The unsymmetric formulation for vibration analysis of frames

Abstract

The unsymmetric formulation is a dynamic model for computing numerically exact free vibration frequencies and modes of structural systems. Based on exact representation of element inertia forces and a frequency independent stiffness matrix, this formulation obtains discretization error-free solutions. Previous studies have shown that in modeling the vibration response of trusses, the unsymmetric formulation is more computationally efficient than the conventional finite element formulation, particularly when accuracy requirements are high. This study extends the development of the unsymmetric formulation to more general vibration problems. The unsymmetric formulation is developed and illustrated here for the vibration analysis of beams and frames with uniform and/or lumped mass distributions. The computational efficiency of the formulation is studied and compared to that of the exact displacement and conventional finite element models. Results from numerical examples suggest that the unsymmetric formulation provides more accurate free vibration modes and frequencies of frames in less computational time than do other dynamic models.