Improvement of C⁰ vibration problems using Helmholtz equation to recover nodal gradients

Abstract

The paper presents a method for the more accurate solution of C0 acoustic vibration problems in finite element (FE) analysis by postprocessing. For each frequency, the method uses the computed eigenvector and the Helmholtz equation to calculate gradients of dependent variables at element centers. Gradients at element centers are then used as sampling 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 quotient that provides an accurate eigenvalue. One‐, two‐ and three‐dimensional vibration problems are used as numerical examples.