Nonlinear dynamic characteristics of crank train inerters for vibration isolation

The crank train inerter (CTI) is a recently developed vibration inerter consisting of a crank, a linking rod, a flywheel, several gears and pinions. The inertance of CTI is nonlinear when CTI undergoes large displacements. This study explores the nonlinear effect of inertance of a CTI for vibration isolation. The accurate expression of the inertial force in CTI is first derived, and its accuracy is verified by experiment. The equation of motion for the coupled structure-CTI system is formulated, in which a simplified expression of inertial force is adopted. The analytical solutions in forms of the frequency response, peak response and stability boundary are obtained via the harmonic balance method. The transmissibility of the CTI system is derived, and the vibration isolation performance of the CTI is evaluated. Finally, the control effect of CTI on a multistory isolated building for harmonic and seismic excitations is studied. The results show that the nonlinearity of CTI leads to stiffness softening and an unstable response. For the most unfavorable response, the CTI has better vibration isolation control performance than the linear inerter for harmonic and seismic excitations under the same inertance/mass ratio.