• Volume/Page
  • Keyword
  • DOI
  • Citation
  • Advanced
   
 
 
 

Journal of the Acoustical Society of America

BROWSE VOLUMES

Year Range: 
Search Issue | RSS Feeds RSS
Previous Issue Next Issue

Apr 2010

Volume 127, Issue 4, pp. EL121-2714

Return to All Sections
back to top
RSS Feeds

A detailed analysis about penumbra caustics

Régis Marchiano

J. Acoust. Soc. Am. Volume 127, Issue 4, pp. 2129-2140 (2010); (12 pages)

Full Text: Read Online (HTML) | Download PDF

Show Abstract
A penumbra caustic is an interrupted fold caustic. It looks like a fold caustic but with a finite size. This kind of caustic results from the focusing of a semi-infinite concave wavefront. The pressure around the extremity of the penumbra caustic can be expressed analytically in terms of incomplete Airy function for linear monochromatic waves. Using asymptotic expansions in the vicinity of the extremity, that classical result is rederived. It can be matched with the classical Fresnel diffraction before the extremity and with the classical diffraction catastrophe theory after the extremity. Nevertheless the linear modeling is not valid for incoming shock waves. A theoretical description of the phenomenon of focusing of shock waves at a penumbra caustic is given. It relies on the Zabolotskaya–Khokhlov equation. Numerical simulations are used to compute the behavior of this phenomenon. In particular, the numerical simulations show the presence of a triple point inside the pressure field. Finally, the theory and the numerical simulations are applied to explain the apparent paradox of non-causality around fold caustic.
Show PACS
43.25.Cb Macrosonic propagation, finite amplitude sound; shock waves
43.25.Jh Reflection, refraction, interference, scattering, and diffraction of intense sound waves

Characteristics of second harmonic generation of Lamb waves in nonlinear elastic plates

Martin F. Müller, Jin-Yeon Kim, Jianmin Qu, and Laurence J. Jacobs

J. Acoust. Soc. Am. Volume 127, Issue 4, pp. 2141-2152 (2010); (12 pages) | Cited 12 times

Full Text: Read Online (HTML) | Download PDF

Show Abstract
This paper investigates the characteristics of the second harmonic generation of Lamb waves in a plate with quadratic nonlinearity. Analytical asymptotic solutions to Lamb waves are first obtained through the use of a perturbation method. Then, based on a careful analysis of these asymptotic solutions, it is shown that the cross-modal generation of a symmetric second harmonic mode by an antisymmetric primary mode is possible. These solutions also demonstrate that modes showing internal resonance—nonzero power flux to the second harmonic mode, plus phase velocity matching—are most useful for measurements. In addition, when using finite wave packets, which is the case in most experimental measurements, group velocity matching is required for a cumulative increase in the second harmonic amplitude with propagation distance. Finally, five mode types (which are independent of material properties) that satisfy all three requirements for this cumulative increase in second harmonic amplitude—nonzero power flux, plus phase and group velocity matching—are identified. These results are important for the development of an experimental procedure to measure material nonlinearity with Lamb waves.
Show PACS
43.25.Dc Nonlinear acoustics of solids
43.20.Mv Waveguides, wave propagation in tubes and ducts
43.35.Cg Ultrasonic velocity, dispersion, scattering, diffraction, and attenuation in solids; elastic constants

Limiting factors in acoustic separation of carbon particles in air

David Karpul, Jonathan Tapson, Michael Rapson, Adrian Jongens, and Gregory Cohen

J. Acoust. Soc. Am. Volume 127, Issue 4, pp. 2153-2158 (2010); (6 pages) | Cited 1 time

Online Publication Date: 05 Apr 2010

Full Text: Read Online (HTML) | Download PDF

Show Abstract
Particles suspended in a fluid that is exposed to an acoustic standing wave experience a time-averaged force that drives them to either the pressure nodes or anti-nodes of the wave. Several filter designs have been successfully implemented using this force to filter small particles in liquids with low flow rates and small cross-sectional areas. It has been suggested that the filtration of small solid particles out of a gas, such as carbon in air (smoke), would be a possible application of acoustic standing wave based particle separation. This study shows the limiting factors, in both power requirements and design factors, of an acoustic filter designed for filtering smoke particles across large cross-sectional areas. It is shown that while filtration is possible, the power needed is impractical. It is also shown that operating the filter within certain settling time parameters optimizes the energy usage of the filter.
Show PACS
43.25.Qp Radiation pressure
43.20.Ks Standing waves, resonance, normal modes
43.25.Gf Standing waves; resonance
Return to All Sections
Close

Home Publications Meetings Contact ASA Site Map Back to Top

Copyright © Acoustical Society of America

close