In-plane dynamic behavior of cable networks. Part 1: formulation and basic solutions

Caracoglia, Luca; Jones, Nicholas P.

doi:10.1016/j.jsv.2003.11.058

Cited by 80 publications

(55 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Considering continuity of displacement, Y j , p ( x j , p ) can be expressed as

Y_{j, p} ((), x_{j p}) = A_{j, p} \frac{normalsinh ((), π f_{j} λ x_{j, p} true/ L_{j})}{normalsinh ((), π f_{j} λ l_{j, p} true/ L_{j})} + B_{j, p} \frac{normalcosh ((), π f_{j} λ x_{j, p} true/ L_{j})}{normalcosh ((), π f_{j} λ l_{j, p} true/ L_{j})}

Where f j = ω 01 / ω 0 j is the j th cable frequency ratio ,

ω_{0 j} = π true/ L_{j} \sqrt{T_{j} true/ m_{j}}

, and A j , p and B j , p are complex parameters; two terms of hyperbolic functions are retained because of the presence of nonzero end displacements of cable segment .…”

Section: General Problem Formulationmentioning

confidence: 99%

“…To have a nontrivial solution ( Φ ≠ 0 ), the determinant of the matrix S must be zero. After simplifying hyperbolic functions, the equation det( S ) = 0 can be written as

\begin{matrix} left \\ \prod_{j = 1, 2} [\sinh {normalΓ}_{j} + η_{j} \sinh {normalΓ}_{j, 1} \sinh ({normalΓ}_{j, 2} + {normalΓ}_{j, 3})] \\ + \frac{γ_{1}}{λ} \sum_{j = 1, 2} \{\begin{matrix} left \\ ν_{3 - j} \sinh {normalΓ}_{3 - j, 3} [\sinh {normalΓ}_{j} + η_{j} \sinh {normalΓ}_{j, 1} \sinh ({normalΓ}_{j, 2} + {normalΓ}_{j, 3})] \\ [\sinh ({normalΓ}_{3 - j, 1} + {normalΓ}_{3 - j, 2}) + η_{3 - j} \sinh {normalΓ}_{3 - j, 1} \sinh {normalΓ}_{3 - j, 2}] \end{matrix}\} = 0 \end{matrix}

in which γ 1 = kL 1 / πT 1 is the nondimensional spring stiffness,

η_{j} = c_{j} true/ \sqrt{T_{j} m_{j}}

is the nondimensional damping coefficient of the damper attached to the j th cable,

ν_{j} = \sqrt{T_{1} m_{1} true/ T_{j} m_{j}}

is the mass–tension ratio of the j th cable, Γ j , p = πf j λl j , p / L j , and Γ j = πf j λ .…”

Section: General Problem Formulationmentioning

confidence: 99%

“…Theoretically, the nondimensional spring stiffness is related to the axial stiffness of the cross‐link, and it can vary from 0 (no connection spring) to ∞ (perfectly rigid connection). The reported nondimensional axial stiffness parameter γ 1 for cross‐link on real cable stayed bridges ranges from 0.32 to 32 . When γ 1 → ∞, the following equation can be derived from Equation :

normalsinh Γ_{03} ({}, \begin{array}{l} 2 normalsinh Γ_{0} normalsinh ((), Γ_{01} + Γ_{02}) \\ + η normalsinh Γ_{01} ([], normalsinh ((), Γ_{02} + Γ_{03}) normalsinh ((), Γ_{01} + Γ_{02}) + normalsinh Γ_{0} normalsinh Γ_{02}) \end{array}) = 0

…”

Section: Two Identical Cablesmentioning

confidence: 99%

See 2 more Smart Citations

Free vibrations of a two-cable network with near-support dampers and a cross-link

Zhou

Xia

Sun

et al. 2015

Struct. Control Health Monit.

View full text Add to dashboard Cite

SUMMARYVibration mitigation of cables is a crucial problem for cable-supported bridges. A hybrid method for cable vibration mitigation that combines cross-ties and dampers has been applied in engineering practice; however, the damping and frequency of this kind of system needs to be further assessed. In this paper, a system of two parallel cables with a cross-link and dampers located near the cable anchorage is proposed and analyzed. Based on displacement continuity and force equilibrium at the damper and spring locations, the characteristic equation of the system is derived by applying the transfer matrix method. The complex characteristic equation is then numerically solved to obtain the modal damping and frequencies. The damping and frequency characteristics are discussed in detail for the case when the two cables are identical. Special attention is given to the case when only one damper is installed, and the approximate damping evaluation formulations are proposed when spring stiffness approaches infinity. Effects of mass-tension ratio, cable length ratio and frequency ratio on damping are also addressed. Finally, a case study of multimode damping optimization for bridge hangers is given. The results of this paper could be useful for vibration mitigation of two parallel cables and further development of design guidelines for cable networks with attached dampers.

show abstract

“…Considering continuity of displacement, Y j , p ( x j , p ) can be expressed as

Y_{j, p} ((), x_{j p}) = A_{j, p} \frac{normalsinh ((), π f_{j} λ x_{j, p} true/ L_{j})}{normalsinh ((), π f_{j} λ l_{j, p} true/ L_{j})} + B_{j, p} \frac{normalcosh ((), π f_{j} λ x_{j, p} true/ L_{j})}{normalcosh ((), π f_{j} λ l_{j, p} true/ L_{j})}

Where f j = ω 01 / ω 0 j is the j th cable frequency ratio ,

ω_{0 j} = π true/ L_{j} \sqrt{T_{j} true/ m_{j}}

, and A j , p and B j , p are complex parameters; two terms of hyperbolic functions are retained because of the presence of nonzero end displacements of cable segment .…”

