Dynamics analysis of flexible mechanisms based on mixed numerical integration methods of Hilber-Huges-Taylor and Rossenbrock-Wanner

Numerical solution of dynamical systems with widely varying motion characteristics, such as relatively slow motion coupled with high frequency as it would be in flexible mechanisms, likely to pose problems. In this paper the mathematical model of a flexible mechanism is solved by using a mixed integration method that attempts to deal with the complexity of the coupled differential equations of the rigid-body and elastic motion. The mixed integration method consists of two integration methods (Rossenbrock-Wanner and Hilber-Hughes-Taylor methods) that have been combined in order to minimize the computational complexity required for the approximation of the real system. The a Hilber-Hughes-Taylor methods incorporates numerical damping that selectively affects only the higher modes of vibration. The improvement of the stability and the accuracy of the solution due to the numerical damping has been demonstrated via a numerical example that represents a stiff system. The example system was selected to contain a physically important low frequency and spurious highly frequency oscillations. The solution method filtered the high numerical oscillations from the response results. The Rossenbrock-Wanner integration technique was also presented. In this case it is also shown that fine adjustment of integration parameters could effect the degree of numerical damping. A mixed integration method, combination of the two found to give the best performance and accuracy in the case of stiff problems