The Accuracy of Doubly Asymptotic Approximations for an Acoustic Half-Space

1992 ◽  
Vol 114 (4) ◽  
pp. 555-563 ◽  
Author(s):  
M. Hasheminejad ◽  
T. L. Geers
Keyword(s):  
Half Space ◽  
Acoustic Impedance ◽  
Spherical Surface ◽  
Broad Band ◽  
Asymptotic Approximations ◽  
Rigid Surface ◽  
Planar Boundary ◽  
First Order ◽  
Pressure Surface ◽  
Bispherical Coordinates

The accuracy of doubly asymptotic approximations (DAAs) for acoustic half-space problems is assessed by examining their performance for a canonical problem in bispherical coordinates. Exact specific acoustic impedance curves for axisymmetric modal vibrations of a spherical surface near a planar boundary are generated, and corresponding curves based on the first-order DAA and the curvature-corrected DAA are compared with their exact counterparts. The comparisons show that the curvature-corrected DAA is substantially more accurate than the first-order DAA. Also, the curvature-corrected DAA is found to be satisfactory for broad-band excitations regardless of the sphere’s proximity to a compliant (zero-pressure) surface; for a rigid surface, the approximation is satisfactory only if the sphere is located at least one diameter away from the boundary.

Reconstruction of Acoustic Radiation of a Vibrating Structure Located in a Half-Space Bounded by a Passive Surface with Finite Acoustic Impedance

2020 ◽  
Vol 28 (04) ◽  
pp. 2050019
Author(s):  
Daren Zhou ◽  
Huancai Lu ◽  
D. Michael McFarland ◽  
Yongxiong Xiao
Keyword(s):  
Half Space ◽  
Acoustic Impedance ◽  
Free Space ◽  
Plane Surface ◽  
Spherical Wave ◽  
Boundary Surface ◽  
Sound Field ◽  
Wave Functions ◽  
Reconstruction Method ◽  
Direct Radiation

Vibrating structures are often mounted on or located near a passive plane surface with finite acoustic impedance, and hence the acoustic pressures measured in a half-space bounded by the surface consist of both the direct radiation from the structure and the reflection from the boundary surface. In order to visualize the direct radiation from the source into free space, a reconstruction method based on expansion in half-space spherical wave functions is proposed. First, the series of half-space spherical wave functions is derived based on the analytical solution of the sound field due to a multipole source located near an impedance plane. Then the sound field in the half-space is approximated by the superposition of a finite number of half-space expansion terms. The expansion coefficients are determined by solving an overdetermined linear system of equations obtained by matching this assumed solution to the total acoustic pressures in the half-space. The free-space radiation can finally be reconstructed via multiplying the free-space spherical wave functions by the corresponding coefficients. Numerical simulation examples of a vibrating sphere and a vibrating baffled plate are demonstrated. The effects of specific acoustic impedance of the boundary and the locations of the measurement points on the accuracy of reconstruction are examined.

Friction Reduction in the Sliding of an Elastic Half-Space Against a Rigid Surface Due to Incident Rectangular Dilatational Waves

1999 ◽  
Vol 122 (1) ◽  
pp. 10-15 ◽  
Author(s):  
George G. Adams
Keyword(s):  
Normal Stress ◽  
Half Space ◽  
Coefficient Of Friction ◽  
Tangential Velocity ◽  
Elastic Half Space ◽  
Body Waves ◽  
Friction Reduction ◽  
Rigid Surface ◽  
Rectangular Wave ◽  
The Coefficient Of Friction

The steady sliding of a flat homogeneous and isotropic elastic half-space against a flat rigid surface, under the influence of incident plane dilatational waves, is investigated. The interfacial coefficient of friction is constant with no distinction between static and kinetic friction. It is shown here that the reflection of a harmonic wave under steady sliding consists of a pair of body waves (a plane dilatational wave and a plane shear wave) radiated from the sliding interface. Each wave propagates at a different angle such that the trace velocities along the interface are equal and supersonic. The angles of wave propagation are determined by the angle of the incident wave, by the Poisson’s ratio, and by the coefficient of friction. The amplitude of the incident waves is subject only to the restriction that the perturbations in interface contact pressure and tangential velocity satisfy the inequality constraints for unilateral sliding contact. It is also found that an incident rectangular wave can allow for relative sliding motion of the two bodies with a ratio of remote shear to normal stress which is less than the coefficient of friction. Thus the apparent coefficient of friction is less than the interface coefficient of friction. This reduction in friction is due to periodic stick zones which propagate supersonically along the interface. The influences of the angle, amplitude, and shape of the incident rectangular wave, the interfacial friction coefficient, the sliding speed, and of the remotely applied normal stress, on friction reduction are determined. Under appropriate conditions, the bodies can move tangentially with respect to each other in the absence of an applied shear stress. [S0742-4787(00)00201-0]

