Preface. Introduction. Background of vibration. Plate vibration. About this monograph. Mindlin Plate Theory and Ritz Method. Mindlin plate theory. Energy functionals. Governing differential equations. Boundary conditions. Relations between Kirchhoff and Mindlin plates. Reduction of Mindlin theory to Kirchhoff. Frequency relationship for a class of plates. Shear correction factor. Ritz method. Preliminary remarks. Application of Ritz method to Mindlin plates. Formulation in Polar Coordinates. Introduction. Energy functionals. Eigenvalue equation. Circular and annular plates. Sectorial and annular sectorial plates. Computer program. Software code: VPRITZP1. Sample files for VPRITZP1. Software code: VPRITZP2. Sample files for VPRITZP2. Benchmark checks. Annular plates. Sectorial plates. Annular sectorial plates. Formulation in Rectangular Coordinates. Introduction. Energy functionals. Eigenvalue equation. Computer program. Software code: VPRITZRE. Input file. Output file. Benchmark checks. Isosceles triangular plates. Trapezoidal plates. Elliptical plates. Formulation in Skew Coordinates. Introduction. Skew coordinates transformation. Energy functional in skew coordinates. Eigenvalue equation. Computer program. Software code: VPRITZSK. Sample files. Benchmark checks. Plates with Complicating Effects. Introduction. Initial inplane stresses. Elastic foundations. Stiffeners. Nonuniform thickness. Line/curved/loop internal supports. Point supports. Mixed boundary conditions. Reentrant corners. Perforated plates. Sandwich construction. References. Appendix I - Gaussian quadrature subroutines. Appendix II - Subroutines for mathematical operations on polynomials. Subject index.