Vibration of Mindlin plates. Programming the p‐version Ritz method. (Liew, K. M., Wang, C. M., Xiang, Y., Kitipornchai, S.)

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. Formulas in polar co-ordinates: energy functionals Eignevalue 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 co-ordinates: energy functionals Eigenvalue equation computer program software code - VPRITZE input file output file benchmark checks Isosceles triangular plates trapezoidal plates elliptical plates. Formulation in skew co-ordinates: skew co-ordinates transformation energy functionals Eigenvalue equation computer program software code -VPRITZSK sample files benchmark checks. Plates with complicating effects: initial inplane stress elastic foundations stiffeners nonuniform thickness line/curve/loop internal supports point supports mixed boundary conditions re-entrant corners perforated plates sandwich construction. Appendix: Gaussian quadrature subroutines subrutines for mathematical operations on polynomials.