Global modes for the reduction of flexible multibody systems: Methodology and complexity

Modeling a flexible multibody system employing the floating frame of reference formulation (FFRF) requires significant computational resources when the flexible components are represented through finite elements. Reducing the complexity of the governing equations of motion through component-level reduced-order models (ROM) can be an effective strategy. Usually, the assumed field of deformation is created considering local modes, such as normal, static, or attachment modes, obtained from a single component. A different approach has been proposed in Cammarata (J. Sound Vibr. 489, 115668, 2020) for planar systems only and involves a reduction based on global flexible modes of the whole mechanism. Through the use of global modes, i.e., obtained from an eigenvalue analysis performed on the linearized dynamic system around a certain configuration, it is possible to obtain a modal basis for the flexible coordinates of the multibody system. Here, the same method is extended to spatial mechanisms to verify its applicability and reliability. It is demonstrated that global modes can be used to create ROM both at the system and component levels. Studies on the complexity of the method reveal this approach can significantly reduce the calculation times and the computational effort compared to the unreduced model. Unlike the planar case, the numerical experiments reveal that the system-level approach based on global modes can suffer from slow convergence speed and low accuracy in results.