Analytical and experimental parametric vibration stability studies in elastic mechanisms

This thesis presents a study of parametric stability of mechanisms with flexible members. Mathematical models are presented to account for shaft and member flexibilities in slider-crank mechanisms. Flexible coupler and crankshaft are considered and equations governing their motions are obtained using a continuous and a lumped parameter model, respectively. The linearization of equations is facilitated by considering the total motion to be comprised of rigid-body and perturbational elastic motions. Efficient methods are devised to solve for the steady-state dynamic response of rigid-body mechanisms. These are shown to result in significant reductions in computation time. A general method for calculating the steady-state response of periodic systems is presented. The effectiveness of the method is demonstrated by its application in determining the response of a slider-crank mechanism with an elastic coupler. Using the above models, a comprehensive study of parametric stability of slider-crank mechanisms with flexible members is presented. Effects of geometric stiffening, relative member weights, offset, internal material damping and balancing on parametric stability is studied. An experimental validation of the response predicted from these models is also included