chapter 1 Background of Vibration -- chapter 2 Methods of Analysis for Vibration Problems -- chapter 3 Vibration Basics for Plates -- chapter 4 Exact, Series-Type, and Approximate Methods for Transverse Vibration of Plates -- chapter 5 Development of Characteristic Orthogonal Polynomials (COPs) in Vibration Problems -- chapter 6 Boundary Characteristic Orthogonal Polynomials (BCOPs) in Vibration of Plates -- chapter 7 Transverse Vibration of Elliptic and Circular Plates -- chapter 8 Triangular Plates -- chapter 9 Rectangular and Skew Plates -- chapter 10 Circular Annular and Elliptic Annular Plates -- chapter 11 Plates with Nonhomogeneous Material Properties -- chapter 12 Plates with Variable Thickness -- chapter 13 Plates with Orthotropic Material Properties -- chapter 14 Plates with Hybrid Complicating Effects.