Free vibration analysis of square plate by finite element method
by
Salil Haldar
Department of Applied Mechanics, B. E. College (Deemede University), P .O- B.Garden, Howrah - 711103gar

A high precision triangular plate bending element has been used to analyse free vibration of isotropic plate. The element has twelve nodes on the edges and four nodes inside the element. The displacements and bending rotations have been taken as independent field variables and they have approximated with polynomials of different orders. This has helped to include the effect of shear deformation as well as made the element free from locking in shear. The element has thirty-five degrees of freedom initially, which is reduced to thirty by eliminating the degrees of freedom of the internal nodes. This has been done by static condensation. To utilise the condensation process, an efficient mass lumping scheme has been recommended to form the mass matrix having zero mass for the internal nodes. Recommendation has also been made for the inclusion of the rotary inertia in a lumped mass matrix. Numerical examples of square plates having concentrated mass and internal cut-out at the plate centre have been studied with different thickness ratios and boundary conditions by this element. The results obtained have been compared with the published results (where available) to show the accuracy and range of applicability of the element.

Date received: August 24, 2004