Nonlinear bulk and surface shear acoustic waves in materials with hysteresis and end-point memory

Abstract Nonlinear shear wave propagation in inhomogeneous materials is described by evolution equations in which second-order nonlinear processes account for hysteresis and end-point memory phenomena. It is demonstrated that odd harmonic generation and hysteresis absorption lead to the transformation of a monochromatic signal into a sawtooth-shaped wave. Nonlinear refraction phenomena cause an instability of the plane waves, self-trapping of acoustic beams and the existence of a nonlinear shear horizontal surface acoustic wave.

[1]  David J. Holcomb,et al.  Memory, relaxation, and microfracturing in dilatant rock , 1981 .

[2]  M. Breazeale,et al.  ULTRASONIC NONLINEAR PROPERTIES OF LEAD ZIRCONATE-TITANATE CERAMICS , 1994 .

[3]  V. Nazarov,et al.  Sound damping by sound in metals , 1991 .

[4]  Paul A. Johnson,et al.  Resonance and elastic nonlinear phenomena in rock , 1996 .

[5]  Isaak D. Mayergoyz,et al.  Hysteresis models from the mathematical and control theory points of view , 1985 .

[6]  Paul A. Johnson,et al.  Nonlinear Generation of Elastic Waves in Crystalline Rock , 1987 .

[7]  Paul A. Johnson,et al.  On the quasi-analytic treatment of hysteretic nonlinear response in elastic wave propagation , 1997 .

[8]  McCall,et al.  Hysteresis, Discrete Memory, and Nonlinear Wave Propagation in Rock: A New Paradigm. , 1995, Physical review letters.

[9]  Stephen H. Hickman,et al.  Hysteresis in the closure of a nominally flat crack , 1983 .

[10]  R. Khokhlov,et al.  Reviews of Topical Problems: Self-Focusing and Diffraction of Light in a Nonlinear Medium , 1968 .

[11]  P. Johnson,et al.  Observation and implications of nonlinear elastic wave response in rock , 1994 .

[12]  Paul A. Johnson,et al.  Observations of nonlinear elastic wave behavior in sandstone , 1993 .

[13]  Paul A. Johnson,et al.  Nonlinear generation of elastic waves in granite and sandstone: Continuous wave and travel time observations , 1989 .

[14]  A. Mayer.  Surface acoustic waves in nonlinear elastic media , 1995 .

[15]  J. Thoen,et al.  Theory for the time evolution of nonlinear Rayleigh waves in an isotropic solid , 1997 .

[16]  P. Johnson,et al.  Evaluating hysteresis in earth materials under dynamic resonance , 1996 .

[17]  Veniamin E. Nazarov,et al.  Nonlinear acoustics of micro-inhomogeneous media , 1988 .

[18]  V. Mozhaev.  A new type of surface acoustic waves in solids due to nonlinear elasticity , 1989 .

[19]  M. Toksöz,et al.  Inversion of seismic velocities for the pore aspect ratio spectrum of a rock , 1979 .

[20]  J. B. Walsh.  The effect of cracks on the compressibility of rock , 1965 .

[21]  V. A. Krasil'nikov,et al.  Reviews of Topical Problems: Nonlinear Phenomena in the Propagation of Elastic Waves in Solids , 1971 .

[22]  Robert A. Guyer,et al.  Equation of state and wave propagation in hysteretic nonlinear elastic materials , 1994 .

[23]  Charles Elbaum,et al.  Generation of Ultrasonic Second and Third Harmonics due to Dislocations. II , 1966 .

[24]  Oleg V. Rudenko,et al.  Theoretical Foundations of Nonlinear Acoustics , 1977 .