Analysis On the In-Plane 2:2:1 Internal Resonance of a Complex Cable-Stayed Bridge System Under External Harmonic Excitation

Nonlinear dynamic analysis of a cable-stayed bridge has been a hot topic due to its structural flexibility. Based on integro-partial differential equations of a double-cable-stayed shallow-arch model, in-plane 2:2:1 internal resonance among three first in-plane modes of two cables and a shallow arch under external primary or subharmonic resonance is considered. Galerkin's method and the method of multiple scales are used to derive averaged equations of the cable-stayed bridge system. Nonlinear dynamic behaviours of the system are investigated via the numerical simulation. Results show rich nonlinear phenomena of the cable-stayed bridge system and some new phenomena are observed. Two identical cables that are symmetrically located above the shallow arch can have different dynamic behaviours even when initial conditions of the system are symmetrically given. Two cables with some differences between their parameters can exhibit either softening or hardening characteristics.

Mary Elmes Bridge. An urban pedestrian bridge, from concept to opening

<p>Mary Elmes bridge is a new 66m single span pedestrian and cyclist bridge opened in Cork in July 2019. In September 2016, Cork City Council launched a design competition for a single span low level bridge as part of its key objective to encourage greater sustainable travel in the form of walking and cycling within the city Centre. The overriding challenge was to deliver a considered design - sympathetic to the existing fabric of the city and easy to install within the confined urban environment.</p><p>The solution was a visually appealing design; a slender, 66-metre steel shallow arch, establishing a connective dialogue with its surrounds and compliant with challenging flooding and visual requirements. The structural system is a fully integral, single span with variable depth, central steel box girder and variable width cantilevered walkways. The concept adopts a clever strategy to integrate at grade landings with existing footpath levels while making the structure compatible with future city flood defenses.</p>

Modeling and 1 : 1 Internal Resonance Analysis of Cable-Stayed Shallow Arches

In this paper, an analytical model of a cable-stayed shallow arch is developed in order to investigate the 1 : 1 internal resonance between modes of a cable and a shallow arch. Integrodifferential equations with quadratic and cubic nonlinearities are used to model the in-plane motion of a simple cable-stayed shallow arch. Nonlinear dynamic responses of a cable-stayed shallow arch subjected to external excitations with simultaneous 1 : 1 internal resonances are investigated. Firstly, the Galerkin method is used to discretize the governing nonlinear integral-partial-differential equations. Secondly, the multiple scales method (MSM) is used to derive the modulation equations of the system under external excitation of the shallow arch. Thirdly, the equilibrium, the periodic, and the chaotic solutions of the modulation equations are also analyzed in detail. The frequency- and force-response curves are obtained by using the Newton–Raphson method in conjunction with the pseudoarclength path-following algorithm. The cascades of period-doubling bifurcations leading to chaos are obtained by applying numerical simulations. Finally, the effects of key parameters on the responses are examined, such as initial tension, inclined angle of the cable, and rise and inclined angle of shallow arch. The comprehensive numerical results and research findings will provide essential information for the safety evaluation of cable-supported structures that have widely been used in civil engineering.

Geometrical Nonlinear Analysis of Slender Micro Arch-Beams Pulled by Magnetic Loadings

In this study, a nonlinear model of micro arch-beams under the action of electrostatic loadings with an initial air gap is presented. Based on the well-developed 3D beam theory proposed by Yang and Kuo [4], the arch beam is modelled as a series of uniform straight beam elements and the pull-in magnetic force is simulated as an electric-induced force by an electrode lying. Then the nonlinear structural analysis of snap-through and pull-in stability for a simply supported shallow arch subjected to a concentrated electrostatic loading will be investigated. To tackle the path-dependent features of electric forces due to presence of air gaps and nonlinear deformations, this study regards the electric forces as pseudo-forces acting at the arch-beam and solves the structure equations using an incremental-iterative procedure. From the numerical results, the present approach demonstrates that the micro-arch beam has the capacity to withstand further electrostatic loading after the snapthrough jump.