The diffraction of a plane compressional elastic wave by a rigid circular disc

Author:
S. K. Datta

Journal:
Quart. Appl. Math. **28** (1970), 1-14

DOI:
https://doi.org/10.1090/qam/99806

MathSciNet review:
QAM99806

Full-text PDF Free Access

Abstract | References | Additional Information

Abstract: The paper deals with the low-frequency diffraction of a plane compressional elastic wave incident obliquely on a rigid circular disc embedded in an infinite elastic medium. The motion of the disc, both rotational and translational, has been discussed in detail. By letting the mass of the disc go to infinity one obtains the results for diffraction by a fixed disc. Far-field amplitude of the scattered field has also been obtained. This can be used to calculate the scattering cross-section of the disc. It is found that for long wavelengths the scattering coefficient varies as the fourth power of the wave number if the disc is movable, whereas it is independent of the wave number if the disc is fixed.

**[1]**D. S. Jones,*Diffraction at high frequencies by a circular disc*, Proc. Cambridge Philos. Soc.**61**, 223-245 (1965) MR**0171502****[2]**-,*Diffraction of a high-frequency plane electromagnetic wave by a perfectly conducting circular disc*, Proc. Cambridge Philos. Soc.**61**, 247-270 (1965) MR**0171503****[3]**K. A. Lure'e,*Diffraction of a plane electromagnetic wave on an ideally conducting circular disc*, Soviet Physics--Technical Physics**4**, 1313-1325 (1960)**[4]**A. K. Mal, D. D. Ang and L. Knopoff,*Diffraction of elastic waves by a rigid circular disc*, Proc. Cambridge Philos. Soc.**64**, 237-247 (1968)**[5]**I. N. Sneddon,*Fourier transforms*, McGraw-Hill, New York, 1951 MR**0041963****[6]**A. K. Mal,*Diffraction of elastic waves by a penny-shaped crack*, Quart. Appl. Math.**27**, 231-238 (1968) MR**0231573****[7]**I. A. Robertson,*Diffraction of a plane longitudinal wave by a penny-shaped crack*, Proc. Cambridge Philos. Soc.**63**, 229-238 (1967)**[8]**A. K. Mal,*Dynamic stress-intensity factor for a non-axisymmetric loading of the penny-shaped crack*, Int. J. Engng. Sci.**6**, 725-733 (1968)**[9]**P. J. Barratt and W. D. Collins,*The scattering cross-section of an obstacle in an elastic solid for plane harmonic waves*, Proc. Cambridge Philos. Soc.**61**, 969-981 (1965)**[10]**D. S. Jones,*On the scattering cross-section of an obstacle*, Philos. Mag.**46**, 957-962 (1955) MR**0082901****[11]**B. Noble,*The solution of Bessel function dual integral equation by multiplying factor method*, Proc. Cambridge Philos. Soc.**59**, 351-362 (1963) MR**0145311****[12]**-,*Integral equation perturbation methods in low-frequency diffractions*, in*Electromagnetic waves*, Ed. R. Langer, Univ. of Wisconsin Press, Madison, Wisc., 1962 MR**0135459****[13]**S. K. Datta,*A note on diffraction of plane compressional elastic waves by a rigid circular disc*(to appear).

Additional Information

DOI:
https://doi.org/10.1090/qam/99806

Article copyright:
© Copyright 1970
American Mathematical Society