An exact dynamic stiffness element using a higher order shear deformation theory for free vibration analysis of composite plate assemblies

An exact dynamic stiffness method based on higher order shear deformation theory is developed for the first time using symbolic computation in order to carry out free vibration analysis of composite plate assemblies. Hamilton’s principle is applied to derive the governing differential equations of motion and natural boundary conditions. Then by imposing the geometric boundary conditions in algebraic form the dynamic stiffness matrix is developed. The Wittrick–Williams algorithm is used as solution technique to compute the natural frequencies and mode shapes for a range of laminated composite plates and stepped panels. The effects of significant parameters such as thickness ratio, orthotropy ratio, step ratio, number of layers, lay-up and stacking sequence and boundary conditions on the natural frequencies and mode shapes are critically examined and discussed. The accuracy of the method is demonstrated by comparing results with those available in the literature.