Internal resonance analysis of bio-inspired X-shaped structure with nonlinear vibration absorber

In this paper, a vibration isolation system based on bio-inspired structure with a nonlinear absorber is proposed. The nonlinear vibration properties and complex dynamical characteristics are explored elaborately in the presence of internal resonance. Lagrange's principle is employed to derive the governing equations, which can describe the coupled nonlinear vibration system. The method of multiple scales is utilized to obtain the steady-state responses of the coupled system. It is found that the frequency-amplitude relationships reveal the typical nonlinear phe-nomena including jumping and multi-value. The influences of parameters on the dynamical characteristics are discussed in detail. Numerical integrations are directly implemented on the vibration equations to verify the aforementioned analytical results. And furthermore, bifurcations and chaotic motions are detected in the bifurcation diagrams via the Poincare section techniques. The proposed system and the corresponding researches would be of significance for the design and practical applications of the passive vibration control.