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Download or read book Free Vibration Analysis of Rectangular Mindlin Plates Resting on Uniform Elastic Edge Supports by the Superposition Method written by and published by . This book was released on 1997 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Hai Qi
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (137 download)
Download or read book Free Vibration Analysis of Rectangular Mindlin Plates Resting on Uniform Elastic Edge Supports by the Superposition Method written by Hai Qi and published by . This book was released on 1997 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the present study, it is demonstrated that the traditional superposition method lends itself successfully to obtaining of eigenvalues and mode shapes for rectangular shear deformable plates resting on uniform elastic edge supports. The effect of transverse shear deformation is taken into account by means of the first order shear deformation relationship developed by Mindlin. Uniform elastic rotational and translational supports of any stiffness magnitudes are considered to act simultaneously along the four edges. The effects of twisting edge restraint are investigated for the first time. The governing differential equations are satisfied exactly throughout the plate domain. Eigenvalues are tabulated for the first six vibration modes of square plates with identical stiffnesses along all edges. It is shown that all the three classical boundary conditions, namely, free, simply supported, and clamped, are approached when the stiffness coefficients are allowed to take on appropriate limits. These appear to be the first analytical solutions to these important elastically supported plate vibration problems obtained by the superposition method.
Author : Daniel J Gorman
Publisher : World Scientific
ISBN 13 : 9814495468
Total Pages : 383 pages
Book Rating : 4.8/5 (144 download)
Download or read book Vibration Analysis Of Plates By The Superposition Method written by Daniel J Gorman and published by World Scientific. This book was released on 1999-05-21 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Isaac E Elishakoff
Publisher : World Scientific
ISBN 13 : 9813236531
Total Pages : 798 pages
Book Rating : 4.8/5 (132 download)
Download or read book Handbook On Timoshenko-ehrenfest Beam And Uflyand- Mindlin Plate Theories written by Isaac E Elishakoff and published by World Scientific. This book was released on 2019-10-29 with total page 798 pages. Available in PDF, EPUB and Kindle. Book excerpt: The refined theory of beams, which takes into account both rotary inertia and shear deformation, was developed jointly by Timoshenko and Ehrenfest in the years 1911-1912. In over a century since the theory was first articulated, tens of thousands of studies have been performed utilizing this theory in various contexts. Likewise, the generalization of the Timoshenko-Ehrenfest beam theory to plates was given by Uflyand and Mindlin in the years 1948-1951.The importance of these theories stems from the fact that beams and plates are indispensable, and are often occurring elements of every civil, mechanical, ocean, and aerospace structure.Despite a long history and many papers, there is not a single book that summarizes these two celebrated theories. This book is dedicated to closing the existing gap within the literature. It also deals extensively with several controversial topics, namely those of priority, the so-called 'second spectrum' shear coefficient, and other issues, and shows vividly that the above beam and plate theories are unnecessarily overcomplicated.In the spirit of Einstein's dictum, 'Everything should be made as simple as possible but not simpler,' this book works to clarify both the Timoshenko-Ehrenfest beam and Uflyand-Mindlin plate theories, and seeks to articulate everything in the simplest possible language, including their numerous applications.This book is addressed to graduate students, practicing engineers, researchers in their early career, and active scientists who may want to have a different look at the above theories, as well as readers at all levels of their academic or scientific career who want to know the history of the subject. The Timoshenko-Ehrenfest Beam and Uflyand-Mindlin Plate Theories are the key reference works in the study of stocky beams and thick plates that should be given their due and remain important for generations to come, since classical Bernoulli-Euler beam and Kirchhoff-Love theories are applicable for slender beams and thin plates, respectively.Related Link(s)
Author : American Society of Mechanical Engineers. Winter Annual Meeting
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (139 download)
Download or read book A Comprehensive Study of the Free Vibration of Rectangular Plates Resting on Symmetrically-distributed Uniform Elastic Edge Supports written by American Society of Mechanical Engineers. Winter Annual Meeting and published by . This book was released on 1989 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: An analytical-type solution is developed for the free vibration analysis of rectangular plates with uniform elastic edge support symmetrically distributed about the plate central axes. Both linear elastic rotational and translational support are considered to act simultaneously. Rapid convergence is encountered. Because of the symmetry of the problem, the free vibration modes fall into three distinct families. Eigenvalues are tabulated for the first four modes of vibration of a square plate with identical stiffnesses on each edge and with various ratios of translational to rotational stiffnesses. This represents, to the author's knowledge, the first comprehensive treatment of this problem.
