Free vibration of tapered isotropic rectangular plates

摘要

In this paper, free vibration analysis of isotropic rectangular plates with linearly varying thickness in one direction has been investigated using a high-order triangular element. The first order shear deformation theory is used to include the effect of transverse shear deformation. The element has 18 nodes on the sides and six internal nodes. The geometry of element is expressed by three linear shape functions of area coordinates. The formulation is displacement-based. The element has 51 degrees-of-freedom, which can be reduced to 39 degrees-of-freedom by Guyan reduction, mass condensation, or eigenvalue economization scheme for the degrees-of-freedom associated with the internal nodes. Rotary inertia has been included in the consistent mass matrix. Numerical examples are presented to show the accuracy and convergence characteristics of the element. Isotropic plates with different thickness ratios (varies from 0.01 to 0.2), tapered ratios, aspect ratios and boundary conditions are analyzed. The results obtained by present element show a close agreement with the available published results. Some numerical results have been given as new results.