Analysis of a bio-inspired multistage nonlinear vibration isolator: an elliptic harmonic balance approach

Recently, studies on isolation of low- and ultra-low-frequency micro-vibrations have been gaining attention to protect sensitive components, improve operating comfort, and enhance control accuracy. In this study, a modified elliptic harmonic balance method (EHBM) was used to investigate the transmissibility characteristics of a bio-inspired multistage nonlinear vibration isolation system. After decoupling the stiffness and damping matrix of the multistage nonlinear isolator, which has both stiffness and damping nonlinearities, the equation of motion can be established in a matrix form. The force equilibrium relationship at each stage of the isolator was analysed when it was at steady-state. Using Jacobi elliptic functions, we analyse the relationship between the excitation frequency and the Jacobi elliptic frequency and modulus during the steady-state response of the system. The modified stiffness and damping force components, as well as the amplitude and phase differences of each force component at each stage, are presented as vectors in an orthogonal relationship. A three-stage isolator, which is a simple case of a multistage nonlinear isolation system, and a twelve-stage nonlinear isolation system, representing twelve cervical vertebrae in birds, are chosen as examples. The EHBM and the first-order harmonic balance method (HB1) were used to obtain the force and displacement transmissibilities of these two systems. The EHBM can maintain the same number and form of balancing equations as the HB1 but delivers better accuracy within the resonance regimes.

Automated summary

This study focused on investigating the transmissibility characteristics of a bio-inspired multistage nonlinear vibration isolation system using a modified elliptic harmonic balance method (EHBM). The stiffness and damping matrix of the isolator were decoupled to establish the equation of motion in a matrix form, and force equilibrium relationships were analysed at steady-state. The results showed that the EHBM can provide better accuracy within the resonance regimes compared to the first-order harmonic balance method (HB1).