAL LIMITED
ISBN: 8184872801
Category : Mathematics
Languages : en
Pages : 198
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This book deals with the classical plate theory most commonly used for the analysis of thin metallic plate structures. The basic assumptions of the plate theory are not straightaway taken for granted, but are deduced as logical inferences from a three-dimensional elasticity solution for a thin rectangular slab. In addition, the elasticity results are used to verify the accuracy of the plate theory. Statics, dynamics as well as stability of plates are dealt with. Besides a lucid explanation of the theory, exact and approximate solution methodologies are discussed. The approach adopted throughout--with emphasis on close correspondence with the three-dimensional theory of elasticity, and on the implications of each assumption of the plate theory--enables the reader to easily progress on to the study of state-of-the-art topics such as geometric and material nonlinearities, refined plate theories accounting for warping and stretching of the normal and laminated construction and material orthotropy typical of fibre-reinforced composites.
Author: Manuel Stein
Publisher:
ISBN:
Category : Buckling (Mechanics)
Languages : en
Pages : 40
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Book Description
The nonlinear large-deflection equations of von Kármán for plates are converted into a set of linear equations by expanding the displacements into a power series in terms of an arbitrary parameter. The post-buckling behavior of simply supported rectangular plates subjected to longitudinal compression and subject to a uniform temperature rise is investigated in detail by solving the first few of the equations. Experimental data are presented for the compression problem. Comparisons are made for total shortening and local strains and deflections which indicate good agreement between experimental and theoretical results.
Author:
Publisher:
ISBN:
Category : Mechanics, Applied
Languages : en
Pages : 1116
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Author: National Aeronautics and Space Administration (NASA)
Publisher: Createspace Independent Publishing Platform
ISBN: 9781722408596
Category :
Languages : en
Pages : 54
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The method of matched asymptotic expansions is used to solve the transverse free vibration of a slightly curved, thin rectangular plate. Analytical results for natural frequencies and mode shapes are presented in the limit when the dimensionless bending rigidity, epsilon, is small compared with in-plane forces. Results for different boundary conditions are obtained when the initial deflection is: (1) a polynomial in both directions, and (2) the product of a polynomial and a trigonometric function, and arbitrary. For the arbitrary initial deflection case, the Fourier series technique is used to define the initial deflection. The results obtained show that the natural frequencies of vibration of slightly curved plates are coincident with those of perfectly flat, prestressed rectangular plates. However, the eigenmodes are very different from those of initially flat prestressed rectangular plates. The total deflection is found to be the sum of the initial deflection, the deflection resulting from the solution of the flat plate problem, and the deflection resulting from the static problem. Adeniji-Fashola, A. A. and Oyediran, A. A. Unspecified Center...
Author: Chandru M. Kalro
Publisher:
ISBN:
Category : Buckling (Mechanics)
Languages : en
Pages : 104
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Author: Louis Bauer
Publisher: Palala Press
ISBN: 9781379153016
Category : History
Languages : en
Pages : 106
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