Section: General Problem Formulationmentioning

confidence: 99%

“…To have a nontrivial solution ( Φ ≠ 0 ), the determinant of the matrix S must be zero. After simplifying hyperbolic functions, the equation det( S ) = 0 can be written as

\begin{matrix} left \\ \prod_{j = 1, 2} [\sinh {normalΓ}_{j} + η_{j} \sinh {normalΓ}_{j, 1} \sinh ({normalΓ}_{j, 2} + {normalΓ}_{j, 3})] \\ + \frac{γ_{1}}{λ} \sum_{j = 1, 2} \{\begin{matrix} left \\ ν_{3 - j} \sinh {normalΓ}_{3 - j, 3} [\sinh {normalΓ}_{j} + η_{j} \sinh {normalΓ}_{j, 1} \sinh ({normalΓ}_{j, 2} + {normalΓ}_{j, 3})] \\ [\sinh ({normalΓ}_{3 - j, 1} + {normalΓ}_{3 - j, 2}) + η_{3 - j} \sinh {normalΓ}_{3 - j, 1} \sinh {normalΓ}_{3 - j, 2}] \end{matrix}\} = 0 \end{matrix}

in which γ 1 = kL 1 / πT 1 is the nondimensional spring stiffness,

η_{j} = c_{j} true/ \sqrt{T_{j} m_{j}}

is the nondimensional damping coefficient of the damper attached to the j th cable,

ν_{j} = \sqrt{T_{1} m_{1} true/ T_{j} m_{j}}

is the mass–tension ratio of the j th cable, Γ j , p = πf j λl j , p / L j , and Γ j = πf j λ .…”

Section: General Problem Formulationmentioning

confidence: 99%

normalsinh Γ_{03} ({}, \begin{array}{l} 2 normalsinh Γ_{0} normalsinh ((), Γ_{01} + Γ_{02}) \\ + η normalsinh Γ_{01} ([], normalsinh ((), Γ_{02} + Γ_{03}) normalsinh ((), Γ_{01} + Γ_{02}) + normalsinh Γ_{0} normalsinh Γ_{02}) \end{array}) = 0

…”

Section: Two Identical Cablesmentioning

confidence: 99%

See 1 more Smart Citation

Free vibrations of a two-cable network with near-support dampers and a cross-link

Zhou

Xia

Sun

et al. 2015

Struct. Control Health Monit.

View full text Add to dashboard Cite

show abstract

“…In [3][4][5][6], analytical studies are performed on cross-ties or hybrid systems consisting of viscous dampers and cross-ties.…”

Section: Introductionmentioning

confidence: 99%

Simple Program to Investigate Hysteresis Damping Effect of Cross-Ties on Cables Vibration of Cable-Stayed Bridges

Papadopoulos

Diamantopoulos

Xenidis

et al. 2012

AMR

View full text Add to dashboard Cite

A short computer program, fully documented, is presented, for the step-by-step dynamic analysis of isolated cables or couples of parallel cables of a cable-stayed bridge, connected to each other and possibly with the deck of the bridge, by very thin pretensioned wires (cross-ties) and subjected to variation of their axial forces due to traffic or to successive pulses of a wind drag force. A simplified SDOF model, approximating the fundamental vibration mode, is adopted for every individual cable. The geometric nonlinearity of the cables is taken into account by their geometric stiffness, whereas the material nonlinearities of the cross-ties include compressive loosening, tensile yielding, and hysteresis stress-strain loops. Seven numerical experiments are performed. Based on them, it is observed that if two interconnected parallel cables have different dynamic characteristics, for example different lengths, thus different masses, weights, and geometric stiffnesses, too, or if one of them has a small additional mass, then a single pretensioned very thin wire, connecting them to each other and possibly with the deck of the bridge, proves effective in suppressing, by its hysteresis damping, the vibrations of the cables.

show abstract

“…They also emphasised the time-consuming aspect of these numerical computations. The problem of modelling a cable was further investigated by Caracoglia and Jones (2005). The vibration characteristics and behaviour of a cable network were presented.…”

Section: Introductionmentioning

confidence: 99%

Complete function collocation method for solving preliminary cable-stayed bridge pretension forces

Shum¹,

Tsang²

2008

Bridge Structures

View full text Add to dashboard Cite

A proposal for a numerical method based on the complete solution collocation method is presented to solve the cable-stayed bridge engineering structural problem. This complete function collocation method is presented from the viewpoint of calculating the pretension forces required for the final completed bridge structure, which is one of the most important and practical considerations in cable-stayed bridge design. The complete function collocation method is used to calculate stay cable forces by solving a set of partial differential equations. The study shows that this mesh-free collocation method can be used to solve practical structural engineering problems and provides an alternative to traditional finite element methods. A simple two-dimensional cable-stayed bridge is presented and is solved to illustrate this numerical method. Governing equations of deformation for a bridge structure are formulated in either Eulerian or Lagrangian coordinate systems according to the situation. Point loads due to stay cables on bridge pylons and bridge deck are modelled by Fourier or Gaussian representations. Transverse natural frequencies of stay cables subject to no body forces and caused by flow-induced vibration due to blowing wind are proposed. The preliminary computational procedure presented in this paper provides the basis for further analysis toward more realistic cable-stayed bridges, which would include nonlinear effects, live loadings and construction stage loadings.

show abstract

In-plane dynamic behavior of cable networks. Part 1: formulation and basic solutions

Cited by 80 publications

References 7 publications

Free vibrations of a two-cable network with near-support dampers and a cross-link

Free vibrations of a two-cable network with near-support dampers and a cross-link

Simple Program to Investigate Hysteresis Damping Effect of Cross-Ties on Cables Vibration of Cable-Stayed Bridges

Complete function collocation method for solving preliminary cable-stayed bridge pretension forces

Contact Info

Product

Resources

About