Improved eigenfrequencies and eigenmodes in free vibration analysis

Abstract

This paper presents an application of local and global updating methods to improve natural frequencies and mode shapes of the finite element solution in free vibration analysis. The local updating is based upon superconvergent patch recovery technique for displacements (SPRD). This approach provides reliable results for a sufficiently fine finite element mesh for the reason that it strongly depends on the original finite element solution. In order to overcome aforementioned shortcoming a preconditioned conjugate gradient method is applied for the global updating using p+1 finite element formulation. To increase the rate of convergence of the iterative procedure, a diagonal of the sum of stiffness and mass matrices is implemented as a preconditioning matrix in the general eigenvalue problem and initial trial eigenvectors are obtained by the SPRD technique. Numerical examples show for the eigenfrequencies an improved accuracy and an improved convergence rate of the error of the improved eigenfrequencies compared to the FE solution.