On the Transversal Vibrations of an Axially Moving Continuum With a Time-Varying Velocity: Transient From String to Beam Behavior

Пономарева, С. В.; Horssen, Wim T. van

doi:10.1115/detc2007-34363

Cited by 4 publications

(4 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…There are numerous applications in engineering such as elevators [1][2][3][4][5], aerial cables, crane and mining hoists, conveyor belts [6][7][8][9], oil pipelines [10,11], magnetic and paper tapes and band-saw blades [12], are often known as axially moving systems. Since last few decades, there has been vast research activity on examining the stability of such systems, for instance, see [13][14][15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

On applicability of truncation method for damped axially moving string

Dehraj¹,

Sandilo²,

Malookani³

2020

J. vibroeng.

View full text Add to dashboard Cite

In this paper, the detailed study of the transversal vibrations of a damped axially moving string is considered. Two end pulleys of the string are taken to be fixed and the initial conditions are assumed to be of general displacement field and the general velocity field. The axial speed of the string is considered to be sinusoidal, time-dependent and small compared to wave-velocity. A two timescales perturbation method with a combination of Fourier-sine series which fits the boundary conditions is employed in order to formulate the valid and uniform asymptotic approximations of the exact solutions for the equation. It is found that there are infinitely many values of frequency parameter Ω which cause the internal resonances in system. The fundamental resonant frequency, the non-resonant frequency and the detuning cases have been discussed and analyzed in detail. It has been found explicitly that the total mechanical energy of the infinite dimensional system decreases for two cases of the damping parameter, that is, for 2 and for 2. By truncation method it has been shown that the mode-amplitude response for first few modes is stable. So, Galerkin's truncation method may be possible for these two cases of the parameter. But for case 2 the total mechanical energy of belt system is increasing exponentially. Therefore, it is evident that the Galerkin's truncation method cannot be applied in order to obtain valid approximations on long timescales, that is, on timescales of 1⁄ .

show abstract

Section: Introductionmentioning

confidence: 99%

On applicability of truncation method for damped axially moving string

Dehraj¹,

Sandilo²,

Malookani³

2020

J. vibroeng.

View full text Add to dashboard Cite

show abstract

“…Ponomareva, Sandilo, and van Horssen [7,8] concentrated on studying the transversal vibrations of continuum with time-varying velocity and variable length: transient from string to beam behaviour where the velocity is given by V = (V 0 + sin(Ω )). In their papers, it is explicitly shown how to work with a combined model that is a string model at the low frequencies and a tensioned beam model at the higher frequencies.…”

Section: Introductionmentioning

confidence: 99%

Transverse Free Vibration of Axially Moving Stepped Beam with Different Length and Tip Mass

Ma¹,

Chen³

et al. 2015

Shock and Vibration

View full text Add to dashboard Cite

Axially moving stepped beam (AMSB) with different length and tip mass is represented by adopting Euler-Bernoulli beam theory, and its characteristics and displacements of transverse free vibration are calculated by using semianalytical method. Firstly, the governing equation of the transverse free vibration is established based on Hamilton’s principle. The equation is cast into eigenvalue equation through the complex modal analysis. Then, a scheme is proposed to derive the continuous condition accordingly as the displacement, rotation, bending moment, and shear force are all equal at the connections of any two segments. Another scheme is to derive frequency equation from the given boundary conditions which contain a tip mass in the last segment. Finally, the natural frequency and modal function are calculated by using numerical method according to the eigenvalue equation and frequency equation. Due to the introduction of modal truncation, displacement and, the free vibration solution can be obtained by adopting modal superposition after Hilbert transform. The numerical examples illustrate that length, velocity, mass, and geometry affect characteristics and displacements significantly; the series of methods are effective and accurate to investigate the vibration of the AMSB with different length and tip mass after comparing several results.

show abstract

“…Van Horssen and Ponomareva [7] extended their study by constructing the solution of an initial boundary value problem for a linear, nonhomogeneous axially moving string equation. And they also investigated the transversal vibrations of an axially moving continuum with a time varying velocity [8]. Pakdemirli and Boyaci [9] concentrated on the dynamics of a transportation system carrying moving distributed and concentrated inertial loads.…”

Section: Introductionmentioning

confidence: 99%

Transversal Vibration of Chain Ropeway System Having Support Boundary Conditions with Polygonal Action

Zhou

et al. 2015

Shock and Vibration

View full text Add to dashboard Cite

The purpose of this paper is to characterize the modal parameters and transverse vibrations of a monochain ropeway system for hilly orchards. The moving chain is modeled with uniform distribution and concentrated inertial loads. In order to study the dynamical behavior of the moving chain, Hamilton’s principle is applied to obtain the homogenous differential equation of transverse vibration. With the boundary conditions subjected to the polygonal action caused by chain-support engagement, the coupling effect of concentrated load, variable tension, and time-dependent speed on transverse vibration is investigated. The contribution of residue of singularity to total vibrations in phase space is numerically analyzed by using the Laplace transform method. The influence of the boundary condition considering the polygonal action is investigated in terms of excitation frequency and amplitude coupled with transport speed. The transverse vibrations are calculated numerically and measured experimentally. The numerical results are in agreement with the experimental data, which suggest that the amplitude and frequency of vibration are proportional to the value of propagation speed. The analytical solution to the moving chain problem provides a feasible reference for its stability analysis and wind-induced vibration control.

show abstract

On the Transversal Vibrations of an Axially Moving Continuum With a Time-Varying Velocity: Transient From String to Beam Behavior

Cited by 4 publications

References 0 publications

On applicability of truncation method for damped axially moving string

On applicability of truncation method for damped axially moving string

Transverse Free Vibration of Axially Moving Stepped Beam with Different Length and Tip Mass

Transversal Vibration of Chain Ropeway System Having Support Boundary Conditions with Polygonal Action

Contact Info

Product

Resources

About