Vibration properties of a knee bio-inspired nonlinear isolation structure

Inspired that the knee joint of birds can buffer the impact and vibration from the foot, a novel vibration isolator constructed by the Knee-Like structure (KLS) is proposed in this paper. Considering that the bones and muscles are very different in material strength, the leg bones are described by rigid rods and the muscles around the knee joint are described by the elastic components. Simulating the construction of the whole leg, in the bionic isolation structure, there are three adjustable structural parameters, which correspond to the angles for ankle and knee, and the length of the thigh. According to the dynamic model, the effects of structural parameters on linear and nonlinear coefficients and the widths for effective isolation bands are illustrated. By the transmissibility curves for different structural parameters by the Harmonic Balance Method (HBM), it discovers that the KLS bionic isolator has optimum design for the knee angle, different from the existing nonlinear isolation structure as the structural parameters monotonously affect the width of isolation band. Then, the analytical solution including transient and steady states are solved by the Method of Multiple Scales (MMS). For different frequency band excitation, the order determinations of excitation and nonlinearity are different. The comparison between the analytical solution and numerical simulation shows that the MMS is applicable for the asymmetric nonlinear nonautonomous dynamic system, and describes the buffering process and steady states for the vibration. The analysis of the proposed KLS bionic isolator not only illustrates the significant vibration isolation effectiveness for ultralow frequency, but also gives the mechanical explanations for the biological phenomenon that the leg knee presents a specific angle for vibration buffering and isolation.