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Related Concept Videos

Sound as Pressure Waves01:17

Sound as Pressure Waves

Sound waves, which are longitudinal waves, can be modeled as the displacement amplitude varying as a function of the spatial and temporal coordinates. As a column of the medium is displaced, its successive columns are also displaced. As the successive displacements differ relatively, a pressure difference with the surrounding pressure is created. The gauge pressure varies across the medium.
The pressure fluctuation depends on the difference in displacements between the successive points in the...
Stress Concentrations in Circular Shafts01:18

Stress Concentrations in Circular Shafts

Consider the elastic torsion formula, which applies to a circular shaft with a consistent cross-section. This formula assumes that the shaft's ends are loaded with rigid plates firmly attached. However, in many cases, torques are applied to the shaft through mechanisms like flange couplings or gears, which are connected by keys inserted into keyways. This application method modifies the stress distribution near the point of torque application, causing it to deviate from the distributions...
Stress Concentrations01:13

Stress Concentrations

The concept of stress concentration is crucial for understanding how materials respond under bending stresses, particularly when there are irregularities or discontinuities in the material's geometry. Normally, stress in a symmetric member subjected to pure bending is assumed to be uniformly distributed across the entire cross-section. However, this assumption does not hold when there are variations in the cross-sectional geometry or the presence of notches and holes.
The stress concentration...
Stress Concentrations01:24

Stress Concentrations

Stress concentration is when stress intensifies near discontinuities such as holes or abrupt cross-sectional changes in a structural member. This localized stress can often surpass the average stress within the member. The stress distribution in flat bars, either with a circular hole or varying widths connected by fillets, can be determined experimentally using a photoelastic method. The results are based on ratios of geometric parameters like the ratio of the hole's radius to the smaller width...
Elastic Strain Energy for Shearing Stresses01:20

Elastic Strain Energy for Shearing Stresses

As discussed in previous lessons, strain energy in a material is the energy stored when it is elastically deformed, a concept crucial in materials science and mechanical engineering. This energy results from the internal work done against the cohesive forces within the material. When a material undergoes shearing stress and corresponding shearing strain, the strain energy density, which is the energy stored per unit volume, is calculated. Within the elastic limit, where the stress is...
Intensity and Pressure of Sound Waves01:05

Intensity and Pressure of Sound Waves

The intensity of sound waves can be related to displacement and pressure amplitudes by using their wave expressions and the definition of intensity. The critical step to achieve this is to write the power delivered by the particles on the wave as the product of force and velocity and simplify the force per unit area as the pressure. The velocity of the medium's particles can be derived from the displacement.
Unlike the time average of a sinusoidal term, which is zero since it is positive and...

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Induction of Microstreaming by Nonspherical Bubble Oscillations in an Acoustic Levitation System
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Experiments on stress dependent borehole acoustic waves.

Chaur-Jian Hsu1, Michael R Kane, Kenneth Winkler

  • 1Schlumberger-Doll Research, One Hampshire Street, Cambridge, Massachusetts 02139, USA.

The Journal of the Acoustical Society of America
|October 7, 2011
PubMed
Summary
This summary is machine-generated.

This study quantifies sandstone elastic parameters under uniaxial stress using borehole acoustic wave analysis. Results predict borehole wave characteristics, aiding geomechanical assessments.

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Published on: August 7, 2018

Area of Science:

  • Geophysics
  • Rock Mechanics
  • Acoustics

Background:

  • Boreholes in rock formations are subject to stress, inducing anisotropy.
  • Understanding stress-induced anisotropy is crucial for accurate geophysical well logging and reservoir characterization.

Purpose of the Study:

  • To quantify linear and non-linear elastic parameters of sandstone under uniaxial stress.
  • To predict borehole acoustic wave characteristics using measured elastic parameters and elastic theories.

Main Methods:

  • Laboratory experiments on a dry sandstone core under controlled uniaxial stress (0-10 MPa).
  • Generation and detection of acoustic waves (compressional, shear, monopole, dipole, quadrupole) in a water-filled borehole.
  • Independent quantification of linear and non-linear elastic parameters.

Main Results:

  • Uniaxial stress and borehole presence induce azimuthal and radial anisotropy and stress concentration.
  • An analytic theory successfully estimated changes in low-frequency monopole tube waves due to uniaxial stress.
  • Experimental and theoretical predictions of borehole wave characteristics were compared.

Conclusions:

  • Measured third-order elastic parameters accurately predict stress-induced changes in borehole acoustic wave behavior.
  • The study provides a framework for utilizing elastic parameters to understand borehole wave propagation under stress.
  • This research enhances the interpretation of acoustic data in stressed rock formations.