Sensitivity-Based Substructure Error Propagation for Efficient Assembly Model Reduction

Due to ever-increasing complexity of structural dynamic systems in various fields of engineering, model reduction techniques using a substructuring approach, a.k.a. component mode synthesis techniques, still form an active field of research. This paper proposes an efficient, novel method for error approximation for model reduction of coupled substructures in structural dynamics. When coupling multiple reduced substructure models, the influence of individual substructure modes on the dynamic behavior of the total reduced mechanical assembly is generally unknown. Rather than selecting substructure eigenmodes, which are used to constitute the reduction bases, solely based on their eigenfrequencies, this paper proposes a different selection method. This method inspects the influence of individual substructure modes on an assembly receptance using so-called modal receptance error contributions. These modal receptance error contributions are defined as the assembly receptance reduction error induced by truncating individual substructure modes. By determining the sensitivity of the receptance of the assembly with respect to the uncoupled substructure receptances, a substructure reduction error is propagated through the assembly model, resulting in a first-order approximation of the assembly error. To calculate this sensitivity, the receptance of the assembly is expressed in terms of the individual receptances of the uncoupled substructures and Boolean mapping matrices, used to couple substructures. Comparing different modal receptance error contributions, associated with the reduction of individual substructures, provides insight in the selection of substructure modes which results in an efficient reduction of the assembly. As such, a mode-selection criterion is defined by using the obtained information on the sensitivity of the quality of the assembly reduction to truncating individual substructure modes. This criterion helps to determine a more efficient reduction basis. To illustrate the proposed method, a cantilever Euler beam consisting of two substructures is used.