Displacement of a bubble located at a fluid-viscoelastic medium interface

Abstract A comprehensive investigation on the static and dynamic responses of a sphere located at elastic and viscoelastic medium interfaces is performed in this study. First, the mathematical models commonly used for predicting the static displacement of a sphere located at an elastic medium interface are presented and their performances are compared. After that, based on the finite element analyses, an accurate mathematical model to predict the static displacement of a sphere located at an elastic medium interface valid for different Poisson’s ratios of the medium and small and large sphere displacements is proposed. Then, an improved mathematical model for the dynamic response of a sphere located at a viscoelastic medium interface is developed. In addition to the Young’s modulus of the medium and the radius of the sphere, the model takes into account the density, Poisson’s ratio and viscosity of the medium, the mass of the sphere and the radiation damping. The effects of the radiation damping, the Young’s modulus, density and viscosity of the medium and the density of the sphere on the dynamic response of the sphere located at a viscoelastic medium interface are explored. The developed model can be used to understand the dynamic responses of spherical objects located at viscoelastic medium interfaces in practical applications. Furthermore, the proposed model is a significant tool for graduate students and researchers in the fields of engineering, materials science and physics to gain insight into the dynamic responses of spheres located at viscoelastic medium interfaces.

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Two-Dimensional Solitary Waves in a Strained Nonlinear Viscoelastic Medium

Acoustical Physics ◽

10.1134/1.29853 ◽

2000 ◽

Vol 46 (1) ◽

pp. 100 ◽

Cited By ~ 1

Author(s):

G. A. Arshinov

Keyword(s):

Solitary Waves ◽

Viscoelastic Medium ◽

Two Dimensional ◽

Nonlinear Viscoelastic ◽

Nonlinear Viscoelastic Medium

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Three dimensional waves propagation in thermo-viscoelastic medium with two temperature and void

IOP Conference Series Materials Science and Engineering ◽

10.1088/1757-899x/1033/1/012059 ◽

2021 ◽

Vol 1033 ◽

pp. 012059

Author(s):

K.D. Sharma ◽

Rajneesh Kumar ◽

Mohit Kumar Kakkar ◽

Suniti Ghangas

Keyword(s):

Viscoelastic Medium ◽

Three Dimensional ◽

Waves Propagation ◽

Two Temperature

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On computing ray‐synthetic seismograms for anelastic media using complex rays

Geophysics ◽

10.1190/1.1442851 ◽

1990 ◽

Vol 55 (4) ◽

pp. 422-432 ◽

Cited By ~ 27

Author(s):

D. J. Hearn ◽

E. S. Krebes

Keyword(s):

Surface Layer ◽

Plane Wave ◽

Saddle Point ◽

Viscoelastic Medium ◽

Observation Point ◽

Acute Angle ◽

Synthetic Seismograms ◽

Propagation Angle ◽

Source Point ◽

Complex Rays

A plane wave propagating in a viscoelastic medium is generally inhomogeneous, meaning that the direction in which the spatial rate of amplitude attenuation is maximum is generally different from the direction of travel. The angle between these two directions, which we call the “attenuation angle,” is an acute angle. In order to trace the ray corresponding to a plane wave propagating between a source point and a receiver point in a layered viscoelastic medium, one must know both the initial propagation angle (the angle that the raypath makes with the vertical) and the initial attenuation angle at the source point. In some recent literature on the computation of ray‐synthetic seismograms in anelastic media, values for the initial attenuation angle are chosen arbitrarily; but this approach is fundamentally unsatisfactory, since different choices lead to different results for the computed waveforms. Another approach, which is more deterministic and physically acceptable, is to deduce the value of the initial attenuation angle from the value of the complex ray parameter at the saddle point of the complex traveltime function. This value can be obtained by applying the method of steepest descent to evaluate approximately the integrals giving the exact wave field at the observation point. This well‐known technique results in the ray‐theory limit. The initial propagation angle can also be determined from the saddle point. Among all possible primary rays between source and receiver, each having different initial propagation and attenuation angles, the ray determined by the saddle point, which we call a “stationary ray,” has the smallest traveltime, a result which is consistent with Fermat’s principle of least time. Such stationary rays are complex rays, i.e., the spatial (e.g., Cartesian) coordinates of points on stationary raypaths are complex numbers, whereas the arbitrarily determined rays mentioned above are usually traced as real rays. We compare examples of synthetic seismograms computed with stationary rays with those from some arbitrarily determined rays. If the initial value of the attenuation angle is arbitrarily chosen to be a constant for all initial propagation angles, the differences between the two types of seismograms are generally small or negligible in the subcritical zone, except when the constant is relatively large in value, say, within 10 degrees or so of its upper bound of 90 degrees. In that case, the differences are significant but still not large. However, if the surface layer is highly absorptive, the differences can be quite large and pronounced. For larger offsets, i.e., in the supercritical zone, large phase discrepancies can exist between the waveforms for the stationary rays and those for the arbitrarily determined rays, even if the constant initial attenuation angle is not large and even for moderate absorptivity in the surface layer.

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