Comparison of computational effectiveness of the finite element formulations in free vibration analyses

Abstract

This paper presents a performance comparison of the frequency dependent mixed finite element formulation with the h-and p-formulations of the conventional finite element method for free vibration analysis. Performance is evaluated through a detailed study of accuracy and computational efficiency in obtaining the natural frequencies and modes of skeletal systems. Additional studies compare the computational effectiveness of the mixed finite element formulation with the dynamic element method which involves use of a quadratic eigenvalue problem. Results show that for lower accuracy requirements, the h-formulation is more efficient than the p-formulation due to the increased bandwidth associated with the internal nodes of the p-formulation. This trend is reversed for higher accuracy requirements. When very high accuracy is needed, especially for higher-order modes, the mixed formulation is more computationally efficient than both the h- and p-formulations.