The effect of friction reduction in the presence of in-plane vibrations

A reduction of friction by vibrations has been observed in various experiments. This effect can be applied to actively control frictional forces by modulating vibrations. Moreover, common methods of controlling friction rely on lubricants and suitable material combinations. The superimposition of vibrations can further reduce the friction force. This study presents a theoretical approach based on the Dahl friction model that describes the friction reduction observed in the presence of the tangential vibrations at an arbitrary angle. Analysis results indicated that the tangential compliance should be considered in modeling the effect of vibrations in reducing friction. At any vibration angle, the tangential compliance of the contacts reduces the friction reduction effect. The vibrations parallel to the macroscopic velocity are most effective for friction reduction.     

Basic vibrations and anharmonic analysis of a vibration

We prove that, besides the simple harmonic vibrations, some anharmonic vibrations are basic as well, because a general vibration can be considered as a superposition of such vibrations with different frequencies. The results in this paper are a generalization of Fourier analysis and a new theory of vibration analysis.     

Effect of Vibrations on Pore Fluid Distribution in Porous Media

Understanding the role of shuttle vibrations in pore fluid distribution is an essential task in the exploration of plant growth in root modules aboard space flights. Results from experimental investigations are reported in this paper on the distribution of immiscible fluid phases in glass beads under vibrations. Hexadecane, a petroleum compound immiscible with and lighter than water, was used in the experiments. The higher freezing point of Hexadecane (18 °C) allowed the solidification of the entrapped blobs in the presence of water in porous media, so that their size distribution can be obtained. van Genuchten function, commonly used to express moisture retention curves, is found to be an adequate fit for blob size distribution at residual saturation. The effect of vibrations on the fate (mobilization, stranding, or breakup) of a solitary ganglion in porous media was studied using a network model. A mobility criterion considering viscous, gravity, and capillary forces was developed to determine the fate of a solitary ganglion in a porous medium. It is concluded that the effect of vibrations is to increase the likelihood of breakup and mobilization of blobs entrapped in porous media at residual saturation. The pore fluid distributions after vibrations are less uniform than those before vibrations.     

Two classes of vibrations of a short circular cylinder

This paper gives a solution of the stationary dynamic problem of elasticity which describes two classes of natural nonaxisymmetric vibrations of a finite circular cylinder. In the particular case of axial symmetry, the resulting solution describes two well-known classes of axisymmetric vibrations: vibrations of the first class become longitudinal-transverse vibrations and vibrations of the second class become torsional vibrations. The existence of two classes of nonaxisymmetric vibrations is due to the boundary conditions at the ends. It is shown that as the length (height) of the cylinder increases, the effect of the boundary conditions at the ends on the frequency spectrum reduces, and the vibration frequencies of the two classes become similar and then identical.     

Asymptotic modelling of the linear dynamics of laminated beams

We study the linear dynamics of a layered elastic beam by means of the asymptotic expansion method. The beam consists of three linearly elastic isotropic layers: the middle layer is considered to be thinner and softer than the upper and lower ones. We characterize the limit models by distinguishing three cases of natural frequencies: the low frequencies associated with flexural vibrations, the mean frequencies associated with axial vibrations and the high frequencies, associated with transversal shear and pinching vibrations.     

Improved natural frequencies for plates with a free edge

A simple correction formula is developed for the square of natural frequencies of plates with a free edge. The theory is applied to torsional vibrations of a long plate strip and to vibrations of a circular plate with a free edge and a number of nodal diameters. The paper concludes with the remark that the theory may be extended mutatis mutandis to vibrations of shells with a free edge.     

Dynamic Analysis of the Non-Linear Behavior of a Composite Sandwich Beam with a Magnetorheological Elastomer Core

This work deals with the active control of the vibrations of mechanical structures incorporating magnetorheological elastomer. The damping coefficient and shear modulus of the elastomer increase when exposed to a magnetic field. Compared with the vibration control where the elastomer is permanently exposed to a magnetic field, the control of this process through time reduces vibrations more effectively. The experimental study for the vibrations of a sandwich beam filled with an elastomer is conducted, followed by a numerical study using the Abaqus code.The vibration damping is found to be dependent on the loading rate of micro-size ferromagnetic particles in the elastomer.     

Controlling torsional vibrations of drill strings via decomposition of traveling waves

Torsional vibrations in drill strings, especially stick-slip vibrations, are detrimental to the drilling process as they slow down the rate of penetration and may lead to failure of the drilling equipment. We present a method for controlling these vibrations by exactly decomposing the drill string dynamics into two traveling waves traveling in the direction of the top drive and in the direction of the drill bit. The decomposition is derived from the wave equation governing the string vibrations and is achieved with only two sensors that can be placed directly at the top drive and at a short distance below the top drive (e.g., 5 m). Therefore, downhole measurements along the string and at the bit are not necessary, which is a major advantage compared to other control concepts for drill string dynamics. The velocity of the top drive is then controlled in order to absorb the wave traveling in the direction of the top drive, thus achieving a reflection coefficient of zero for the frequency range of the undesired torsional vibrations. The proposed algorithm is implemented for both a numerical example and an experimental setup; results show that the control concept works very effectively.     

Eigenfrequencies of the three dimensional euler-bernoulli beam system with dissipative joints

In this paper, we will compute the transfer matrices to find the eigenfrequencies for the vibrations of the general non-collinear Euler-Bernoulli or Timoshenko beam structure with dissipative joints. We will allow the structure to be three dimensional, and thus we must consider all types of vibrations simultaneously, including longitudinal and torsional vibrations. The general structure considered will consist of any number of beams joined end to end to form a chain. Many different kinds of dampers are allowed, even within the same structure. We also will allow different materials within the structure as well as different beam widths. We then will show that asymptotic estimates can be used to find the eigenfrequencies approximately.     

