Dynamics and isolation performance of a vibration isolator with a yoke-type nonlinear inerter

Previous studies have shown that nonlinear inerters can achieve superior vibration suppression compared to linear inerters, such as broadening the effective frequency band of the vibration isolator. However, nonlinear inerters are typically implemented by incorporating linear inerters into nonlinear configurations, resulting in indirect configurations and extra connections. This study introduces a direct and simple way to realize a yoke-type nonlinear inerter by employing the Scotch yoke mechanism, which is named the Scotch yoke inerter (SYI). The primary contributions of this paper are introducing a concept about the physical realization of a nonlinear inerter capable of providing both apparent mass and nonlinear inertial effects and investigating the dynamic responses and isolation performances of a vibration isolator enhanced by the proposed nonlinear inerter. The working mechanism for how the proposed SYI generates the nonlinear inertia is introduced and a simple configuration that facilities the application of this nonlinear inerter is proposed. The mechanical model of the SYI is built to describe its inertial behavior using the Euler-Lagrange method. Then, the SYI is incorporated into a vibration isolator to improve its performances. The averaging method is adopted to obtain the analytical responses and dynamic characteristics of the isolator with SYI subjected to force excitation. The stability of this nonlinear isolator is analyzed, and numerical integration using the fourth-order Runge-Kutta method is employed to verify the analytical results. The isolation performance evaluation of the isolator with SYI is conducted through three indices including the peak dynamic displacement, peak force transmissibility and effective isolation frequency band. The mechanical behavior indicates that the SYI can successfully generate the apparent mass effect of an inerter and nonlinear inertial behavior. The analytical responses agree well with the numerical results for different parameters of the isolator with SYI, which verifies the analytical solutions. The use of SYI in the vibration isolator can bend the backbone curve to the low frequencies, which indicates the softening characteristic of the frequency response. The isolator with SYI demonstrates beneficial performances in terms of force transmissibility and effective isolation frequency band. It is concluded that the proposed SYI can be seen as an alternative nonlinear inerter and is beneficial for improving the performance of the vibration isolator.