On Viscoelasticity and Standing Waves in Tires

1976 ◽  
Vol 4 (4) ◽  
pp. 233-246 ◽  
Author(s):  
J. Padovan
Keyword(s):  
Exact Solution ◽  
Standing Wave ◽  
Wave Phenomenon ◽  
Numerical Experiments ◽  
Standing Waves ◽  
Structural Damping ◽  
Resonance Response ◽  
Foundation Model ◽  
Stated Problem ◽  
Classical Ring

Abstract Based on the classical ring on foundation model for the tire, the effect which structural damping has on the development of the standing wave phenomenon is investigated. In particular, the model employed consists of a rotating ring on foundation where, in addition to including Coriolis effects, Kelvin-Voigt-type viscoelasticity is admitted in both the ring and foundation. Enforcing strict periodicity in space and time, the exact solution is obtained to the stated problem. Several parametric numerical experiments employing this solution are reported. These demonstrate that the standing wave phenomenon in tires is essentially a viscoelastic-type resonance response.

scholarly journals Dimensional reduction in 6D standing waves braneworld

2014 ◽  
Vol 24 (01) ◽  
pp. 1550009 ◽  
Author(s):  
Otari Sakhelashvili
Keyword(s):  
Exact Solution ◽  
Standing Wave ◽  
Dimensional Reduction ◽  
Cosmological Solution ◽  
Standing Waves ◽  
Massless Scalar ◽  
Dynamical Mechanism ◽  
Higher Dimensional ◽  
Braneworld Model

We found cosmological solution of the 6D standing wave braneworld model generated by gravity coupled to a massless scalar phantom-like field. By obtaining a full exact solution of the model, we found a novel dynamical mechanism in which the anisotropic nature of the primordial metric gives rise to expansion of three spatial brane dimensions and affectively reduction of other spatial directions. This dynamical mechanism can be relevant for dimensional reduction in string and other higher-dimensional theories in the attempt of getting a 4D isotropic expanding spacetime.

scholarly journals Instability of standing waves for non-linear Schrödinger-type equations

1988 ◽  
Vol 8 (8) ◽  
pp. 119-138 ◽  
Keyword(s):  
Dynamical Systems ◽  
Standing Wave ◽  
Optical Waveguides ◽  
Standing Waves ◽  
Positive Eigenvalue ◽  
Shooting Argument ◽  
Wave Solutions ◽  
Non Linear ◽  
Linearized Operator

AbstractA theorem is proved giving a condition under which certain standing wave solutions of non-linear Schrödinger-type equations are linearly unstable. The eigenvalue equations for the linearized operator at the standing wave can be analysed by dynamical systems methods. A positive eigenvalue is then shown to exist by means of a shooting argument in the space of Lagrangian planes. The theorem is applied to a situation arising in optical waveguides.

Nonlinear compressible magnetoconvection. Part 3. Travelling waves in a horizontal field

1995 ◽  
Vol 300 ◽  
pp. 287-309 ◽  
Author(s):  
D. P. Brownjohn ◽  
N. E. Hurlburt ◽  
M. R. E. Proctor ◽  
N. O. Weiss
Keyword(s):  
Magnetic Field ◽  
Numerical Experiments ◽  
Strong Field ◽  
Travelling Waves ◽  
Standing Waves ◽  
Weak Field ◽  
Horizontal Magnetic Field ◽  
Weakly Nonlinear ◽  
Physical Mechanisms ◽  
The Magnetic Field

We present results of numerical experiments on two-dimensional compressible convection in a polytropic layer with an imposed horizontal magnetic field. Our aim is to determine how far this geometry favours the occurrence of travelling waves. We therefore delineate the region of parameter space where travelling waves are stable, explore the ways in which they lose stability and investigate the physical mechanisms that are involved. In the magnetically dominated regime (with the plasma beta, $\hat{\beta}$ = 8), convection sets in at an oscillatory bifurcation and travelling waves are preferred to standing waves. Standing waves are stable in the strong-field regime ($\hat{\beta}$ = 32) but travelling waves are again preferred in the intermediate region ($\hat{\beta}$ = 128), as suggested by weakly nonlinear Boussinesq results. In the weak-field regime ($\hat{\beta}$ ≥ 512) the steady nonlinear solution undergoes symmetry-breaking bifurcations that lead to travelling waves and to pulsating waves as the Rayleigh number, $\circ{R}$, is increased. The numerical experiments are interpreted by reference to the bifurcation structure in the ($\hat{\beta}$, $\circ{R}$)-plane, which is dominated by the presence of two multiple (Takens-Bogdanov) bifurcations. Physically, the travelling waves correspond to slow magnetoacoustic modes, which travel along the magnetic field and are convectively excited. We conclude that they are indeed more prevalent when the field is horizontal than when it is vertical.

On the observability of finite-depth short-crested water waves

1996 ◽  
Vol 322 ◽  
pp. 1-19 ◽  
Author(s):  
M. Ioualalen ◽  
A. J. Roberts ◽  
C. Kharif
Keyword(s):  
Standing Wave ◽  
Water Waves ◽  
Numerical Study ◽  
Standing Waves ◽  
Finite Depth ◽  
Two Dimensional ◽  
Wave Fields ◽  
Progressive Waves ◽  
Wave Limit ◽  
Narrow Bands

A numerical study of the superharmonic instabilities of short-crested waves on water of finite depth is performed in order to measure their time scales. It is shown that these superharmonic instabilities can be significant-unlike the deep-water case-in parts of the parameter regime. New resonances associated with the standing wave limit are studied closely. These instabilities ‘contaminate’ most of the parameter space, excluding that near two-dimensional progressive waves; however, they are significant only near the standing wave limit. The main result is that very narrow bands of both short-crested waves ‘close’ to two-dimensional standing waves, and of well developed short-crested waves, perturbed by superharmonic instabilities, are unstable for depths shallower than approximately a non-dimensional depth d= 1; the study is performed down to depth d= 0.5 beyond which the computations do not converge sufficiently. As a corollary, the present study predicts that these very narrow sub-domains of short-crested wave fields will not be observable, although most of the short-crested wave fields will be.

