Vibration Analysis Of Plate Assemblies Research Articles

Free vibration analysis of plate assemblies using the dynamic stiffness method based on the higher order shear deformation theory

This paper deals with the free vibration analysis of isotropic plate assemblies using the dynamic stiffness method (DSM) based on the Reddy’s higher-order shear deformation theory (HSDT). Using the proposed method, the isotropic rectangular plate assemblies of non-uniform thickness and material properties can be analyzed. The proposed model does not have any restrictions regarding the boundary conditions or the frequency limitations. It enables free vibration analysis of both thin and thick plates, making it advantageous in comparison with the conventional finite element method (FEM) regarding the computational cost and the accuracy of the results.Three coupled Euler-Lagrange equations of motion based on the HSDT have been transformed into two uncoupled equations of motion introducing a boundary layer function. The dynamic stiffness matrix for a completely free rectangular plate element has been derived using the superposition and the projection method.The proposed numerical model has been applied in the free vibration analysis of rectangular plate assemblies. Along with the convergence study, the results for natural frequencies have been validated against the existing data from the literature, the previous results from the authors as well as the results obtained by using the finite element software Abaqus. Excellent agreement has been obtained. Finally, a variety of new results is provided as a benchmark for future investigations.

Dynamic stiffness elements and their applications for plates using first order shear deformation theory

Dynamic stiffness elements for plates are developed using first order shear deformation theory to carry out exact free vibration analysis of plate assemblies. The analysis has been facilitated by the application of Hamiltonian mechanics and symbolic computation. The Wittrick–Williams algorithm has been used as the solution technique. Results have been extensively validated using published literature for both uniform and non-uniform plates. Some finite element results are also provided. The accuracy and computational efficiency of the method are demonstrated. In the final part of the investigation, significant plate parameters are varied and their subsequent effects on the free vibration characteristics are studied.

An elastic wave technique for the free vibration analysis of plate assemblies

A method is presented for the free vibration analysis of a class of plate assembly which includes an orthogonally stiffened flat plate as a special case. The method is based on the analysis of free elastic wave propagation through the structure, and consists of applying the relevant wave transmission and reflection coefficients at the structural discontinuities. Regardless of the structural complexity, the problem of calculating the natural frequencies is reduced to that of solving two simultaneous non-linear algebraic equations. In the case of a periodic plate assembly the method yields closed form solutions for the propagation constants. It is shown that the method is basically a reformulation of Bolotin's asymptotic method, and the relative simplicity of the approach is illustrated by application to a number of example structures.