Transversal vibrations of an axially moving string under boundary damping are investigated. Mathematically, it represents a homogenous linear partial differential equation subject to nonhomogeneous boundary conditions. The string is moving with a relatively (low) constant speed, which is considered to be positive.  The string is kept fixed at the first end, while the other end is tied with the ...

in this paper, the dynamical behavior of an axially moving string modeled by fractional derivative is investigated. the governing equation represented motion is solved by the method of multiple scales. considering principal parametric resonance, the stability boundaries for string with simple supports are obtained. numerical results indicate the effects of fractional damping on stability.

In this research, dynamic analysis of the rotational slender axially moving string is investigated. String assumed as Euler Bernoulli beam. The axial motion of the string, gyroscopic force and mass eccentricity were considered in the study. Equations of motion are derived using Hamilton’s principle, resulting in two partial differential equations for the transverse motions. The equations are ch...

The stabilization of the transverse vibration of an axially moving string is implemented using time-varying control of either the boundary transverse motion or the external boundary forces. The total mechanical energy of the translating string is a Lyapunov functional and boundary control laws are designed to dissipate the total vibration energy of the string at the left and/or right boundary. ...

In this paper, a nonlinear axially moving string with the Kelvin-Voigt damping is considered. It is proved that the string is stable, i.e., its transversal displacement converges to zero when the axial speed of the string is less than a certain critical value. The proof is established by showing that a Lyapunov function corresponding to the string decays to zero exponentially. It is also shown ...

In this paper, an active vibration control of a tensioned, elastic, axially moving string is investigated. The dynamics of the translating string are described with a non-linear partial differential equation coupled with an ordinary differential equation. A right boundary control to suppress the transverse vibrations of the translating continuum is proposed. The control law is derived via the L...