Sensitivity Analysis of Rigid-Flexible Multibody Systems

An important step in the application of automated design techniques to rigid-flexible multibody systems is the calculation of the sensitivities with respect to design variables. This paper presents a general formulation for the calculation of the first order analytical design sensitivities based on the direct differentiation method. The analytical sensitivities are compared with the numerical results obtained by the finite differences method and the accuracy and validity of both methods is discussed. Cartesian co-ordinates are used for the dynamic analysis of rigid-flexible multibody systems. To reduce the number of co-ordinates associated with the flexible bodies, the component mode synthesis method is used. The equations of the sensitivities are obtained symbolically and integrated in time simultaneously with the dynamic equations. Examples of 2D sensitivity analysis of the transient response of a slider-crank and of a vehicle with a flexible chassis are presented, and the accuracy and characteristics of the sensitivities are analyzed and discussed.