Three-dimensional Vibration Analysis of Structural Elements
Using Chebyshev-Ritz Method

This book studies the three-dimensional vibration characteristics of structural elements based on the Ritz method. The trial functions are defined as the product of boundary characteristic function and Chebyshev polynomial series. For simple boundary conditions, the boundary characteristic functions can be given directly. For complex boundary conditions, the boundary characteristic functions can be developed by using the R-function method.
The features of the book are novel in content and clear in organization. The explanation of the mechanism is simple but profound. The results can be directly applied to actual engineering. This book is valuable for the study on the theory of structural dynamics and the method in numerical computation.

Chapter 1 Introduction
Chapter 2 Chebyshev Polynomials
Chapter 3 Ritz Method
Chapter 4 3-D Vibration of Rectangular Plates
Chapter 5 3-D Vibration of Rectangular Plates on Pasternak Foundation
Chapter 6 3-D Vibration of Circular and Annular Plates
Chapter 7 3-D Vibration of Circular Plates on Pasternak Foundation
Chapter 8 3-D Vibration of Solid and Hollow Circular Cylinders
Chapter 9 3-D Vibration of A Torus with Circular Cross-Section
Chapter 10 3-D Vibration of Isosceles Trianglar Plates
Chapter 11 3-D Vibration of Prisms with Isosceles Triangular
Chapter 12 3-D Vibration of Skew Thick Plates
Chapter 13 3-D Vibration of Prisms with Skew Cross-section
Chapter 14 3-D Vibration of Generalized Super Elliptical Plates
Chapter 15 3-D Vibration of Thick Circular Plates with Built-in Edges
Chapter 16 3-D Vibration of Rectangular Plates with Mixed Boundary Conditions