## 5 Conclusions  
This paper presented a reduced-order modeling approach using the receptance coupling method integrated with frequency-based substructuring (RCFBS), demonstrating its effectiveness for dynamic systems with both continuous and lumped-mass properties, particularly those involving both translational and rotational degrees of freedom (DoFs). Two case studies validated RCFBS against the numerical finite element analysis (FEA), the modal method, and the direct (exact) solution. While both RCFBS and the modal method are based on linear theory, RCFBS offers superior reliability for systems with distributed parameters, free from the mode truncation limitations of the modal method. However, for systems with lumped parameters, both methods yielded comparable results. In thefirst case study, focusing on a flexible structure, errors were observed across the methods: minimal discrepancies in dominant natural frequencies, noticeable deviations between dominant and non-dominant frequencies (particularly in the modal method), and significant deviations at higher natural frequencies in the modal method. The modal method's mode truncation led to the inadequate representation of higher-frequency dynamics, unlike FEA and FBS, which account for these dynamics through discretization. Up to 400 Hz, all methods exhibited consistent trends, although the modal method showed noticeable shifts in peak resonance and anti-resonance frequencies at higher modes, reflecting its limitations. In the second case study involving lumped parameters, RCFBS was compared with the direct method and the modal method, showing strong correlation across all modes within the selected frequency range covering all vibrational modes. The results of this study align with previous findings by [PERSON] (2005) [14; 30], demonstrating that the RC-FBS method can handle complex dynamic interactions involving both rotational and translational DoFs effectively. Like [PERSON]'s work (2013) [8], the RC-FBS approach effectively manages systems with coupled translational and rotational dynamics, especially in high-frequency regimes. Both methods demonstrate an improvement over traditional modal analysis, particularly in higher-frequency ranges, where modal methods often oversimplify these complex dynamics. [PERSON] et al. (2021) [29] utilized receptance coupling substructure analysis (RCSA) to estimate the rotational frequency response functions (FRFs) by leveraging translational FRFs. Their research highlights the importance of accurate rotational FRF estimation for dynamic characteristics in machining systems, which aligns with our goal of enhancing model precision in complex systems. The novelty of the RC-FBS approach lies in its enhanced accuracy in high-frequency ranges for substructures with flexible or distributed parameters. This method demonstrates a better correlation with finite element analysis (FEA) and direct solutions compared to traditional modal analysis, primarily because it avoids the mode truncation inherent in the modal method. Furthermore, during the decomposition process, when subsystems with greater flexibility are involved, the RC-FBS approach yields more accurate results, particularly in higher-frequency ranges. These characteristics and flexibilities position the RC-FBS method as a significant advancement in modeling dynamic systems where both rotational and translational dynamics are present. Overall, RCFBS emerges as a robust and reliable method for reduced-order modeling, particularly for complex structures and higher-frequency ranges where traditional modal methods may fall short. Its ability to accurately capture dynamic responses in both flexible and lumped-parameter systems makes it an invaluable tool for engineers in various applications, like cars and robots. As future directions, the RC-FBS method can be expanded in several potential areas of research.