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. Thispaper presents a general formulation for thecalculation of the first order analytical designsensitivities based on the direct differentiationmethod. The analytical sensitivities are comparedwith the numerical results obtained by the finitedifferences method and the accuracy and validity ofboth methods is discussed. Cartesian co-ordinates areused for the dynamic analysis of rigid-flexiblemultibody systems. To reduce the number ofco-ordinates associated with the flexible bodies, thecomponent mode synthesis method is used. Theequations of the sensitivities are obtainedsymbolically and integrated in time simultaneouslywith the dynamic equations. Examples of 2Dsensitivity analysis of the transient response of aslider-crank and of a vehicle with a flexible chassisare presented, and the accuracy and characteristics ofthe sensitivities are analyzed and discussed.