## 1 Introduction  
Modeling dynamic systems with both continuous or lumped characteristics presents significant challenges, particularly as the number of degrees of freedom (DoFs) increases when both rotational and translational DoFs are involved. These challenges are further compounded by the presence of constraints and boundary conditions, which affect the system's dynamic behavior. To address these complexities, a reduced-order modeling approach is essential, offering a practical alternative for predicting system responses without requiring detailed, resource-intensive modeling as a backup and effective solution. This approach provides a balance between accuracy and computational efficiency, making it feasible to handle even highly complex systems. To develop an effective reduced-order model with hybrid and modular capabilities, receptance coupling frequency-based substructuring (RCFBS) offers a robust framework for predicting system responses. RCFBS combines subsystem receptance matrices, enabling reliable predictions of the system's dynamic behavior across a specific frequency range, particularly in regions where the system behaves linearly. This methodology is highly beneficial for engineers, especially during early product development phases, when constructing a full vehicle finite element model (FEM) or multi-body dynamic model (MBD) may be impractical. In the context of dynamic modeling, certain components, elements, or subsystems may lack sufficient data for numerical FEA, necessitating experimental measurements instead. In such cases, a hybrid and modular approach becomes essential for integrating various sources of subsystem acceptance blocks, enabling reliable predictions of the overall system's receptance and dynamic response. The RCFBS method offers a promising solution to these challenges. This methodology simplifies the modeling of components with either translational or rotational degrees of freedom (DoFs), although additional complexities arise when both types of DoFs are involved. The concept of frequency response function (FRF) coupling was first introduced by [PERSON] and [PERSON] [1], laying the groundwork for later developments in the field. [PERSON] et al. [2] further advanced this by formulating the receptance coupling method, which involved coupling the FRF blocks of subsystems and introduced a generalized coupling formulation. This method has since become the foundation for more generalized formulae involving multiple subsystems with both translational and rotational DoFs. [PERSON] [3] contributed to the field by discussing the use of experimental modal analysis techniques to predict point mobility plots using limited measured mobility parameters. However, accurately measuring rotational degrees of freedom (DoFs), including rotational moments and accelerations, has historically posed significant challenges, often leading to the neglect of rotational DoF mobilities. Numerous techniques have since been developed to capture these rotational mobilities [4]. The versatility of FRF-based substructuring (FBS) methods has been demonstrated in numerous studies, including joint identification in modular tools and mechanical systems [5; 6; 7]. [PERSON] et al. [8], for instance, introduced the receptance coupling substructure analysis (RCSA) methodology, enhancing the prediction of chatter-free cutting conditions in high-speed machining by addressing the limitations in estimating receptance, particularly those involving rotational and moment contributions. Additionally, the Euler-Bernoulli and Timoshenko beam theories have been discussed to provide linear elastic models [9; 10; 11; 12]. [PERSON] and [PERSON] [13] focused on addressing the decoupling problem in structural dynamics using FBS, underscoring the challenges of insufficient data on coupling DoFs and issues with ill-conditioning at specific frequencies. [PERSON] et al. [14] introduced the finite-difference technique into RCSA, which has been extensively applied in tool point dynamics prediction.