Wave Theory of Free Torsional Vibration of Composite Systems of Shafts

Abstract

This paper gives a general theory of free torsional vibration of systems in which allowance is made for both elasticity and inertia of each component shaft. The governing equation of motion is the elementary wave equation in one dimension and the problem is solved by wave methods that use the concepts of reflection and transmission. Both the frequency equation and the equations of modal shape are derived in terms of defined reflection and transmission coefficients. The theory is illustrated by two examples that include stepped shafts, rigid discs, a light elastic coupling and shafts connected by rigid gears.