Vibration response and isolation of X-shaped two-stage vibration isolators: Analysis of multiple parameters

To exploit its advantages in passive vibration isolation, an X-shaped structure is integrated into a two-stage vibration isolation system so as to realize the broadband vibration isolation capability. The Lagrange equation is employed to establish the nonlinear equation of motion of the proposed X-shaped two-stage vibration isolator, which takes into account both rotational and vertical displacements. The incremental harmonic balance method is used to examine the effects of the key parameters of the system on the frequency response characteristics and vibration isolation frequency bands. The correctness and feasibility of the present analytical approach are validated by comparing with the numerical simulation and the experimental results. The investigation results indicate that the vibration isolation frequency of the designed system can be as low as 2-5 Hz, and the performance of low-frequency vibration isolation can be improved considerably by softening nonlinearity. Additionally, systematic revelations behind the occurrence of softening-hardening, softening, and hardening nonlinear behaviors are made. To assess the effectiveness of the system in vibration isolation, random vibration tests are also conducted. In conclusion, the designed X-shaped two-stage mechanism offers a novel point of view on low-frequency vibration isolation.