Research On Nonlinear Vibration Properties Of A Cable-Stayed Beam

The cable-stayed beam has been widely used in civil engineering structures and mechanical systems in recent years. Dow to the cable's large flexibility, light weight and small damping, external excitation may cause its nonlinear vibration. In particular frequency ratios of the cable to the beam, resonance occurs which leads to the failure of the local structure and impacts the overall stability. Therefore, detailed analysis of the cable-stayed beam's vibration causes scholars' attention, which will provide effective theoretical references for engineering application. In this paper, the vibration mechanism of a cable-stayed beam is studied, by combining analytic solutions and numerical computations. There are five chapters in the paper. The main contents of each chapter are shown as below.Chapter 1 is the introduction, in which the research background and the state-of-the-art of the cable vibration are presented. In addition, some related concepts and basic theories and research methods of nonlinear vibration are introduced.In Chapter 2, firstly, basic mechanical properties and three-dimensional nonlinear vibration equations of the cable are shown. Secondly, based on the previous reseach, nonlinear vibration of a small-sag cable with movable boundary is analyzed. The model is estabilished and the one-dimensional oscillation equation is deduced. Then Runge-Kutta method is used for the numerical calculation, through which the single-degree-of-freedom response of the cable is attained. Meanwhile, how the frequency ratios and the amplitude of the excitation inflent the cable's vibration is studied.In Chapter 3, firstly, based on the vibration characteristics of the cable and taking account of the inflence of axial force of the beam over its vibration and the cable's in-plane transverse vibration, the vibration model and corresponding two-dimensional partical differential equations are estabilished. Then Galerkin method is used to transform partical differential equations into ordinary differential equations. The multi-scale method is used to attain the frequency ratios corresponding to resonance and the relation of the vibration amplitudes of the cable and the beam. It is found that internal resonance occurs in the frequency ratio of 1:2,1:1 and 2:1. Secondly, the stability of zero solution is analyzed. Furthermore, Runge-Kutta method is used for the numerical calculation of a cable-stayed beam, through which the time-displacement responses of the system and how various parameters, such as mass ratio, initial tension, cable's angle of inclination, effect the responses is attained. Finally, considering the in-plane transverse simpleharmonic force applied on the cable, through numerical calculation the amplitude-frequency response curves and time-displacement response of the cable-stayed beam in different frequency ratios are obtained.In Chapter 4, based on Chapter 3, considering the out-of-plane vibration of the cable, three-dimensional differential equations of the cable-stayed beam are estabilished. Firstly , multi-scale method is used for analysis, through which energy conservation equation is deduced and the stability of zero solution is discussed. Secondly, Runge-Kutta method is used for the numerical calculation, through which the features of energy transfer and time-displacement curves are derived.In Chapter 5 , the conlusions and prospects are presented.