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Related Concept Videos

Electric Field of Parallel Conducting Plates01:16

Electric Field of Parallel Conducting Plates

Gauss' law relates the electric flux through a closed surface to the net charge enclosed by that surface. Gauss's law can be applied to find the electric field and the charge enclosed in a region depending on its charge distribution.
Consider a cross-section of a thin, infinite conducting plate having a positive charge. For such a large thin plate, as the thickness of the plate tends to zero, the positive charges lie on the plate's two large faces. Without an external electric field, the...
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When a flat plate is submerged in a fluid, the fluid exerts pressure on the plate. This pressure can lead to many different phenomena, including drag and buoyancy. To understand the behavior of the fluid over a flat plate of variable width, it is essential to analyze the distribution of the pressure exerted.
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Lens-free Video Microscopy for the Dynamic and Quantitative Analysis of Adherent Cell Culture
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Far-field approximation for a point-excited anisotropic plate.

Elizabeth A Magliula1, J Gregory McDaniel, Allan D Pierce

  • 1NAVSEA Newport, Newport, Rhode Island 02841-5047, USA. elizabeth.magliula@navy.mil

The Journal of the Acoustical Society of America
|June 21, 2012
PubMed
Summary

This study presents an analytic approximation for anisotropic plate response to point forces. The method accurately predicts flexural wave directivity, aiding in anisotropic plate design and testing.

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Area of Science:

  • Solid Mechanics
  • Wave Propagation
  • Materials Science

Background:

  • Anisotropic plates exhibit complex wave propagation behavior.
  • Understanding far-field response is crucial for structural analysis and design.
  • Existing methods may lack analytical precision for anisotropic materials.

Purpose of the Study:

  • To derive an analytic approximation for the far-field response of anisotropic plates.
  • To quantify the directivity of flexural waves generated by a normal point force.
  • To provide a tool for the design and testing of anisotropic plate structures.

Main Methods:

  • Utilized a two-dimensional Fourier transform of the flexural equation of motion.
  • Employed contour integration and the method of stationary phase for spatial inversion.
  • Validated the approximation against numerical simulations for layered composite plates.

Main Results:

  • Developed an approximation for far-field response, accounting for anisotropy.
  • The approximation shows angle-dependent wave numbers, amplitudes, and phases.
  • Numerical results demonstrate good agreement with discrete Fourier analysis simulations.

Conclusions:

  • The derived analytic approximation is accurate for predicting flexural wave directivity in anisotropic plates.
  • The method is effective for distances greater than a few wavelengths.
  • This approximation serves as a valuable tool for engineering applications involving anisotropic plates.