Optimisation of frequencies of a two-span shaft system joined with a hinge

A driveshaft with discontinuities (i.e. joints) is a major component in various industries. A multi-piece driveshaft in automotive applications is joined using constant velocity or universal joints or a combination of both. This article presents an exact solution for the vibration of a two-piece driveshaft with an intermediate single joint. The joint is modelled as a frictionless internal hinge. The Euler-Bernoulli beam theory is used. Lumped masses are placed on each side of the joint to represent the joint mass. Equations of motion are developed using the appropriate boundary conditions and then solved using exact solutions. Natural frequencies and modes shapes are obtained. Numerical results obtained here are compared with those obtained using experimental and analytical tools (e.g. finite elements). Parametric studies are performed and optimisation studies are conducted to maximise bending frequencies. Effects of many parameters are examined.