Dynamic effect of constant inertial acceleration on vibration isolation system with high-order stiffness and Bouc–Wen hysteresis

Nonlinear vibration isolation provides with an effective way for vibration reduction with broad band and high efficiency. This investigation focuses on the dynamic effects of a constant inertial acceleration on a nonlinear vibration isolation system with high-order stiffness and Bouc–Wen hysteresis. A wire rope-based isolator subject to the inertial acceleration is analyzed to illustrate the uncertainty of the static equilibrium state and the diverse dynamic effects of the acceleration. The frequency responses are obtained through a semianalytical method based on the harmonic balance method. A recursive method is proposed to deal with the polynomial function derived from the nonlinear stiffness. An alternating frequency/time domain technique is adopted to treat the implicit function of the Bouc–Wen hysteresis. The calculation results are verified by a numerical simulation with the Runge–Kutta method. The analysis and the simulations reveal that the inertial acceleration leads to different static equilibrium states according to the paths to the equilibriums. The inertial acceleration, respectively, affects the static equilibrium displacement and the residual hysteretic force, and they change the dynamic responses differently. The acceleration effect on the static equilibrium displacement leads to additional coupling stiffness making the system harder/softener with positive/negative high-order stiffness. Furthermore, the acceleration has a significant effect on the dynamic equilibrium location, and the equilibrium reaches the minimum around the resonance and increases gradually at higher frequencies. The acceleration effect on the residual hysteretic force changes the amplitude–frequency responses indirectly through additional coupling stiffness. A positive residual hysteretic force leads to a positive overall deviation of the dynamic equilibrium location regardless of the positive or negative high-order stiffness.