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This edtion by Acoustical Society of America, 1993 Originally issued by NASA, 1973 ISBN-13: 978-1563962936 ISBN-10: 1563962934 This monograph is the second in a series dedicated to the organization and summarization of knowledge existing in the field of continuum vibrations. The first monograph, entitled Vibration of Plates, was published in 1969, also by the National Aeronautics and Space Administration. The objectives of the present work are the same as those of the previous one, namely, to provide (1) A comprehensive presentation of available results for free vibration frequencies and mode shapes which can be used by the design or development engineer. (2) A summary of known results for the researcher, facilitating comparison of future theoretical and experimental results, and delineating by implication those problems which need further study. The scope of the present monograph is also the same as that of the previous one in that (1) Materials are assumed to be linearly elastic. (2) Structes were not included in this study, although some attention has been given to the accuracy of representing a stiffened shell as an orthotropic shell for purposes of vibration analysis. The vibrational characteristics and mechanical properties of shell structures are discussed. The subjects presented are: (1) fundamental equations of thin shell theory, (2) characteristics of thin circular cylindrical shells, (3) complicating effects in circular cylindrical shells, (4) noncircular cylindrical shell properties, (5) characteristics of spherical shells, and (6) solution of three-dimensional equations of motion for cylinders.

Preface to the Reprinted edition Preface to the Original edition Chapters 1 Fundamental Equations of Thin Shell Theory 1.1 Brief Outline of the Theory of Surfaces 1.2 Shell Coordinates and the Fundamental Shell Element 1.3 Love's First Approximation 1.4 Strain-Displacement Equation 1.5 Force and Moment Resultants 1.6 Equations of Motion 1.7 Synthesis of Equations 1.8 Boundary Conditions 1.9 Shallow Shell Theory References for Chapter 1 2 Thin Circular Cylindrical Shells 2.1 Equations of Motion 2.2 Shells of Infinite Length 2.3 Closed Shells--Shear Diaphragms at Both Ends 2.4 Other Simple Edge Conditions 2.5 Elastic Supports 2.6 Added Mass 2.7 Noncircular Boundaries and Cutouts 2.8 Open Circular Cylindrical Shells References for Chapter 2 3 Complicating Effects in Circular Cylindrical Shells 3.1 Anisotropy 3.2 Variable Thickness 3.3 Large (Nonlinear) Displacements 3.4 Initial Stress 3.5 Other Complicating Effects in Circular Cylindrical Shells References for Chapter 3 4 Noncircular Cylindrical Shells 4.1 Equations of Motion 4.2 Elliptical Cylindrical 4.3 Oval Cylindrical 4.4 Open Shells References for Chapter 4 5 Conical Shells 5.1 Equations of Motion 5.2 Complete Cone 5.3 Frustum of a Cone 5.4 Open Conical Shells 5.5 Anisotropy 5.6 Large Displacements 5.7 Initial Stress 5.8 Other Effects References for Chapter 5 6 Spherical and Other Shells (Bibliographies) 6.1 Spherical Shells 6.2 Ellipsoidal (or Spheroidal) Shells 6.3 Paraboloidal Shells 6.4 Toroidal Shells 6.5 Other Shells of Revolution 6.6 Others Appendix: Solution of the Three Dimensional Equations of Motion for Cylinders A.1 Equations of Motion A.2 End Conditions A.3 Displacement Potential Functions A.4 Solution of the Equations of Motion A.5 Expressions for Stresses A.6 Frequency Equation References for Appendix Author Index Subject Index

Leissa, A. W. The Ohio State University Columbus, OH, United States

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