Extending Generalized Explicit Terms and Applying Euler–Bernoulli Beam Theory to Enhance Dynamic Response Prediction in Receptance Coupling Method

This paper presents a theoretical framework to enhance the prediction of dynamic responses in complex mechanical systems, such as vehicle structures, by incorporating both translational and rotational degrees of freedom. Traditional receptance coupling methods often neglect rotational effects, leading to significant inaccuracies at higher frequencies. Additionally, approaches that implicitly include full dynamics frequently result in redundancy of generalized coordinates, especially at connection points. To address these limitations, the generalized receptance coupling method using Frequency-Based Substructuring is extended to explicitly account for rotational dynamics resulting in a refined GRCFBS approach. This extension enhances both the understanding and prediction of system responses, which are represented through the receptance matrix or Frequency Response Function. Building on Jetmundsen’s foundational work, the proposed framework introduces a practical, generalized formulation that explicitly incorporates full translational and rotational dynamics at each substructure node. This explicit definition provides deeper insights into system behavior, particularly for complex interactions between substructures under weak and strong coupling scenarios at interface points. The Euler–Bernoulli beam theory is employed to model rotational behavior at critical points, yielding reduced-order and explicit receptance matrices for substructures in the coupling process. The methodology’s accuracy and applicability in capturing resonance and anti-resonance modes are validated through two case studies: the coupling of two flexible subsystems and the integration of flexible and rigid components. Results are benchmarked against numerical finite element analysis, and all limitations and potential improvements are discussed. By directly incorporating rotational dynamics directly, this approach enables more reliable dynamic response predictions under multi-directional loading conditions, particularly for vehicle and machinery system design. The GRCFBS method offers a versatile and reliable tool for dynamic system analysis, with significant potential for vibration analysis over a broad frequency range.