Nonlinear wave motion governed by the modified Burgers equation

Lee-Bapty, I.P.; Crighton, D. G.

doi:10.1098/rsta.1987.0081

Cited by 64 publications

(18 citation statements)

References 16 publications

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“…For parts 3 (left curve), 4 (tail shock), 5 (right curve) and 6 (head shock) analytic lowest approximation solutions are given by Lee-Bapty and Crighton [10]. For part 7 (right tail) an analytic solution is still not yet found.…”

Section: Propagating N-waves In a Cubically Nonlinear Mediummentioning

confidence: 99%

Standing and propagating waves in cubically nonlinear media

Enflo¹,

Hedberg²,

Руденко³

2006

AIP Conference Proceedings

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Abstract. The paper has three parts. In the first part a cubically nonlinear equation is derived for a transverse finite-amplitude wave in an isotropic solid. The cubic nonlinearity is expressed in terms of elastic constants. In the second part a simplified approach for a resonator filled by a cubically nonlinear medium results in functional equations. The frequency response shows the dependence of the amplitude of the resonance on the difference between one of the resonator's eigenfrequencies and the driving frequency. The frequency response curves are plotted for different values of the dissipation and differ very much for quadratic and cubic nonlinearities. In the third part a propagating N-wave is studied, which fulfils a modified Burgers' equation with a cubic nonlinearity. Approximate solutions to this equation are found for new parts of the wave profile.

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Section: Propagating N-waves In a Cubically Nonlinear Mediummentioning

confidence: 99%

Standing and propagating waves in cubically nonlinear media

Enflo¹,

Hedberg²,

Руденко³

2006

AIP Conference Proceedings

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“…In some special cases it is reducible to cubic Burgers-type equation studied in Ref. [9] for plane waves and in Ref. [5,10] for spatially-limited beams.…”

Section: Cubic Resonatormentioning

confidence: 99%

Standing Waves In Quadratic And Cubic Nonlinear Resonators: Q-Factor And Frequency Response

Enflo¹,

Hedberg²,

Руденко³

2006

AIP Conference Proceedings

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Abstract. High-Q acoustic resonators are used to significantly increase the wave energy volume density. For high-intensity waves the magnitude of Q-factor is determined not only by the design of the resonator, but by the strength of internal field as well. Methods to calculate the Q-factor and both the spatio-temporal and spectral structure of this field are described. Results are given for quadratic and cubic nonlinear resonators demonstrating quite different physical properties.

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“…For example, the shock formation time is on the order of the inverse square of the wave amplitude when the nonlinearity is cubic as compared to inversely proportional when the nonlinearity is quadratic. A more complete discussion of these nonclassical dynamics may be found in the thesis by Lee-Bapty ( 1981 ) or the article by Lee-Bapty and Crighton (1987).…”

Section: Introductionmentioning

confidence: 99%

“…A more detailed study of the distortion of shear waves is presented by Lee-Bapty ( 1981 ) who demonstrated that the basic wave evolution is fundamentally different than that exhibited by longitudinal waves. The nonlinearity of relatively weak longitudinal waves is quadratic leading to the generation of second harmonics when wave trains are considered, whereas the nonlinearity of shear waves in an initially unstrained matehal is seen to be cubic.…”

Section: Introductionmentioning

confidence: 99%

Nonlinearity parameters for pulse propagation in isotropic elastomers

Carman

Cramer

1992

The Journal of the Acoustical Society of America

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The propagation of one-dimensional shear waves in isotropic hyperelastic materials is examined. Both compressible and incompressible materials subject to arbitrarily large shear prestrains are considered. The nonlinear evolution equation governing small disturbances on prestrained undisturbed states is derived. The prestrain is seen to change the nonlinearity from the cubic form found in the unstrained case to the stronger quadratic form governed by the conventional Burgers' equation. Additional results include explicit and general expressions for the quadratic and cubic nonlinearity parameters. Numerical estimates are also provided for natural rubber and foamed polyurethane. It is demonstrated that the quadratic nonlinearity parameter does not increase monotonically with prestrain and may actually vanish at nonzero values of the prestrain.

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Nonlinear wave motion governed by the modified Burgers equation

Abstract: The modified Burgers equation (MBE) &PartialD; V &PartialD; X + V 2 &PartialD; V … Show more

Cited by 64 publications

References 16 publications

Standing and propagating waves in cubically nonlinear media

Standing and propagating waves in cubically nonlinear media

Standing Waves In Quadratic And Cubic Nonlinear Resonators: Q-Factor And Frequency Response

Nonlinearity parameters for pulse propagation in isotropic elastomers

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