# Simulation Analysis of a Three-Degree-of-Freedom Low-Frequency Resonant Mixer
###### Abstract  
This study aims to model and analyze the performance of a three-degree-of-freedom low-frequency resonant mixer to verify the feasibility of its design approach. Based on the completion of the device design in reference to related theories, the working performance and vibration isolation characteristics of the device at different resonance frequencies were determined through modeling and simulation. The results indicate that at the third-order natural frequency, the phase difference between the payload assembly and the vibration-isolating assembly is 180\({}^{\circ}\), which counteracts a portion of the force applied to the rack, thereby demonstrating effective vibration isolation. Moreover, it is found that the phase difference between the excitation force and the excitation assembly response has a great influence on the vibration isolation effect of the equipment. The acceleration and amplitude were amplified, which facilitated efficient mixing. It has been verified that at the third-order natural frequency, the device can achieve amplification of acceleration and amplitude as well as vibration isolation. This ensures efficient mixing while reducing the impact on the external environment. a 2025 15 4861  
Despite numerous vibration isolation measures having been proposed to address the issue of vibration isolation, it remains a challenging problem for vibratory equipment [8]. In order to balance efficient mixing with effective vibration isolation, three-degree-of-freedom resonant mixers are increasingly being implemented in various applications [9; 10]. The resonant mixer operates near the natural frequency, enabling it to achieve high-intensity vibrations that are difficult to attain with non-resonant vibration systems. Under the same conditions, vibration devices employing the resonance principle typically consume only half or even less power than conventional vibration devices, with the sine excitation force being less than one-fifth, and the load transmitted to the external environment is also reduced accordingly [11]. In recent years, significant progress has been made in the research of low-frequency resonance mixing equipment [12]. For instance, [PERSON] et al. [13] have theoretically derived the characteristics of a three-degree-of-freedom resonant hybrid device at the third-order natural frequency. [PERSON] et al. [14] adopted a linear regression to obtain a simple relation between the natural frequency of each component and its weight, which is of reference significance for the research on the natural frequency of the mixer. [PERSON] et al. [15] conducted numerical calculations to study the influence of system dynamics parameters on the performance indices of vibration equipment, providing reference for the determination of related parameters during the design process. However, current research primarily focuses on theoretical aspects, lacking studies based on the modeling and simulation of equipment performance. The objective of this study is to investigate the operational characteristics and vibration isolation mechanism of a three-degree-of-freedom low-frequency resonance mixer through modal analysis and harmonic response analysis. This research aims to provide valuable references for subsequent design work. Key contributions of this paper include the following:  
1. This paper explores the dynamic performance characteristics of a three-degree-of-freedom low-frequency resonance mixer, revealing that when operated at the third-order natural frequency, the significant acceleration amplitude and vibration amplitude of the payload assembly contribute to achieving enhanced mixing performance. Concurrently, the smaller acceleration amplitude and vibration amplitude of the excitation assembly ensure stable operation of the drive component attached to it. This provides a reference for future designs of three-degree-of-freedom low-frequency resonance mixers concerning mixing effectiveness and stability. 2.