Vibration analysis of plates by the superposition method / Daniel J. Gorman.

Format:

Book

Author/Creator:

Gorman, D. J. (Daniel J.), 1930-

Series:

Series on stability, vibration, and control of systems. Series A ; v. 3.

Series on stability, vibration and control of systems, Series A ; v. 3

Language:

English

Subjects (All):

Plates (Engineering)--Vibration--Mathematical models.

Plates (Engineering).

Superposition principle (Physics).

Physical Description:

1 online resource (383 p.)

Place of Publication:

Singapore ; River Edge, N.J. : World Scientific, c1999.

Language Note:

English

Summary:

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 vib

Contents:

PREFACE; NOMENCLATURE; CONTENTS; Chapter 1 PLATE VIBRATION ANALYSIS BY THE METHOD OF SUPERPOSITION; 1.1 GENERAL INTRODUCTION TO THE SUPERPOSITION METHOD; 1.2 HISTORICAL BACKGROUND; 1.3 OBJECTIVES UNDERTAKEN; 1.4 DETAILED ILLUSTRATIVE PROBLEM; Dimensionless Boundary Conditions; Governing differential equation; 1.5 CONVERGENCE TOWARD EXACT EIGENVALUES; 1.6 VERIFICATION TESTS FOR THE EIGENVALUE MATRIX; 1.6.1 Boundary verification Tests; 1.6.2 Matrix Element Continuity Test; 1.6.3 Verification by Focusing on Submatrices; 1.7 COMPANION SOLUTIONS FOR THE ILLUSTRATIVE EXAMPLE

1.7.1 Modes Fully Antisymmetric About the Central Axis of the Completely Free Plate1.7.2 Modes Antisymmetric About the Central η Axis and Symmetric about the Central ξ-axis.; 1.8 GENERAL SOLUTION FOR THE COMPLETELY FREE PLATE; 1.9 UTILIZATION OF PRESCRIBED ROTATION INSTEAD OF BENDING MOMENT ALONG DRIVEN EDGES.; 1.10 PRACTICAL APPLICATION OF THE THEORY.; 1.11 COMPUTER PROGRAM FOR ILLUSTRATIVE PROBLEM.; 1.12 GENERAL COMMENTS ON PROGRAM LISTING OF APPENDIX III.; 1.13 SUMMARY; REFERENCES; Chapter 2 THE VIBRATION OF ORTHOTROPIC RECTANGULAR PLATES; 2.1 THE ORTHOTROPIC PLATE

2.2 ELASTIC PROPERTIES OF THE ORTHOTROPIC PLATE2.3 DEVELOPMENT OF ORTHOTROPIC PLATE BOUNDARY CONDITIONS; 2.4 DEVELOPMENT OF THE EQUILIBRIUM EQUATION; 2.5 SOLUTIONS TO THE GOVERNING DIFFERENTIAL EQUATION; 2.6 BRIEF REVIEW OF SOME ORTHOTROPIC PLATE PROBLEMS RESOLVED BY THE SUPERPOSITION METHOD.; 2.7 SUMMARY; REFERENCES; Chapter 3 PLATES WITH ELASTIC EDGE SUPPORT; 3.1 PLATES WITH LINEAR LATERAL ELASTIC EDGE SUPPORT.; 3.2 COMPUTED EIGENVALUES FOR PLATES WITH UNIFORM LATERAL ELASTIC EDGE SUPPORT.; 3.3 PLATES WITH UNIFORM ROTATIONAL ELASTIC SUPPORT ALONG THE EDGES.

3.4 VIBRATION OF PLATES WITH COMBINATIONS OF LATERAL AND ROTATIONAL ELASTIC SUPPORT.3.5 PLATES WITH ARBITRARILY DISTRIBUTED LATERAL AND ROTATIONAL ELASTIC SUPPORT ALONG THE BOUNDARIES.; Computed Results for Plates with Non-Uniform Elastic Edge Support; 3.6 SUMMARY; REFERENCES; Chapter 4 POINT SUPPORTED PLATES AND PLATES WITH ATTACHED MASSES; 4.1 THE COMPLETELY FREE PLATE RESTING ON POINT SUPPORTS.; 4.2 PRESENTATION OF COMPUTED RESULTS.; 4.3 FREE VIBRATION OF PLATES WITH POINT SUPPORT ON THE EDGES.; 4.4 FREE VIBRATION OF PLATES WITH ATTACHED MASSES.

4.5 FREE VIBRATION OF PLATES RESTING ON LINEAR ELASTIC SPRINGS.4.6 REVIEW OF PERTINENT PUBLICATIONS; 4.6.1 Free Vibration of Point Supported Orthotropic Plates.; 4.7 SUMMARY; REFERENCES; Chapter 5 VIBRATION OF PLATES WITH MIXED BOUNDARY CONDITIONS; 5.1 FREE VIBRATION OF A PLATE WITH CLAMPED-SIMPLE SUPPORT ALONG ONE EDGE; 5.2 PLATES WITH DISCONTINUITIES IN VERTICAL EDGE REACTION.; 5.3 COMPUTATION OF EIGENVALUES; 5.4 FREE VIBRATION OF PARTIALLY CLAMPED CANTILEVER PLATES WITH RIGID POINT SUPPORTS.; 5.4.1 Development of the Eigenvalue Matrix

5.4.2 Generation of Eigenvalues and Presentation of Computed Results

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

9789812815798

9812815791