Subharmonics and ultra-subharmonics of a bio-inspired nonlinear isolation system

Abstract

This paper deals with ultra-subharmonics and subharmonics of a novel nonlinear isolation system with a bio-inspired structure. The analytic formulations of frequency-responses, bifurcation sets and stability of the subharmonic (1/2, 1/3, and 1/4 order) and ultra-subharmonic (2/3 order) responses are exhaustively derived. Due to the generic form of the nonlinear equation, the results about the subharmonic or ultra-subharmonic properties might be actually applicable to a wide variety of physical and engineering problems. The influences of the structural parameters of the bio-inspired structure on nonlinear responses and bifurcation sets are discussed in detail. Furthermore, the obtained theoretical results are validated by numerical simulations and vibration experiments. From the results, the substantial topological distinction of the bifurcation sets between the 1/3 subharmonic resonance and 2/3 ultra-subharmonic resonance are revealed. The discontinuous relationship between the 2/3 ultra-subharmonic response and excitation amplitude is clearly unveiled. A novel phenomenon is observed that 1/4 subharmonic resonance could appear even though there are only quadratic and cubic nonlinear terms in the vibration equation. Other than the coexistence of two different 1/2 (resp. 1/4) subharmonic solutions, the appearance of only one 1/2 (resp. 1/4) subharmonic solution in a certain frequency range is also uncovered. Furthermore, it is shown experimentally that, suppression or enhancement of the subharmonic response can be achieved by tuning the structural parameters of the bio-inspired structure. Such new findings could be of significance for the design and practical applications of the bio-inspired isolation system.