Dynamic and Energetic Analyses of a String/Slider Non-Linear Coupling System by Variable Grid Finite Difference

Fung, Rong‐Fong; Chang, Han-Chi

doi:10.1006/jsvi.2000.3140

Cited by 7 publications

(8 citation statements)

References 14 publications

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“…The physical understanding of the motion of the beam is provided by using a phase-closure principle [7]. Equations of motion for systems with time-dependent boundary conditions were often derived by Hamilton's principle [2,11]. Wang et al [11] investigated the vibrations of three-dimensional underwater cable by using the finite element method (FEM) with a variable grid.…”

Section: Introductionmentioning

confidence: 99%

“…There are also works on vibrations of axially moving strings with timevarying lengths [2,3,6,8,9], though it is difficult to find works which address vibrations of objects with non-zero stiffness. The latter ones are also of great interest due to a variety of possible boundary conditions and their influence on vibrations.…”

Section: Introductionmentioning

confidence: 99%

“…The finite differences method (FDM) was applied after transforming a time-dependent solution domain into a constant one. The FDM [2,12] allows to simplify the process of formulation and programming the problem while being a less time-consuming method than the FEM.…”

Section: Introductionmentioning

confidence: 99%

“…Natural frequencies and non-linear modes were derived from equations obtained using the phase-closure principle [7]. A coupled string/slider system was investigated by Fung and Chang [2]. The partial differential equation governing the transverse string vibration of small amplitude was coupled with the non-linear ordinary differential equation describing the horizontal displacement of a slider.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A dynamic analysis of a coupled beam/slider system

Buśkiewicz

2008

Applied Mathematical Modelling

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The paper deals with transverse vibration of a beam with moving boundary conditions. In order to examine the transfer of energy between a moving support and a vibrating beam under assumption of zero slope of the beam elastic line at the moving support, dynamic analysis of a coupled beam/slider system is carried out. The moving support is modelled as a slider attached to a spring which realizes definite boundary conditions. Equations of motion are derived using Hamilton's principle. Because length of the beam varies appropriate transformations of time and position variables are made to convert the solution space into a rectangle and, subsequently, to solve the partial differential equation of transverse vibration of the beam using the FDM. The phenomenon of the energy flow between the slider and the beam is a subject of the detailed analysis. The beam vibration with a fixed formula of length is examined, too. The dynamic characteristics of the system is brought forward from spectral analysis of numerical solutions.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A dynamic analysis of a coupled beam/slider system

Buśkiewicz

2008

Applied Mathematical Modelling

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“…Yuh and Young [2] studied the dynamic modelling of an axially moving beam in rotation. Fung and Cheng [3] investigated the free vibration of a non-linear-coupled string/slider system with moving boundary. The cables of cable-stayed bridges subjected to combined parametric and forced excitations was studied by Uhrig [4], but they did not describe the constraint of the tied point between the beam and the cable in detail.…”

Section: Introductionmentioning

confidence: 99%