Nonlinear Resonance Response Of Long-span Suspended Cable Structure Based On Time-delay Vibration Absorption Technique

Suspended cable structure plays an important role in civil,marine and electric engineering.However,because of its light weight,large flexibility and small damping,the suspended cable structure shows obvious nonlinearity,which make the cables easily excitable under the action of external load(wind,rain,etc.),thus causing fatigue damage of the structure and resulting in engineering disasters.Therefore,the vibration control of suspended cable structure becomes an urgent problem to be solved in practical engineering application.Time-delay vibration absorption technique is a new vibration control method proposed in recent years.It has attracted wide attention due to its advantages of less parameter setting and strong adjustability.In this paper,based on the time-delay vibration absorption technique,the nonlinear resonance response of controlled long-span suspended structures is studied,and the dynamic model of the controlled suspended cable system is established.The time-delay ordinary differential equation in the plane of the suspended cable is discretized by using the Galerkin method.The nonlinear resonance response of the controlled cable is analyzed by multi-scale method.The details are as follows:Based on Hamilton principle and boundary conditions,the differential equations of motion of the controlled cable system are derived.Linear velocity time-delay feedback control strategy is chosen.The time-delay ordinary differential equations are discretized by Galerkin method.The primary resonance response and super-harmonic/sub-harmonic resonance response of the cable under linear time-delay feedback control are analyzed by using multi-scale method.The nonlinear response of the controlled suspended cable under the two-frequency excitation is investigated.The nonlinear behavior of the controlled suspended structure and the influence of the system parameters on the response are analyzed.Moreover,the two-mode nonlinear planar response of the controlled cable subjected to external excitation with one-to-three internal resonance is investigated.The averaging equation of the case of primary resonance of the first order is obtained by using multi-scale method to perturb the discrete ordinary differential equations with time delay.After that,the steady state solution and periodic solution of the controlled suspended cable in this case are analyzed.Considering the mechanical model of the controlled suspended cable under axial excitation,the influence of the system parameters on the vibration stability of the controlled suspended is studied.