Standing Wave Phenomenon Research Articles

On Standing Waves in Tires

Abstract By using a comprehensive rotating laminated shell model of the tire, the effects of viscoelastic damping on the standing wave phenomenon are investigated in more detail than was previously possible. The shell theory employed is a nonlinear version of Novoshilov's work and the onset of the standing wave is characterized as a small dynamic deformation superposed on a finite deformation. To expand the scope of the model, the viscoelastic constitutive law is treated as either of the differential or hereditary integral type. The solution for the stated model is obtained by the finite element procedure, and the results of several numerical experiments are presented. The substantial role of viscoelastic effects in the development of the standing wave phenomenon of tires is emphasized by the results.

On Viscoelasticity and Standing Waves in Tires

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.

On the dynamic response of rolling tires according to thin shell approximations

The response of the rolling tire is formulated in terms of the natural modes and frequencies of the non-contacting tire for contact loading due to rolling, braking, accelerating or cornering. The tire is viewed as an equivalent thin shell. Formulation is by way of the three-dimensional dynamic Green function of this shell. As the application example, the response of the tire during pure rolling is evaluated. The critical rolling speed at which the tire develops its first large amplitude standing waves is calculated in a novel fashion, showing the relationship between the standing wave phenomenon and natural tire modes and frequencies. Findings underline the need for measuring or calculating higher order tire modes than those considered in what seems to be the present standard practice.

A theory for multiple fire-whirl formation

In an effort to gain a better understanding of the mechanics involved in the formation ofvortices in buoyancy driven flows, an analysis on the stability of the laminar free convection, due to a line source of heat with ambient shear, was performed by numerical solution of a viscous linear stability equation. The formation yielded a curve of neutral stability, based on plume thickness and ambient shear, delineating stable and unstable domains. It was thereby indicated that increased buoyancy increases stability at a given elevation in the flow field, and that the instability first occurs at a critical elevation. This critical elevation increases with buoyancy strength, but decreases with ambient shear. The solution yielded that the disturbed motion must be a standing-wave phenomenon, of thetype typically developing into vortex flows. For a given disturbance wavelength, the analysis demonstrated a periodic row of vortices, and an optimization analysis of all wavelengths indicated that the flow should break up into a vortex pattern at a most unstable wavelength or vortex spacing upon the attainment of a most unstable plume thickness Reynolds Number. These results have been found to agree closely, in functional form, with experimental results on the formation of multiple fire whirls. In the natural occurrence of vortices, the analysis suggested that the vertical distribution of ambient vorticity is a determinant factor. It was also indicated that a strong enough convection column can overpower the ambient vorticity and thereby prevent or destroy a vortex flow.

Nature of Non-Volcanic Microtremor Observed on the Aso Caldera

Seismic measurements at over seventy points on the Aso caldera have revealed the nature of stationary ground tremor on the atrio area, which cannot be attributed to traffic passage nor to the volcanic activity.The tremor is sinusoidal and stationary, the wave characteristics suffering little temporal change at any fixed point. On the contrary, it changes remarkably with change of observation location.The spatial trend of observed waveform has a definite correlation with the topography, which suggests the possibility of its usefulness to structural interpretations of the Aso caldera.The particle motion at the ground surface is observed to be confined in a horizontal plane. The spatial phase relation of the tremor shows that it is not a simple standing wave phenomenon but has a complicated propagating nature and that the particle motion is transversal to the direction of wave propagation.