IMPROVEMENT OF C-0 VIBRATION PROBLEMS USING HELMHOLTZ-EQUATION TO RECOVER NODAL GRADIENTS

The paper presents a method for the more accurate solution of C-0 acou stic vibration problems in finite element (FE) analysis by postprocess ing. For each frequency, the method uses the computed eigenvector and the Helmholtz equation to calculate gradients of dependent variables a t element centers. Gradients at element centers are then used as sampl ing points in a patch recovery technique to obtain gradients at nodes. The nodal primary field and its gradients are used to interpolate the dependent variables over each element. This interpolation yields the potential and kinetic energies of each element, and hence a Rayleigh q uotient that provides an accurate eigenvalue. One-, two-and three-dime nsional vibration problems are used as numerical examples.