The Analysis Of Wire Ropes Using Harmonic Balance-alternating Time/frequency Domain Method

The vibration isolation technique is a kind of vibration control method.The payload is isolated from the vibration source by stiffness and damping elements.Thus,the impact from the vibration is reduced.The introduction of nonlinearities endows the vibration isolation system with the advantages of broad-band and large-amplitude isolation.The performace depends on the selection and design of the nonlinear elements.The wire ropes exhibit both nonliear stiffness and nonlinear damping characteristics under axial constraints.The application of the wire ropes is expected to achieve better vibration isolation performance.In this research,the axially constrained wire ropes are studied to establish the dynamic model of the vibration isolation system.An analysis method for multi-nonlinear dynamic systems is developed and applied to reveal the influences of the system parameters.The applicability and accuracy of the proposed model and the dynamic analysis method are verified.A comprehensive modeling method is developed to establish the relationship between the restoring force and the deformation of wire ropes.The restoring force consists of an elastic deformation restoring force characterized by high-order stiffness and a hysteretic restoring force represented by Bouc-Wen model.The model is applied to establish the dynamic equation of vibration isolation system under harmonic excitation.The nonlinear stiffness,the hysteretic damping and the pinching effect of phase-transition material are expressed by cubic polynomial function,first-order differential implicit function and pinching function,respectively.A dynamic analysis method aiming at systems with first-order differential implicit functions is developed.The method consists of three parts: steady state response solution,solution curve path tracing and stability analysis.An alternating frequency/time domain technique is used to solve the problem of acquiring the harmonic coefficients of the nonlinear terms.The arc-length continuum method is used to solve the tracing problem at the turning points.The stability of the solution is determined by the Floquet theory.The accuracy and applicability of the proposed analytical method are verified by comparing with the numerica l results.The analytical method is applied to the nonlinear vibration isolation system used wire ropes structure.The influences of the stiffness parameters,the damping parameters and the pinching parameters on the dynamic performances are revealed.As simulation results show,changing the linear stiffness,higher-order stiffness and Bouc-Wen model equivalent stiffness affect the stiffness-varying characteristics of the nonlinear system.Thus the resonant frequency and amplitude are affected but in three different ways.Increasing the linear damping or the hysteretic damping can suppress the resonance.While the hysteretic damping does not affect the system isolation performances at higher frequency region.Increasing the pinching parameters can further broaden the vibration isolation frequency band,which reflects the advantages of the phase-transition materials for nonlinear vibration isolation.The advanced restoring force model and the dynamic system analysis method are verified through the experimental data of the wire ropes structure.It shows that the calculating results are basically accordant with the experimental results.Only when the relative displacement is increasing,the relative error becomes larger.The frequency response curves of the steel wire ropes and the nitinol wire ropes are both in good agreement with the experimental results.The calculation errors of the resonant frequency are less than 0.6 Hz.