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This paper presents a two-node catenary cable element for the analysis of three-dimensional cable-supported structures. The stiffness matrix of the catenary cable element was derived as the inverse of the flexibility matrix, with allowances for selfweight and pretension effects. The element was then included, along with the beam and truss elements, in a geometric nonlinear analysis program, for which the procedure for computing the stiffness matrix and for performing iterations was clearly outlined. With the present element, each cable with no internal joints can be modeled by a single element, even for cables with large sags, as encountered in cable nets, suspension bridges and long-span cable-stayed bridges. The solutions obtained for all the examples are in good agreement with the existing ones, which indicates the accuracy and applicability of the element presented.

Bending and torsional vibrations caused by moving vehicle loads are likely to affect the traffic safety and comfort for girder bridges with limited torsional rigidity. This paper studies the use of cables made of shape memory alloy (SMA) as the devices of reinforcement and vibration reduction for girder bridges. The SMA cables are featured by their small volume, expedient installation. To investigate their effect on the vibration of girder bridges, theoretical analysis, numerical simulation and experimental study were conducted in this paper. For bending vibration, the governing equations of the girder with and without SMA cables subjected to moving vehicle loads were derived, while for torsional vibration, the finite element (FE) simulations were used instead. The results of bending and torsional vibrations obtained by the analytical approach and FE simulations, respectively, were compared with the experimental ones from model testing. It was confirmed that the SMA cables can restrain the vibration of the girder bridge effectively.

The presence of intermediate supports usually imposes difficulties in identifying the tension force of stayed cables in cable-stayed bridges or hanger cables in arch bridges. This paper establishes the partial differential equations of motion of the cable and derives two numerical models with (Model 1) and without (Model 2) considering the flexural rigidity. The effects of two intermediate supports on the identification accuracy of the cable tension force are further studied analytically and experimentally. The effects of several non-dimensional parameters (e.g. damper location, support stiffness, flexural rigidity, and mode order of the cable) on the identification accuracy of the models are also investigated. It is theoretically concluded that the simplified Model 2 provides acceptable accuracy on tension force identification when the non-dimensional parameter $\xi$ is greater than 90 (slender cables), whereas the accurate Model 1 can be applied for tension force identification at any scenarios. The feasibility of two models is further verified by three numerical examples and field tests on two real-world arch bridges.

This paper developed a new Hamiltonian nodal position finite element method (FEM) to treat the nonlinear dynamics of cable system in which the large rigid-body motion is coupled with small elastic cable elongation. The FEM is derived from the Hamiltonian theory using canonical coordinates. The resulting Hamiltonian finite element model of cable contains low frequency mode of rigid-body motion and high frequency mode of axial elastic deformation, which is prone to numerical instability due to error accumulation over a very long period. A second-order explicit Symplectic integration scheme is used naturally to enforce the conservation of energy and momentum of the Hamiltonian finite element system. Numerical analyses are conducted and compared with theoretical and experimental results as well as the commercial software LS-DYNA. The comparisons demonstrate that the new Hamiltonian nodal position FEM is numerically efficient, stable and robust for simulation of long-period motion of cable systems.

Introduced herein is a new structural damping identification approach based on a two-dimensional (2D) amplitude and phase estimation (APES) method. The original APES method is suitable for application to an undamped and complex harmonic vibration signal. Hence, it has to be modified for application to real damped vibration signals such as the vibration test signals in engineering structures. This modified approach will be named as dr_APES. It can transform one-dimensional (1D) signals in time domain into their corresponding signals in the 2D domain of frequency and damping factor. By applying this dr_APES approach, the three-dimensional (3D) amplitude spectrum, with peaks corresponding to the vibration modes, can be obtained for any given vibration signals. By accurately locating the coordinates of the peaks, modal frequencies and damping factors can be identified. Owing to the high-resolution of the location of 2D ordinates of the spectral line and the value of spectrum, the accurate location of peaks can be estimated, and therefore, the modal frequencies and damping factor can be accurately determined. This is demonstrated by a numerical case study. Moreover, by applying the proposed approach to a real onsite dynamic test on two cables in a cable-stayed bridge, the inherent damping of the two cables was identified accurately, thereby verifying the ability of proposed damping identification approach in meeting the requirement of weak damping characteristics identification in flexible structures such as naked cables.

A macroscopic cable equation, which describes the passive linear ("electrotonic") response of a myelinated axon, was previously derived from a segmented cable equation using Keller's two-space homogenization method [Basser, PJ, Med. and Biol. Comput., 1993, Vol. 31, pp. S87–S92]. Here we use the space and length constants of this averaged cable equation to predict classical scaling laws that govern relationships among the inner and outer diameters of the axon's myelin sheath and the distance separating adjacent nodes of Ranvier. These laws are derived by maximizing the characteristic speed of an electrical disturbance along the axon, i.e., the ratio of the characteristic length and the characteristic time constants of the macroscopic cable, subject to the constraint that the nodal width is constant. Using this result, it is also possible to show that all myelinated axons are equally fault tolerant. No free parameters were used in this analysis; all variables and physical constants used in these calculations were taken from published experimental data.