Improving finite element predictions of modes of vibration

A technique is presented whereby the standard finite element approximations used in vibration analysis are modified in order to allow them to accurately predict the frequencies of the higher modes. This is done by using the results of dispersion analysis of the numerical approximations. The method is applied to the longitudinal vibration of a bar, and is shown to give good results for a uniform bar, a bar with continuously varying properties, and a bar with a step change in properties. Dispersion correction gives improved accuracy for the flexural vibration of a beam. The results of the method are also applied to the mode superposition method of dynamic analysis, and again a marked improvement in performance is obtained.