On the theory and application of one-step numerical schemes for solving quantum stochastic differential equation (QSDE)

2014 ◽  
Vol 07 (03) ◽  
pp. 1450037
Author(s):  
T. O. Akinwumi ◽  
B. J. Adegboyegun
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Stochastic Differential Equation ◽  
Numerical Experiments ◽  
Numerical Schemes ◽  
Quantum Stochastic Differential Equation ◽  
One Step ◽  
Definition Of ◽  
Convergent Sequences ◽  
Solution Techniques

This paper presents one-step numerical schemes for solving quantum stochastic differential equation (QSDE). The algorithms are developed based on the definition of QSDE and the solution techniques yield rapidly convergent sequences which are readily computable. As well as developing the schemes, we perform some numerical experiments and the solutions obtained compete favorably with exact solutions. The solution techniques presented in this work can handle all class of QSDEs most especially when the exact solution does not exist.

A smart device for particle separation in water using ultrasonic standing waves

2006 ◽  
Vol 6 (1) ◽  
pp. 173-183 ◽  
Author(s):  
Y.S. Lee ◽  
J.H. Kwon
Keyword(s):  
Standing Wave ◽  
Standing Waves ◽  
Smart Device ◽  
Zoom Lens ◽  
Electric Impedance ◽  
Separation Channel ◽  
Separation Device ◽  
Standing Wave Field ◽  
Ultrasonic Standing Wave ◽  
Separation Force

This paper presents the theory, design, and evaluation of a smart device for the enhanced separation of particles mixed in fluid. The smart device takes advantage of the ultrasonic standing wave, which was generated by the operation of a piezoceramic PZT patch installed in the smart device. The details of the device design including the electro-acoustical modelling for separation and PZT transducer are described. Based on this design, the separation device was fabricated and evaluated. In the experiments, an optical camera with a zoom lens was used to monitor the position of interested particles within the separation channel layer in the device. The electric impedance of the PZT patch bonded on the separation device was measured. The device shows a strong levitation and separation force against 50 μm diameter particles mixed with water at the separation channel in the device. Experimental results also showed that the device can work with both heavy and light sand particles mixed with water due to the generated standing wave field in the separation channel.

The Concept of X-Ray Standing Wave

2014 ◽  
pp. 431-461
Keyword(s):  
Standing Wave ◽  
Dynamic Theory ◽  
Standing Waves ◽  
Perfect Crystal ◽  
Classical Dynamic ◽  
X Ray ◽  
Imperfect Crystal ◽  
Almost All

The concept of “Standing Waves” (SW) that arise in the crystal dynamically “attacked” by the frequency fields X is analytically analyzed towards expressing, in almost all the cases, the total intensity of the fields on dispersion branches in the perfect crystal and for the embedded layer on the imperfect crystal using various extensions of the semi-classical dynamic theory, adapted or reparameterized, depending on the specific conditions of analysis performed.

Methods of detectiоn a voids under concrete slabs of water faces of the dam of Novosibirsk hydrostation by the standing wave method

2020 ◽  
Author(s):  
Konstantin V. Fedin ◽  
◽  
Yury I. Kolesnikov ◽  
Luckymore Ngomayezwe ◽  
◽  
...  
Keyword(s):  
Standing Wave ◽  
Acoustic Noise ◽  
Standing Waves ◽  
Hydraulic Structures ◽  
Concrete Slabs ◽  
Wave Method ◽  
Compression Waves ◽  
Standing Wave Method ◽  
Amplitude Spectra ◽  
Base Soil

Using the example of the Novosibirsk hydrostation, the capabilities of the standing wave method to identify defects in the fastenings of water faces of dams of hydraulic structures are demonstrated. The accumulation of amplitude spectra of acoustic noise records allows one to determine the frequencies of the few first modes of standing compression waves generated by noise in concrete slabs. A sharp increase in the frequency of the lowest mode of standing waves is an indicator of the appearance of voids under the slabs or decompression of the base soil.

Study on the Wave Deformation of a Traveling Wave Piezoelectric Stator Using Composite Transducer

2012 ◽  
Vol 516-517 ◽  
pp. 1647-1650
Author(s):  
Ying Xiang Liu ◽  
Pei Lian Feng ◽  
Wei Shan Chen ◽  
Jun Kao Liu
Keyword(s):  
Standing Wave ◽  
Traveling Wave ◽  
Vibration Amplitude ◽  
Longitudinal Vibration ◽  
Standing Waves ◽  
Piezoelectric Motor ◽  
Wave Shape ◽  
Bending Vibration ◽  
Motion Trajectories ◽  
Wave Deformation

In a previous study, the authors have presented and developed a cylindrical traveling wave piezoelectric motor using a composite transducer. This study focuses the research on the wave deformation problems in the proposed stator. Firstly, the standing wave excited by the longitudinal vibration of the transducer is analyzed, and the vibration amplitudes of particles on the driving teeth are extracted to present the objective wave shape. Then, the wave deformation of the standing wave excited by the bending vibration of the transducer is analyzed. Finally, the longitudinal and bending PZT are excited together to gain a flexural traveling wave in the stator, and the vibration amplitude distributions in radial and circumferential directions are gained. Study result indicates that there are obvious deformations on the two standing waves, which cause the motion trajectories of the surface particles are inconsistent.

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