## 1 Introduction
[PERSON] [11] developed methods for experimentally determining rotational mobilities, while [PERSON] [12] introduced Receptance Coupling Substructure Analysis (RCSA) to synthesize FRFs at various locations for predicting assembly dynamics. Building on this, [PERSON] and colleagues [13; 14; 15; 16; 17; 18; 19] extended RCSA to predict tool-point dynamics in machining, integrating analytic, experimental, and empirical connection parameters. [PERSON] et al. [20] proposed Generalized RCSA (GRCSA) for parameter-varying mechanical systems, and [PERSON] et al. [21] integrated TPA with RCSA for machining applications using impact tests. [PERSON] et al. [22] further enhanced tool-holder models by incorporating Timoshenko beam equations for predicting tool-point frequency responses. These advancements collectively provide foundational tools for advancing vibration analysis and dynamic system design. The authors have recently introduced innovative and practical methodologies in dynamic system modeling and vibration analysis. The first paper introduces foundational approaches for modular modeling, featuring partitioning schemes such as the Minimal Segmentation Approach (MSA) and Systematic Element Partitioning (SEP), validated through analytical solutions. It also presents a computationally efficient method for identifying natural frequencies via subsystems' acceptance coupling, even without a physical or FEM model of the entire system [23]. The second paper develops a reduced-order modeling framework for both lumped and distributed parameter systems using Acceptance Coupling methods using Frequency-Based Substructuring (RCFBS), delivering enhanced accuracy and efficiency for system identification. The RCFBS method demonstrates superior accuracy for high-frequency dynamics in systems with flexible or distributed parameters, showing closer alignment with FEA and direct solution techniques compared to traditional modal analysis, effectively addressing mode truncation issues [24]. The third paper introduced generalized receptance coupling methods using Frequency-Based Substructuring (GRCFBS), which indirectly incorporated rotational DoFs, obtaining full dynamics. The application of this method is demonstrated in the development of a half-vehicle model, enabling modular analysis of dynamic interactions between subsystems like the chassis and suspension [25]. Recent advancements in dynamic substructuring have explored the integration of data-driven techniques, such as machine learning (ML), to enhance predictive capabilities and improve computational efficiency. For instance, [PERSON] et al. (2024) [26] proposed a hybrid approach that combines traditional finite element (FE) models with ML-based meta-models in the frequency domain. This approach allows for the coupling of physics-based models with data-driven methods, offering improved predictions and computational efficiency. Despite these developments, most generalized receptance coupling methods using FBS either overlook rotational dynamics, leading to inaccuracies, or implicitly include full dynamics, resulting in redundancy in generalized coordinates during the coupling process, particularly at connection points. To address these challenges, this study builds on [PERSON]'s foundational work, extending GRCFBS to explicitly incorporate rotational DoFs, thereby enhancing the accuracy of system dynamics and synthesizing weak and strong coupling scenarios at interfaces. This explicit approach provides a comprehensive description of the relationship between rotational and translational dynamics, improving system behavior predictions for complex interactions at interfaces and avoiding redundancy issues encountered in methods like LM-FBS. The methodology is demonstrated through two case studies: coupling two flexible components of a cantilever beam and integrating flexible and rigid components. Additionally, Euler-Bernoulli beam theory (EBT) is employed to derive reduced-order, explicit receptance matrices for substructures, capturing translational and rotational dynamics effectively.