Continuum element method for analysing free-vibration behaviour of crankshafts

Abstract

The continuum element method for determining natural frequencies and mode shapes of the crankshaft is developed. The crankshaft is modelled into a series of space continuum beam elements. They include the effects of shear deformation and rotary inertia of the cross-section. An analytical expression for the dynamic stiffness matrix for each of the elements is derived. The overall dynamic stiffness matrix of the crankshaft is assembled in turn. The natural frequencies are calculated with the Wittrick—Williams algorithm. The mode shapes of the crankshaft are computed by the recursive Newton method. Two illustrative crankshafts are discussed to evaluate the performance of the method. Solutions calculated by the finite element method and experimental work are also enumerated for comparison. The results show that the current method is appropriate for free vibration analysis of the crankshaft.