A chaotic behavior and stability analysis on quasi-zero stiffness vibration isolators with multi-control methodologies

Abstract

A quasi-zero stiffness vibration isolator (QZSVI) is used in applications like precision instruments, aerospace, microelectronics manufacturing, and seismic isolation to protect sensitive equipment from low-frequency vibrations. Their key advantage lies in achieving near-zero stiffness, allowing for highly effective vibration attenuation while maintaining system stability. These passive systems are cost-effective and reliable, offering superior vibration isolation without the need for external power or active control. This work proposes the use of negative displacement, velocity, and cubic velocity feedback control techniques to enhance the QZSVI’s isolation performance. We found that the composite negative velocity and cubic velocity control (NVFC + NCVFC) is more effective with low cost compared to other types of controller (its effectiveness is about 94.8%). The approximate solutions (AS) of the controlling system of equations of motion (EOM) are acquired using a multiple-scales procedure (MSP) up to the second order, and it is subsequently validated numerically through the Runge–Kutta method (RKM) from the fourth-order. Modulation equations (ME) are obtained by exploring resonance instances and solvability conditions. Time history graphs and frequency response curves, generated via MATLAB and Wolfram Mathematica 13.2, are presented to analyze stability and steady-state solutions. It is investigated how altering the parameters affects the system amplitude. Poincaré maps, Lyapunov exponent spectra (LEs), and bifurcation diagrams are presented to illustrate the system’s diverse behavior patterns. Furthermore, the transmissibility of force, displacement, and acceleration is computed and displayed. A QZSVI minimizes low-frequency vibrations, making it ideal for precision applications in metrology, automotive, aerospace, civil engineering, medical equipment, and renewable energy. It achieves superior damping, ensuring high stability and precision.