Summary
Rayleigh waves excited by an impulsive force imbedded in a linear viscoelastic half-space are synthesized by applying an approximate inversion of the Fourier transform which yields reliable results. The method is general enough and can be applied to general models of viscoelasticity described by the Boltzmann superposition principle, with a relaxation or creep function given analytically or numerically in the time or frequency domain. Illustrations are given in cases of simple and complicated models of viscoelasticity.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
H. Kolsky, The Propagation of Stress Waves in Viscoelastic Solids,Applied Mechanics Surveys (1966) 841–846.
C. C. Chao and J. D. Achenbach, A Simple Viscoelastic Analogy for Stress Waves,Stress Waves in Anelastic Solids, H. Kolsky and W. Prager (Eds.), Springer, Berlin (1964) 222–238.
Y. M. Tsai and H. Kolsky, Surface Wave Propagation for Linear Viscoelastic Solids,J. Mech. Phys. Solids, 16 (1968) 99–109.
I. Abubakar, On the Buried Source in a Viscoelastic Half-Space,Pure Appl. Geophys., 72 (1969) 51–60.
J. W. Cooley and J. W. Tukey, An Algorithm for the Machine Calculation of Complex Fourier Series,Math. Comp., 19 (1965) 297–301.
J. Aboudi, Propagation of Transient Pulses from a Spherical Cavity in a Viscoelastic Medium,Int. J. for Num. Meth. in Eng. 4 (1972) 289–299.
C. H. Moke, Effective Dynamic Properties of a Fiber-reinforced Material and the Propagation of Sinusoidal Waves,J. Acoust. Soc. Am., 46 (1969) 631–638.
J. A. Hudson, The Attenuation of Surface Waves by Scattering,Proc. Comb. Phil. Soc., 67 (1970) 215–223.
C. L. Pekeris, The Seismic Surface Pulse,Proc. Nat. Acad. Sci., 41 (1955) 469–480.
G. F. Miller and H. Pursey, The Field and Radiation Impedance of Mechanical Radiators on the Free Surface of a Semi-Infinite Isotropic Solid,Proc. Roy. Soc. A, 223 (1954) 521–541.
M. Ewing, W. Jardetzky and F. Press,Elastic Waves in Layered Media, McGraw-Hill Book Company, New York (1957) 132–135.
A. Papoulis,The Fourier Integral and its Applications, McGraw-Hill Book Company, New York (1962).
D. R. Bland,The Theory of Linear Viscoelasticity, Pergamon Press, Inc., New York (1960).
H. Kolsky,Stress Waves in Solids, Dover Pub., New York (1952).
L. Knopoff and G. J. F. MacDonald, Attenuation of Small Amplitude Stress Waves in Solids,Rev. Mod. Phys., 30 (1958) 1178–1192.
C. Lomnitz, Linear Dissipation in Solids,J. Appl. Phys., 28 (1957) 201–205.
C. Lomnitz, Application of the Logarithmic Creep Law to Stress Wave Attenuation in the Solid Earth,J. Geophys. Res., 67 (1962) 365–368.
M. Abramovitz and I. A. Stegun,Handbook of Mathematical Functions, Dover Pub., Inc., New York (1965).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Aboudi, J. Rayleigh wave propagation in a viscoelastic half-space. J Eng Math 6, 313–321 (1972). https://doi.org/10.1007/BF01535192
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01535192