ON TRANSVERSAL VIBRATIONS OF AN AXIALLY MOVING BEAM UNDER INFLUENCE OF VISCOUS DAMPING

In this paper, a transversal vibration of an axially moving beam under the influence of viscous damping has been studied. The axial velocity of the beam is assumed to be positive, constant and small compared to wave-velocity. The beam is moving in a positive horizontal direction between the pair of pulleys and the length between the two pulleys is fixed. From a physical viewpoint, this model describes externally damped transversal motion for a conveyor belt system. The beam is assumed to be externally damped, where there is no restriction on the damping parameter which can be sufficiently large in contrast to much research material. The straightforward expansion method is applied to obtain approximated analytic solutions. It has been shown that the obtained solutions have not been broken out for any parametric values of the small parameter 𝜀. The constructed solutions are uniform and have been damped out. Even though there are several secular terms in the solutions, but they are small compared to damping.

Damping control in viscoelastic beam dynamics

Viscoelasticity plays a key role in many practical applications and in different research fields, such as in seals, sliding-rolling contacts, and crack propagation. In all these contexts, a proper knowledge of the viscoelastic modulus is very important. However, experimental characterization of the frequency-dependent modulus, carried out through different standard procedures, still presents some complexities; then possible alternative approaches are desirable. For example, experimental investigation of viscoelastic beam dynamics would be challenging, especially for the intrinsic simplicity of this kind of test. This is why a deep understanding of damping mechanisms in viscoelastic beams is found to be a quite important task to better predict their dynamics. With the aim to enlighten damping properties in such structures, an analytical study of the transversal vibrations of a viscoelastic beam is presented in this article. Some dimensionless parameters are defined, depending on the material properties and the beam geometry, which enable to accurately design the beam dynamics. In this way, by properly tuning such disclosed parameters, for example the dimensionless beam length or a chosen material, it is possible to enhance or suppress some resonant peaks, one at a time or more simultaneously. This is a remarkable possibility to efficiently control damping in these structures, and the results presented in this article may help in elucidating experimental procedures for the characterization of viscoelastic materials.

Damping of the track horizontal, transversal vibrations

Knowledge of the oscillation process nature in horizontal plane across the track allows selecting the way of damping for reducing decrease of strength properties of polymer gaskets, rails, sleepers and earthworks under effect of horizontal vibrodynamic loads occurring during the rolling stock movement. Maximum horizontal deformation of polymer gaskets across the track does not exceed 10% therefore stress and deformation of polymer material can be done using the Hooke’s law.This is the first systematization of formulae for calculation of polymer gaskets, as well as the first resolution of the task when not pure shear takes place under effect of tangential stresses with simultaneous effect of vertical load. Damping coefficient of polyurethane gaskets is the same as for rubber gaskets; however, their service life is 2.5 times longer.Based on the presented physical mesomechanics it is demonstrated regarding the surface layer of two metal bodies contact under significant load that the surface mesolayer has damping properties, and vibrating oscillations occurring in the truck wheels when rolling stock moves on the rails will be reflected from the contact pad. The process of wheel and rail sliding in transversal direction is accompanied with increase of the total rolling friction and noise, elevated wear and tear of rails and wheel rims. In order to reduce transversal deformations and amplitude of the rails and sleepers torsion oscillations during rolling movement it is proposed to change the shape of polyurethane gaskets. Gaskets with variable thickness will more effectively reflect the shear transversal oscillating waves and reduce transversal forces.

Three spectra problem for Stieltjes string equation and Neumann conditions

Spectral problems are considered which appear in description of small transversal vibrations of Stieltjes strings. It is shown that the eigenvalues of the Neumann-Neumann problem, i.e. the problem with the Neumann conditions at both ends of the string interlace with the union of the spectra of the Neumann-Dirichlet problems, i.e. problems with the Neumann condition at one end and Dirichlet condition at the other end on two parts of the string. It is shown that the spectrum of Neumann-Neumann problem on the whole string, the spectrum of Neumann-Dirichlet problem on the left part of the string, all but one eigenvalues of the Neumann-Dirichlet problem on the right part of the string and total masses of the parts uniquely determine the masses and the intervals between them.

Stability and vibrations control of a stepped beam using piezoelectric actuation

The objects of this studies are the stability and transversal vibrations of the system composed of three segments, where in the centre part of the system two piezoelectric patches are perfectly bonded to the top and bottom surface of the host beam. The system is kinematically loaded as a result of prescribed displacement of one or both end supports. For the analysis purposes three different beam end supports have been taken into consideration, which prevent longitudinal displacements i.e. clamped-clamped, clamped-pinned and pinned-pinned. This type of beam loading not only affect its natural vibration frequencies but also the system’s stability. By introducing the electric field to the piezo patches, depending on its vector direction, in-plane stretching or compressive residual force may be induced. Presented results show that piezo actuation can significantly modify both the critical buckling force and the vibration frequency.