## 1 Introduction
This method is particularly valuable for systems like vehicle structures, where moments and forces are applied at connection nodes. While EBT remains a suitable approximation for subsystem modeling, Timoshenko beam theory is recommended for higher-frequency ranges to account for inertial effects and achieve greater accuracy. Furthermore, EBT is employed to derive reduced-order and explicit receptance matrices for substructures, capturing the full dynamics of both translational and rotational behaviors at DoFs of interest. By explicitly determining the receptance matrix components corresponding to flexible substructures, EBT provides a reliable approximation for both rotational and translational properties at critical points within subsystems. This approach is particularly effective for systems like vehicle structures, where translational forces and moments are applied at nodes, connection points, and coupling regions, accurately accounting for all relevant DoFs within a reduced-order model. The novelty of this study lies in the development of a practical, generalized formulation for determining the receptance matrix at each substructure node while explicitly incorporating both translational and rotational DoFs (as detailed in Section 2.1). Existing generalized receptance coupling methods, such as those by Jetmundsen, do not fully address the integration of translational and rotational dynamics in their formulations. The explicit definition of rotational dynamics within this framework improves the integrity and comprehensive modeling of the receptance at the critical points, with particular emphasis on connection points, ensuring that both translational and rotational effects are effectively captured. This clarity in system behavior modeling is particularly valuable when addressing complex interactions between substructures. To illustrate this, this paper presents the derivation of receptance coupling formulations for two subsystems, A and B, each with two DoFs (one translational and one rotational). This simplified formulation demonstrates the core mathematical principles without compromising generality or completeness. For subsystems exhibiting bending and translational dynamics, where experimental receptance data may be unavailable due to measurement challenges, the EBT-based model offers a robust method for estimating the required receptance functions. This capability enables broader applications in structural dynamics and aligns with findings presented in high-speed machining systems (e.g., [PERSON] and [PERSON], 2005) [15]. The accuracy of the proposed approach is validated through numerical FEA and comparisons of coupled receptance response elements. The alignment of natural frequencies and the identification of resonance and anti-resonance peaks demonstrate consistent and reliable predictions across various excitation conditions. While EBT serves as a reliable approximation for subsystem receptance modeling, Timoshenko beam theory is recommended for higher frequency ranges, where inertial and shear deformation effects become significant for achieving more accurate predictions. Although this paper focuses on linear systems and modular substructuring, the proposed framework has the potential to be extended to nonlinear systems under certain conditions. Nonlinear joints can be approximated through linearization, and local nonlinear dynamics of substructures can be incorporated as additional dynamic stiffness or represented experimentally as black-box receptance measurements at critical points. These approximations and measurements can then be integrated into the GRCFBS methodology, enabling its application to nonlinear subsystems within a limited range of operating conditions.