Vibration Attenuation Mechanism Of Cable-stayed Beam With Nonlinear Time-delay Feedback Control

As two basic structural units,cable and beam are widely used in civil engineering.With the increase of bridge span and the widespread use of new materials,the length of stay cables increases,the flexibility of structures increases,and the non-linear characteristics become more prominent.Moreover,the cable itself has small damping and light weight,and is prone to produce large vibration under external loads,which results in structural damage.Therefore,it is of practical engineering significance to study the vibration control of c cable-stayed beam.As a new method of vibration reduction,time-delay vibration reduction technology has become a research hotspot in the field of engineering in recent years.In this paper,the nonlinear dynamics of cable-stayed beam with time-delay is studied.The details are as follows: As a method of vibration reduction,time-delay vibration reduction technology has become a research hotspot in the field of engineering in recent years.The dynamics model of cable-stayed beam is established by using Hamilton principle,and the nonlinear dynamics of cable-stayed beam with time delay is studied deeply based on the basic principle of time delay dynamics,theoretical derivation and numerical simulation.Through the research,the vibration attenuation mechanism of nonlinear time-delay feedback control in cable-stayed beam is revealed,which provides a theoretical basis for the optimal design of vibration control system.The main research work of this paper is as follows:Based on the time-delay damping theory,considering the continuity condition,the nonlinear vibration control equation of cable-stayed beam was obtained by using Hamilton principle,the time-delay differential equation was obtained by Galerkin method,and the linear stability of cable-stayed beam vibration control system was analyzed.The large amplitude vibration of cable-beam composite structure is studied by using three time-delay feedback control strategies: displacement,velocity and acceleration.Based on the multi-scale method,the governing equations of the nonlinear dynamics of cable-stayed beam are derived,the primary resonance responses under three control strategies are calculated,and the amplitude-frequency response equations are obtained,these equations was used to study the time delay influence on amplitude and frequency response behavior,and the effects of parameters on nonlinear response of the system are analyzed through a specific example,the damping effect under three kinds of circumstances are compared.The 1/3 subharmonic resonance response and the 3rd super harmonic resonance response under the displacement delay feedback control are calculated and the influence of time delay and control gain on the system response is studied.The one to one internal resonance response between the first and second modes of cable-stayed beam is studied.The steady-state solution of the time-delay ordinary differential equation is studied by perturbation method and the nonlinear responses of cable-stayed beam without control and under control are compared and analyzed.