This paper reports a systematic investigation on the linear and nonlinear dynamics of a suspended cable, taking bending stiffness into account. Firstly, the linear dynamics features, for example, eigen frequencies and modes for in-plane and out-of-plane motions, are formulated. Secondly, parametrical studies are conducted to explore the effect of bending stiffness on the natural frequencies and mode shapes of the symmetrical/antisymmetrical in-plane and out-of-plane modes. Then, the three-to-one internal resonance between the first- and third-order in-plane symmetrical modes is analyzed by applying directly the method of multiple scales dealing with the nonlinear partial differential equation and boundary conditions. Finally, the frequency-response curves and force-response curves are obtained through solving the modulation equations using the Newton–Raphson method and the pseudo-arclength scheme. The results show that the bending stiffness plays a considerable role in changing the natural frequencies and mode shapes, shifting the conditions for the occurring of nonlinear interaction, saddle-node bifurcation and Hopf bifurcation of suspended cables.

No abstract

In this paper, early stage of granular materials flowing through the orifice of a cuboid hopper with flat bottom is investigated based on the results generated by using the discrete element method. The results show that in the start up stage of the flow, a switch curve is formed between static and flowing particles, and a force arch on which the forces are very small is generated below the switch curve. Both curves propagate into the granular bed with the discharge of particles, and reach the top of the bed when a steady state is achieved.

Cable-arch structure is a combined structure, which utilizes flexibility of cable and rigidity of arch. Cable-arch structure has been widely used in bridge engineering. In this work, we proposed a novel mechanical model of cable-arch structure. The out-of-plane buckling and in-plane buckling were studied using the energy method. The formula of critical loads of both the first order out-of-plane buckling and in-plane buckling were derived using Rayleigh-Ritz method. An example is ultimately investigated numerically. The results indicate that the cable can improve considerably the out-of-plane and in-plane stability of arch. Therefore, the research about the stability of cable-arch structure are both valuable not only in theoretical research but also in design of engineering structure.

No abstract