Eigenvalues of inhomogeneous structures : unusual closed-form solutions /: unusual closed-form solutions. (©2005)

• Record Type: Book
• Further Information: Note: Isaac Elishakoff.
• Other Names: Elishakoff, Isaac
• Contents: FOREWORD; PROLOGUE; INTRODUCTION: REVIEW OF DIRECT, SEMI-INVERSE AND INVERSE EIGENVALUE PROBLEMS; Introductory Remarks; Vibration of Uniform Homogeneous Beams; Buckling of Uniform Homogeneous Columns; Some Exact Solutions for the Vibration of Non-Uniform Beams; Exact Solution for Buckling of Non-Uniform Columns; Other Direct Methods (FDM, FEM, DQM); Eisenberger 's Exact Finite Element Method; Semi-Inverse or Semi-Direct Methods; Inverse Eigenvalue Problems; Connection to the Work by ?Zyczkowski and Gajewski; Connection to Functionally Graded Materials; Scope of the Present Monograph; UNUSUAL CLOSED-FORM SOLUTIONS IN COLUMN BUCKLING; New Closed-Form Solutions for Buckling of a Variable Flexural Rigidity Column; Inverse Buckling Problem for Inhomogeneous Columns; Closed-Form Solution for the Generalized Euler Problem; Some Closed-Form Solutions for the Buckling of Inhomogeneous Columns Under Distributed Variable Loading; UNUSUAL CLOSED-FORM SOLUTIONS FOR ROD VIBRATIONS; Reconstructing the Axial Rigidity of a Longitudinally Vibrating Rod by Its Fundamental Mode Shape; The Natural Frequency of an Inhomogeneous Rod May be Independent of Nodal Parameters; Concluding Remarks; UNUSUAL CLOSED-FORM SOLUTIONS FOR BEAM VIBRATIONS; Apparently First Closed-Form Solutions for Frequencies of Deterministically and/or Stochastically Inhomogeneous Beams (Pinned -Pinned Boundary Conditions); Apparently First Closed-Form Solutions for Inhomogeneous Beams (Other Boundary Conditions); Inhomogeneous Beams That May Possess a Prescribed Polynomial Second Mode; Concluding Remarks; BEAMS AND COLUMNS WITH HIGHER-ORDER POLYNOMIAL EIGENFUNCTIONS; Family of Analytical Polynomial Solutions for Pinned Inhomogeneous Beams. Part 1: Buckling; Family of Analytical Polynomial Solutions for Pinned Inhomogeneous Beams. Part 2: Vibration; INFLUENCE OF BOUNDARY CONDITIONS ON EIGENVALUES; The Remarkable Nature of Effect of Boundary Conditions on Closed-Form Solutions for Vibrating Inhomogeneous Bernoulli-Euler Beams; BOUNDARY CONDITIONS INVOLVING GUIDED ENDS; Closed-Form Solutions for the Natural Frequency for Inhomogeneous Beams with One Guided Support and One Pinned Support; Closed-Form Solutions for the Natural Frequency for Inhomogeneous Beams with One Guided Support and One Clamped Support; Class of Analytical Closed-Form Polynomial Solutions for Guided-Pinned Inhomogeneous Beams; Class of Analytical Closed-Form Polynomial Solutions for Clamped -Guided Inhomogeneous Beams; VIBRATION OF BEAMS IN THE PRESENCE OF AN AXIAL LOAD; Closed -Form Solutions for Inhomogeneous Vibrating Beams Under Axially Distributed Loading; A Fifth-Order Polynomial That Serves as Both the Buckling and Vibration Modes of an Inhomogeneous Structure; UNEXPECTED RESULTS FOR A BEAM ON AN ELASTIC FOUNDATION OR WITH ELASTIC SUPPORT; Some Unexpected Results in the Vibration of Inhomogeneous Beams on an Elastic Foundation; Closed-Form Solution for the Natural Frequency of an Inhomogeneous Beam with a Rotational Spring; Closed-Form Solution for the Natural Frequency of an Inhomogeneous Beam with a Translational Spring; NON-POLYNOMIAL EXPRESSIONS FOR THE BEAM'S FLEXURAL RIGIDITY FOR BUCKLING OR VIBRATION; Both the Static Deflection and Vibration Mode of a Uniform Beam Can Serve as Buckling Modes of a Non-Uniform Column; Resurrection of the Method of Successive Approximations to Yield Closed-Form Solutions for Vibrating Inhomogeneous Beams; Additional Closed-Form Solutions for Inhomogeneous Vibrating Beams by the Integral Method; CIRCULAR PLATES; Axisymmetric Vibration of Inhomogeneous Clamped Circular Plates: An Unusual Closed-Form Solution; Axisymmetric Vibration of Inhomogeneous Free Circular Plates: An Unusual, Exact, Closed-Form Solution; Axisymmetric Vibration of Inhomogeneous Pinned Circular Plates: An Unusual, Exact, Closed-Form Solution; EPILOGUE; APPENDICES; REFERENCES; AUTHOR INDEX; SUBJECT INDEX
• Publisher Details: Boca Raton, Fla : CRC Press
• Publication Date: 2005
• Copyright Date: 2005
• Extent: 1 online resource (xiv, 729 pages), illustrations
• Subjects: 624.1/76/015118; Buckling (Mechanics) -- Mathematical models; Eigenvalues; Structural dynamics -- Mathematical models; TECHNOLOGY & ENGINEERING -- Structural; Buckling (Mechanics) -- Mathematical models; Eigenvalues; Structural dynamics -- Mathematical models; Electronic books
• Languages: English
• ISBNs: 0849328926; 9780849328923; 9781420038019
• Related ISBNs: 142003801X
• Notes: Note: Includes bibliographical references (pages 653-710) and indexes.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.