Influence of periodic excitation on self-sustained vibrations of one disk rotors in arbitrary length journals bearings

Interaction of forced and self-sustained vibrations of one disk rotor is described by nonlinear finite-degree-of-freedom dynamical system. The shaft of the rotor is supported by two journal bearings. The combination of the shooting technique and the continuation algorithm is used to study the rotor periodic vibrations. The Floquet multipliers are calculated to analyze periodic vibrations stability. The results of periodic motions analysis are shown on the frequency response. The quasi-periodic motions are investigated. These nonlinear vibrations coexist with the periodic forced vibrations.     

Free vibrations of circular cylindrical shells with a small added concentrated mass

The effect of a small added mass on the frequency and shape of free vibrations of a thin shell is studied using shallow shell theory. The proposed mathematical model assumes that mass asymmetry even in a linear formulation leads to coupled radial flexural vibrations. The interaction of shape-generating waves is studied using modal equations obtained by the Bubnov–Galerkin method. Splitting of the flexural frequency spectrum is found, which is caused not only by the added mass but also by the wave-formation parameters of the shell. The ranges of the relative lengths and shell thicknesses are determined in which the interaction of flexural and radial vibrations can be neglected.     

Rotation of the apparent vibration plane of a swinging spring at the 1:1:2 resonance

Nonlinear spatial vibrations of a mass point on a weightless elastic suspension (pendulum on a spring) are considered. The frequency of vertical vibrations is assumed to be equal to the doubled swinging frequency (the 1:1:2 resonance). In this case, as numerical calculations and experiments show, the vertical vibrations are unstable, which leads to the vertical vibration energy transfer to the pendulum swinging energy. The vertical vibrations of the mass point decay and, after a certain time period, the pendulum starts swinging in a certain vertical plane. This swinging is also unstable, which results in the reverse energy transfer into the vertical vibration mode. The vertical vibrations are again repeated. But after the second transfer of the vertical vibration energy to the pendulum swinging energy, the apparent plane of vibrations rotates by a certain angle. These effects are described analytically; namely, the energy transfer period, the time variations in the amplitudes of both modes, and the variations in the angle of the apparent vibration plane are determined. An asymptotic solution is also constructed for the mass point trajectory in the orbit elements. In projection on the horizonal plane, the mass point moves in a nearly elliptic trajectory. The ellipse semiaxes slowly vary with time, so that their product remains constant, and the major semiaxis slowly rotates at a constant sectorial velocity. The obtained analytic time dependence of the ellipse semiaxes and the precession angle agree well with the results of numerical calculations.     

Vibrations of a complex-shaped panel

The free vibrations of flexible shallow shells with complex planform are studied. To analyze the natural frequencies and modes of linear vibrations, the R-function and Rayleigh–Ritz methods are used. A discrete model is obtained using the Bubnov–Galerkin method. The nonlinear vibrations are studied by combining the nonlinear normal mode method and the multiple-scales method. Skeleton curves of natural vibrations are drawn     

Three‐dimensional computation for flow‐induced vibrations in in‐line and cross‐flow directions of a circular cylinder

We present numerical results for in‐line and cross‐flow vibrations of a circular cylinder, which is immersed in a uniform flow and is elastically supported by damper‐spring systems to compute vibrations of a rigid cylinder. In the case of a circular cylinder with a low Scruton number, it is well‐known that two types of self‐excited vibrations appear in the in‐line direction in the range of low reduced velocities. On the other hand, a cross‐flow vibration of the circular cylinder can be excited in the range of high reduced velocities. Therefore, we compute the flow‐induced vibrations of the circular cylinder in the wide range of the reduced velocities at low and high Scruton numbers and discuss about excitation mechanisms in the in‐line and cross‐flow directions. Copyright © 2011 John Wiley & Sons, Ltd.     

Vibrations of shallow shells rectangular in the horizontal projection with two freely supported opposite edges

The exact mode shapes of linear vibrations of a shallow shell rectangular in the horizontal projection with two freely supported opposite edges are obtained. These shapes are used to construct a discretemodel of vibrations of a shallow shell in geometrically nonlinear deformation. The harmonic balance method is used to study the free and forced nonlinear vibrations under internal resonance. The Lyapunov stability of the obtained periodic vibrations is analyzed.     

Theoretical and experimental investigations of gear-rattling

Rattling vibrations in gear boxes are a noise problem of modern cars following the requirement to be as quiet as possible. The paper presents an uniform approach to model such vibrations based on classical impact theory and applying modern methods of topological dynamics. Some comparisons of theory and measurements utilizing a test set-up of a rattling machine are presented. They demonstrate the practical relevancy of the presented theory.     

Nonlinear Analysis of Experimental Time Series of a Straight Turning Process

We investigate vibrations generated in a straight turning process. Applying correlation functions and the Fourier transform to experimental time series, we have analysed their nature. Particularly, we have identified whipping caused by the non-ideal suspension of the cutting workpiece. Our investigation shows also a large stochastic component of vibrations. It can be the effect of random forcing due to the initial roughness of a cutting surface and/or spontaneous chips breaking.     

Active damping of the resonant vibrations of a flexible cylindrical panel with sensors and actuators

The active damping of the resonant vibrations of a flexible cylindrical panel with rectangular planform and clamped edges is considered. The damping is done with distributed piezoelectric sensors and actuators. It is shown that the amplitude of the resonant vibrations can be substantially decreased by choosing the appropriate feedback factors. The combined effect of geometrical nonlinearity and dissipative properties of the material on the effectiveness of damping is analyzed     

EIGENFREQUENCIES OF THE THREE DIMENSIONAL EULER－BERNOULLI BEAM SYSTEM WITH DISSIPATIVE JOJNTS

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