Structural Vibration Exact Solutions for Strings, Membranes, Beams, and Plates

Structural Vibration: Exact Solutions for Strings, Membranes, Beams, and Plates offers an introduction to structural vibration and highlights the importance of the natural frequencies in design. It focuses on free vibrations for analysis and design of structures and machine and presents the exact vibration solutions for strings, membranes, beams, and plates. This book emphasizes the exact solutions for free transverse vibration of strings, membranes, beams, and plates. It explains the intrinsic, fundamental, and unexpected features of the solutions in terms of known functions as well as solutions determined from exact characteristic equations. The book provides: A single-volume resource for exact solutions of vibration problems in strings, membranes, beams, and plates A reference for checking vibration frequency values and mode shapes of structural problems Governing equations and boundary conditions for vibration of structural elements Analogies of vibration problems Structural Vibration: Exact Solutions for Strings, Membranes, Beams, and Plates provides practicing engineers, academics, and researchers with a reference for data on a specific structural member as well as a benchmark standard for numerical or approximate analytical methods.

Introduction to Structural Vibration What is Vibration? Brief Historical Review on Vibration of Strings, Membranes, Beams, and Plates Importance of Vibration Analysis in Structural Design Scope of Book References Vibration of Strings Introduction Assumptions and Governing Equations for Strings Boundary Conditions Constant Property String Two-Segment Constant Property String Transformation for Nonuniform Tension and Density Constant Tension and Variable Density Variable Tension and Constant Density Free-Hanging Nonuniform String Other Combinations References Vibration of Membranes Introduction Assumptions and Governing Equations Constant Uniform Normal Stress and Constant Density Two-Piece Constant-Property Membranes Nonhomogeneous Membranes Hanging Membranes Discussion References Vibration of Beams Introduction Assumptions and Governing Equations Single-Span Constant-Property Beam Two-Segment Uniform Beam Nonuniform Beam Discussion References Vibration of Isotropic Plates Introduction Governing Equations and Boundary Conditions for Vibrating Thin Plates Exact Vibration Solutions for Thin Plates Governing Equations and Boundary Conditions for Vibrating Thick Plates Exact Vibration Solutions for Thick Plates Vibration of Thick Rectangular Plates Based on 3-D Elasticity Theory References Vibration of Plates with Complicating Effects Introduction Plates with In-Plane Forces Plates with Internal Spring Support Plates with Internal Rotational Hinge Plates with Partial Elastic Foundation Stepped Plates Variable-Thickness Plates Discussion References Vibration of Nonisotropic Plates Introduction Orthotropic Plates Sandwich Plates Laminated Plates Functionally Graded Plates Concluding Remarks References Index

C.Y. Wang, Michigan State UniversityC.M. Wang, National University of Singapore