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One of the main challenges for small deformation flexible multibody simulations is the a priori selection of the required modal basis. Often, to guarantee the accuracy of the component mode synthesis, an excessive amount of mode shapes are accounted for in the model basis. Hence, to address this problem, the variable modal basis for small deformation flexible multibody formulations is introduced. It allows truncation of the initial modal basis to minimize the required amount of active mode shapes while maintaining accurate results. Furthermore, the proposed framework is independent of the chosen small deformation flexible multibody formulation. The modal variation is achieved by neglecting mode shapes based on their individual energy content. Hence, the corresponding set of dynamic and constraint equations, as well as the generalized coordinates and Lagrangian parameters, reduce accordingly. Once mode shapes are neglected, their energy content is no longer evaluated. Therefore, reintroducing these mode shapes is based on the change in total flexible energy of a flexible body. To validate the accuracy of this approach, a comparison is made between the results obtained from implementing a variable modal basis and those obtained from a regular constant modal basis. [ABSTRACT FROM AUTHOR]

This work discusses a sensitivity information methodology for input optimization of flexible multibody systems. Mechanisms often need to perform desired motions, and especially in the case of underactuated flexible systems, the required drive motion or torque are nontrivial to determine. In this work we present an optimization approach which exploits the Adjoint Variable Method (AVM) in combination with the Flexible Natural Coordinates Formulation (FNCF) for obtaining the sensitivity information. The Adjoint Variable Method has the advantage of obtaining accurate sensitivity information at a computational cost that is relatively independent of the number of model parameters. FNCF combines the advantageous properties of the Floating Frame of Reference Formulation (FFRF) and the Generalized Component Mode Synthesis (GCMS) methods for which the equations of motion are characterized by a constant mass and stiffness matrix, and quadratic constraint equations. This work shows how the specific structure of the motion equations obtained through FNCF reduces the complexity of the Adjoint Variable Method as the required simulation derivatives for input optimization can be readily obtained and are of limited order. The approach is illustrated for an input optimization case on a flexible slider–crank multibody model, where the objective is to construct an input torque signal such that the crank's angular velocity matches a predefined reference signal. [ABSTRACT FROM AUTHOR]