Design and Optimization for Three-Degree-of-Freedom Vibration Systems with Viscous Damping

Vibration isolation systems can be classified into single-degree-of-freedom systems, two-degree-of-freedom systems, and multi-degree-of-freedom systems by degree of freedom. Many scholars have conducted extensive researches on single-degree-of-freedom and two-degree-of-freedom systems, but few on three-degree-of-freedom systems. In this paper, a mechanical model was established for a three-degree-of-freedom vibration system with viscous damping, through which a force transmissibility equation was derived using an impedance method, then asymptotic expressions of force transmissibility were given for both low-frequency and high-frequency regions, and finally an optimization design method for three-degree-of-freedom systems was derived under the constraints of equipment displacement and a sum of intermediate masses. In order to minimize the force transmissibility in the high-frequency region, the isolators and intermediate masses should be designed following the equal-rigidity and equal-mass principle under the premise of not exceeding the allowable equipment displacement and the total mass.