Time delays in geophysical consolidation problems

1984 ◽  
Vol 74 (4) ◽  
pp. 1275-1287
Author(s):  
Edo Nyland ◽  
Antonio Uribe-Carvajal
Keyword(s):  
Physical Properties ◽  
Half Space ◽  
Time Delays ◽  
Delayed Response ◽  
Stress Increment ◽  
First Order ◽  
Boundary Change ◽  
History Of ◽  
Consistent Formulation ◽  
First Order Differential Equations

Abstract The tectonic response of the lithosphere to loads applied over a period of years is one of the few relatively direct ways of measuring lithospheric mechanical properties. We discuss here a method for estimating gross permeability of shallow lithosphere if such a lithosphere can be modeled as a Biot solid. Induced seismicity at artificial lakes sometimes lags the history of lake filling. Clearly this indicates the anomalous load takes some finite time to create a stress increment over the tectonic regime associated with the lake. Such delays may result from diffusion into inhomogeneous regimes, but intuitively it seems that the Biot consolidation theory ought to contain the physics required to produce delayed response in the simplest model, an isotropic half-space with arbitrary vertical layering. The response of such a half-space can be calculated most quickly from matrix solutions of first-order differential equations. We explore here a consistent formulation for the physics of the problem and examine the relation between the rate of diffusion of changes on the boundary, the geometry of the boundary change, and the physical properties of the material. The resulting formulas can be used to estimate probable delays in response of the physical system. Unfortunately, the values of physical properties required to make such estimates are hard to obtain.

scholarly journals Transient frictionless contact of a rough rigid surface on a viscoelastic half-space

2017 ◽  
Vol 113 ◽  
pp. 279-285 ◽  
Author(s):  
R. Bugnicourt ◽  
P. Sainsot ◽  
N. Lesaffre ◽  
A.A. Lubrecht
Keyword(s):  
Half Space ◽  
Rigid Surface ◽  
Frictionless Contact

Convective magnetic fields in a dispersive half-space

2010 ◽  
Vol 466 (2120) ◽  
pp. 2383-2400 ◽  
Author(s):  
Gabriel Barton
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Frequency Response ◽  
Half Space ◽  
Frequency Response Function ◽  
First Order ◽  
Instantaneous Position ◽  
The Magnetic Field ◽  
Insight Into ◽  
Zero Frequency

It is known that inside a material half-space the magnetic field B owing to the currents generated there by a slowly moving exterior charge (velocity u ) is almost the same whether the material is a good Ohmic conductor or a highly refractive non-dispersive/non-dissipative insulator. By contrast, the drag force experienced by the charge is completely different for conductors and insulators. To gain insight into the somewhat surprising coincidence regarding B fields, we study a microscopic model whose macroscopic Drude-type dielectric function ε ( ω ) can fit a fair variety of dispersion and dissipation. We look for B only to first order in u / c , but with otherwise arbitrary u . Then, B is given by the Biot–Savart rule. The term linear in u follows directly from the polarization produced as if electrostatically by the charge in its instantaneous position, and depends only on ε (0), the strictly static (zero frequency) response function; only the corrections of higher order in u depend on just how ε varies with ω , and we determine the first such corrections.

Quasi‐static transient response of a conducting half‐space— An approximate representation

Geophysics ◽  
1979 ◽  
Vol 44 (10) ◽  
pp. 1700-1705 ◽  
Author(s):  
Misac N. Nabighian
Keyword(s):  
Half Space ◽  
Transient Response ◽  
Order Approximation ◽  
Step Function ◽  
Approximate Representation ◽  
Current Filament ◽  
First Order ◽  
First Order Approximation

For a step‐function excitation, it is shown that, to a first‐order approximation, the quasi‐static transient response in the air due to an arbitrary loop situated at the earth’s surface can be represented by a downward and outward moving current filament, of diminishing amplitude and having the same shape as the transmitter loop.

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