Author :
Publisher :
ISBN 13 :
Total Pages : 338 pages
Book Rating : 4.3/5 (243 download)
Download or read book Applied Mechanics Reviews written by and published by . This book was released on 1987 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :
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ISBN 13 :
Total Pages : 1060 pages
Book Rating : 4.F/5 ( download)
Download or read book International aerospace abstracts written by and published by . This book was released on 1993 with total page 1060 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Arthur W. Leissa
Publisher :
ISBN 13 :
Total Pages : 368 pages
Book Rating : 4.:/5 (317 download)
Download or read book Vibration of Plates written by Arthur W. Leissa and published by . This book was released on 1969 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :
Publisher :
ISBN 13 :
Total Pages : 502 pages
Book Rating : 4.U/5 (183 download)
Download or read book Acoustics Abstracts written by and published by . This book was released on 1997 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : K.M. Liew
Publisher : Elsevier
ISBN 13 : 0080543545
Total Pages : 213 pages
Book Rating : 4.0/5 (85 download)
Download or read book Vibration of Mindlin Plates written by K.M. Liew and published by Elsevier. This book was released on 1998-11-10 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the last several years, the four authors have jointly conducted research into the analysis of vibrating Mindlin plates as a collaborative project between Nanyang Technological University, The National University of Singapore, and The University of Queensland. The research was prompted by the fact that there is a dearth of vibration results for Mindlin plates when compared to classical thin plate solutions. To generate the vibration results, the authors have successfully employed the Ritz method for general plate shapes and boundary conditions. The Ritz method, once thought to be awkward for general plate analysis, can be automated through suitable trial functions (for displacements) that satisfy the geometric plate boundary conditions a priori. This work has been well-received by academics and researchers, as indicated by the continual requests for the authors' papers and the Ritz software codes. This monograph is written with the view to share this so-called p-Ritz method for the vibration analysis of Mindlin plates and its software codes with the research community. To the authors' knowledge, the monograph contains the first published Ritz plate software codes of its kind.
Author : Adhir Kumar Agrawal
Publisher :
ISBN 13 :
Total Pages : 352 pages
Book Rating : 4.:/5 (464 download)
Download or read book Free Vibration Analysis of Rectangular Plates Resting on a Two-parameter Elastic Medium written by Adhir Kumar Agrawal and published by . This book was released on 1993 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : David J. Michelussi
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (137 download)
Download or read book Free Vibration and Buckling Analysis of Thin Rectangular Plates with Classical Boundary Conditions Under Unilateral In-plane Loads written by David J. Michelussi and published by . This book was released on 1997 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 :
Publisher :
ISBN 13 :
Total Pages : 8 pages
Book Rating : 4.:/5 (61 download)
Download or read book Characterizing the Vibration of an Elastically Point Supported Rectangular Plate Using Eigensensitivity Analysis written by and published by . This book was released on 2009 with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt: Normalized frequencies are computed for a rectangular, isotropic plate resting on elastic supports. The normalized frequencies are determined using eigensensitivity analysis, which approximates the eigenparameters in a Mauclarin series, yielding an approximate closed-form expression. One benefit of the approximate closed-form expression is its computational efficiency and yet another is its application of re-analysis. Accuracy of the approximate expression is assessed by comparing results with the widely used Rayleigh-Ritz method using orthogonal polynomials and beam shape functions in both approaches. Consideration for a variety of edge conditions is given through a combination of simply supported, clamped and free boundary conditions. Results indicate that the accuracy of higher frequencies computed by the sensitivity approach is highly dependent upon choice of basis function.
Author : Khang V. Nguyen
Publisher :
ISBN 13 :
Total Pages : 152 pages
Book Rating : 4.:/5 (872 download)
Download or read book Free Vibration Analysis of Rectangular Orthotropic Cantilever Plates with Point Supports written by Khang V. Nguyen and published by . This book was released on 1993 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: The free vibration analysis of rectangular plates has been of interest to many scholars and practitioners over the years due to their wide range of applications. However, most of the studies involve the typical case of isotropy.
Author : Hans J. L. Öhman
Publisher :
ISBN 13 :
Total Pages : 258 pages
Book Rating : 4.:/5 (541 download)
Download or read book Free Vibration Analysis of Rectangular Plates with Internal Point Supports written by Hans J. L. Öhman and published by . This book was released on 1991 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Daniel J. Gorman
Publisher : Elsevier Publishing Company
ISBN 13 : 9780444006011
Total Pages : 324 pages
Book Rating : 4.0/5 (6 download)
Download or read book Free Vibration Analysis of Rectangular Plates written by Daniel J. Gorman and published by Elsevier Publishing Company. This book was released on 1982 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Wayne Caillouette
Publisher :
ISBN 13 :
Total Pages : 58 pages
Book Rating : 4.:/5 (274 download)
Download or read book Free Vibration Analysis of a Rectangular Plate with Two Edges Simply Supported and Two Edges Fixed written by Wayne Caillouette and published by . This book was released on 1992 with total page 58 pages. Available in PDF, EPUB and Kindle. Book excerpt:
