Topology optimization for eigenfrequencies of a flexible multibody system

The intricate dynamic characteristics of a flexible multibody system (FMBS) have a profound influence on the dynamic behavior of the system. In this paper, a topology optimization approach is proposed to confront the challenge of manipulating the eigenfrequencies of an FMBS. Firstly, an accurate dynamic model of an FMBS is established through the perspective of the absolute nodal coordinate formulation (ANCF). Within the mathematical framework, the eigenvalue problem is appropriately extracted, thereby the frequencies and the corresponding mode shapes of an FMBS can be obtained. To firmly verify the dynamic model and the modal solution, an in-depth validation is carried out by comparing the modal analysis of a four-bar mechanism with the results in ABAQUS. Secondly, the modal solution method and the density-based topology optimization method are combined to formulate a generalized topology optimization problem for the eigenfrequencies of an FMBS. The sensitivities for a single eigenfrequency and multiple repeated eigenfrequencies of an FMBS are derived for efficient optimization computation. Finally, the dynamic characteristic topology optimization of a rigid–flexible inflatable structure is conducted to strongly demonstrate the effectiveness and efficiency of the proposed topology optimization approach, which maximizes the first eigenfrequency and the gap between two consecutive eigenfrequencies of the inflatable structure.