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 Platesprovides 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
Vibration of Strings
Assumptions and Governing Equations for Strings
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
Vibration of Membranes
Assumptions and Governing Equations
Constant Uniform Normal Stress and Constant Density
Two-Piece Constant-Property Membranes
Vibration of Beams
Assumptions and Governing Equations
Single-Span Constant-Property Beam
Two-Segment Uniform Beam
Vibration of Isotropic Plates
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
Vibration of Plates with Complicating Effects
Plates with In-Plane Forces
Plates with Internal Spring Support
Plates with Internal Rotational Hinge
Plates with Partial Elastic Foundation
Vibration of Nonisotropic Plates
Functionally Graded Plates
"The book is arranged in a way from simple to complex, enabling an easy walk into the whole subject. The exact solutions are illustrated not only by the analytical expressions, but also by numerical results in table or figure form. Thus, they can be directly used as benchmarks for comparison with numerical or approximate analytical solutions, or they can be simply taken over in evaluating the dynamic behavior of a practical structure. … The materials presented are very solid. This book presents a collection of exact solutions for vibration of strings, beams (bars), and plates, which are very common both in engineering and natural science. Complicating effects can be involved, however, including non-uniform geometry, non-homogeneous material property, internal support, elastic foundation, etc. The mathematical techniques used to obtain the solutions are very attractive and mathematically strict, and will provide a base for the study of more involved problems. The book should be very useful for researchers, engineers, and students in various engineering areas such as aerospace, civil engineering, mechanical engineering, ocean engineering, chemical engineering, etc. It can also be used as a reference for those who are working in physics, biology, geology, material science, and nanotechnology."
––W. Q. Chen, Department of Engineering Mechanics, Zhejiang University, Hangzhou, China
"The book provides an excellent comprehensive treatment of analytical vibration analysis of continuous structural systems. It provides the exact solutions for strings, membranes, beams, and plates along with tabulated numerical frequencies which makes this book essential not only for academics but also for practicing engineers and designers. … The authors have done an admirable job in the organization and the flow of the book. Direct explanations tell the story of structural vibrations, moving from basic string model to more complex non-uniform plates. In each chapter, the authors present the current research development based upon the latest research articles."
––Huseyin Yuce, New York City College of Technology, Brooklyn, USA
"This book is a new reference on a special topic (exact eigensolutions) for certain structural components, which can be quite useful for people in R&D of structural systems, educators of engineering vibrations, and developers of numerical algorithms for structural vibration problems."
––Bingen Yang, Dept. of Aerospace and Mechanical Engineering, University of Southern California, Los Angeles, CA, U.S.A