Dynamic stifiness formulation for plates using flrst order shear deformation theory

The dynamic stifiness method for plates is developed to carry out an exact free vibration analysis by using both classical theory and flrst order shear deformation theory. Hamiltonian mechanics is used to provide a systematic general procedure for the development of the method. Explicit expressions for the elements of the dynamic stifiness matrices have been derived with the help of symbolic computation. Details of the assembly procedure and application of boundary conditions using the dynamic stifiness elements have been explained when investigating the free vibration characteristics of complex structures modelled by plate assemblies. The usually adopted Wittrick-Williams algorithm has been modifled to avoid the requirement of computing the clamped-clamped natural frequencies of individual plates and yet converging upon any number of natural frequencies of the overall structure within any desired accuracy. The results using both classical and flrst order shear deformation theories are rigorously validated by published results for both uniform and stepped plates with various boundary conditions. Representative mode shapes are presented and the numerical accuracy and computational e‐ciency of the method are demonstrated. Signiflcant plate parameters are varied and their subsequent efiects on the accuracy of classical plate theory when compared to the flrst order shear deformation theory are investigated. For both uniform and stepped plates, the circumstances when the classical theory leads to inaccurate results are identifled and discussed. The investigation ofiers the prospects for dynamic stifiness development of anisotropic plates using Hamiltonian mechanics and symbolic algebra.