Effect of negative stiffness mechanism in a vibration isolator with asymmetric and high-static-low-dynamic stiffness

Abstract

Abstract In this paper, a high-static-low-dynamic stiffness (HSLDS) vibration isolator with a novel parabolic-cam-roller negative stiffness mechanism is proposed to study the effectiveness of negative stiffness on asymmetric spring supporting structures. Based on the physical model, the intrinsic geometrical nonlinearity of the isolator is analyzed and the differential equation of motion is derived by the generalized Lagrange's equation. Here, the multi-term incremental harmonic balance method (MT-IHBM) is employed and extended to capture both primary and subharmonic resonances in nonlinear response. By means of arc-length increment, the adaptability and reliability of this method are enhanced under strong nonlinear vibration. Vibration transmissibility and frequency response relationships of various frequency components are demonstrated in order to better explain the properties of asymmetry vibration. The analysis results indicate that the performance of the isolation system is affected by different parametric excitation. Under some parameters, the introduction of negative stiffness will cause obvious 1/2 subharmonic resonance. The existence of the bias term in response makes the peak and frequency of resonances shift vertically and horizontally, respectively. Due to the asymmetry, the proposed HSLDS isolator does not present quasi-zero stiffness at the static equilibrium position, but it has superior ability to suppress vibration. Meanwhile, comparisons show that adding negative stiffness mechanism can still significantly improve the vibration isolation performance when a supporting structure has the characteristic of asymmetric stiffness.