Nonlinear Coupled Vibration Analysis Of Inclined Cables

Cables are very efficient structural members and hence have been widely used in many long-span structures, including cable-supported roofs, cable-supported bridges, cable-stayed reticulated grid structures and guyed towers. Since cables are very flexible, low damping and light weight, stuctures with cables usually possess complex static and dynamic behaviors. The accurate analysis of both static and dynamic behavior is very important for design of cables in cable-structures. Numerous papers have studied the dynamic behaviors of cable nonlinear vibrations because of their geometric nonlinearity. Based on them, this thesis is devoted to the theoretical and numerical investigations of the nonlinear dynamic coupled effect between the different degrees of freedom in inclined cables and the effect between cables and structures.With the reference of the nonlinear dynamic model firstly present by P. Warnitchai, cable complex motions are separated into modal motions and parametric motions in this thesis. The modal motions are expressed as a combination of the linear undamped modes of a cable with fixed ends which presents the previous coupled effect above, and the parametric motions are the displacements of the cable which moves as an elastic tendon due to the support movements which presents the other. By Newton's kinematic principle, a combination of the two distinct motions may describe the complete dynamic behaviors of cables. As for the dynamic analysis approach of cable systems in this thesis, the finite element method is used to obtain the low-order natural frequencies of the overall structure and then compared them with the natural frequency of each cable. Thus the cable which can generate internal resonance vibration or parametric resonance vibration will be studied individually.Therefore, vector representations for describing motion states of the three-dimensional infinitesimal cable elements are established firstly in Chapter 2 for obtaining the rounded analysis of nonlinear dynamic behaviors. And then the deformation compatibility equations that represent the relation between motion state and dynamic prestress in cables are deduced. Finally, a three-dimensional nonlinear dynamic equilibrium equation is proposed according to the principle of D'Alembert.The thesis assumes that dynamic motion of the chord-wise cable is in its linear mode. Then the two-DOF dynamic equilibrium equation which reveals coupled effect between the modal motions in-plane and the modal motions out-of-plane based on the definition in Chapter 2, and the three-DOF non-linear dynamic equilibrium equation which reveals coupled effect among axial, in-plane and out-of-plane parametric motions are proposed in Chapter 3 and Chapter 4 respectively according to Galerkin method. The analysis of dynamic phenomena in cable, such as internal resonance, forced vibration, parametric vibration and so on, is carried out by using the multiple scales method which is devoted to the dynamic characteristic investigations of frequency matching relations, periodic steady-state motions, frequcncy response equations, etc.The amplitude of variation for dynamic prestress is generally in a wide domain when cables generateresonant phenomena and it is a critical aspect in design of cable-structures. For numerical method is an efficient approach which could obtain more significative information in cable-structure analysis. Therefore, taking the coupled effect between dynamic prestress and motion state of actual inclined cables illustrated in this thesis into consideration, numerical integration of the nonlinear coupled dynamic equilibrium equation is performed by self-programming according to the deformation compatibility equation established in Chapter 2. The numerical analysis focuses on the mid-span displacement response and the dynamic prestress time response of cables. The numerical results may be used for fatigue design of cable-structures and calculating ultimate load-carrying capacity of cables. Furthermore, the first-order modal frequency, the amplitude of vibration response and the damping influence on cable vibration are also investigated respectively for more useful informations about cable's nonlinear vibration.At the end of this thesis, some proposals are derived from the nonlinear coupled vibration system. The importance of dynamic prestress varying effect in resonance vibration is emphasized and some future studies in cable dynamic analysis are proposed.