Dynamics of Viscoelastic Media with Internal Oscillators

Nikolaevskiĭ, V. N.

doi:10.1007/978-3-642-83695-4_21

Cited by 26 publications

(22 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The aim of publications (Nikolaevskiy 1989;Beresnev and Nikolàevskiy 1993) and this article is to explain the dominant frequency effect by free oscillations of porous matrix fragments (grains, for instance) under the complex elastic-viscous response of grain contacts, wetted with foreign fluid or fluid films of special state due to close presence of solid matter.…”

Section: Introductionmentioning

confidence: 99%

Non-linear Evolution of P-waves in Viscous–Elastic Granular Saturated Media

Nikolaevskiy

2007

Transp Porous Med

View full text Add to dashboard Cite

The Frenkel-Biot P-wave of the first type is a seismic longitudinal wave observed in rocks fully saturated with oil, water or high-pressure gas. The P-wave of the second type is observed in unsaturated soils and other porous media saturated with gas of low pressure. Their models include properties of the skeleton, that is, its elastic modules and its own viscosity. If the non-linear terms are accounted for, the asymptotic analysis, usual for weak non-linear waves, might be applied to get the wave spectrum evolution. The wetness of grains contacts in soils and such components of oil as tars or bitumen, which attached to the skeleton, can be described by generalized viscous-elastic stress-strain connections. The latter are nominated in such a way that creates the narrow frequency interval of wave of negative dissipation where the non-linear terms begin to play the main role besides the neutral stability for waves of zero wave number. The corresponding case, relevant to single continuum model, was analyzed in the literature. Here it is shown that the interpenetrating continua with interaction of the Darcy type provide the dissipation sink in the wave evolution equation. This generalization, (Tribelsky, M.I.: Phys. Rev. Lett. (2007, submitted)), can stabilize the asymptotic solution of the evolution equation, where the dispersion terms are omitted. The asymptotic solution of the equation is invariant to initial conditions and it means a transformation of initial wave spectra to unique one while wave is spreading in the viscous-elastic medium under consideration. This explains the phenomenon, observed in wave tests at marine beach, when any dynamics action (impact, explosion, and ultrasound action) created at some distance a wave of a single frequency (∼25 Hz).

show abstract

Section: Introductionmentioning

confidence: 99%

Non-linear Evolution of P-waves in Viscous–Elastic Granular Saturated Media

Nikolaevskiy

2007

Transp Porous Med

View full text Add to dashboard Cite

show abstract

“…As examples of such systems mention fronts of gasless combustion [1,2], certain 1 corresponding author, email: strunin@usq.edu.au, tel. : +61-7-4631-5541, fax: +61-7-4631-5550 type of reaction-diffusion systems [3,4,5] and seismic waves in fluid-saturated rocks [6].…”

Section: Introductionmentioning

confidence: 99%

Range of validity and intermittent dynamics of the phase of oscillators with nonlinear self-excitation

Strunin

Mohammed

2015

Communications in Nonlinear Science and Numerical Simulation

View full text Add to dashboard Cite

“…Reaction-diffusion systems exhibiting oscillatory dynamics near the Hopf bifurcation can be reduced to an evolution equation for the phase of oscillations [1,2] ∂ t ψ = a 1 ∇ 2 ψ + a 2 (∇ψ) 2 + b 1 ∇ 4 ψ + b 2 ∇ 3 ψ∇ψ + b 3 (∇ 2 ψ) 2 + b 4 ∇ 2 ψ(∇ψ) 2 + b 5 (∇ψ) 4 + g 1 ∇ 6 ψ + g 2 ∇ 5 ψ∇ψ + g 3 ∇ 4 ψ∇ 2 ψ + g 4 (∇ 3 ψ) 2 + g 5 ∇ 4 ψ(∇ψ) 2 + g 6 (∇ 2 ψ) 3 + g 7 ∇ 3 ψ∇ 2 ψ∇ψ + g 8 ∇ 3 ψ(∇ψ) 3 + g 9 (∇ 2 ψ) 2 (∇ψ) 2 + g 10 ∇ 2 ψ(∇ψ) 4 + g 11 (∇ψ) 6 + e 1 ∇ 8 ψ + · · · ,…”

Section: Introductionmentioning

confidence: 99%

“…One can say that such terms bring about excitation. In such cases a truncation must be of higher-order in ∇ in order to maintain balance, examples being the 4th order KuramotoSivashinsky (KS) equation [1,3] and the 6th order Nikolaevskii equation [4]. Note that the excitation terms in these equations are linear.…”

Section: Introductionmentioning

confidence: 99%

Phase equation with nonlinear excitation for nonlocally coupled oscillators

Strunin

2009

Physica D: Nonlinear Phenomena

View full text Add to dashboard Cite

Some reaction-diffusion systems feature nonlocal interaction and, near the point of Hopf bifurcation, can be represented as a system of nonlocally coupled oscillators. Phase of oscillations satisfies an evolution pde which takes different forms depending on the values of parameters. In the simplest case the equation is effectively a diffusion equation which is excitation-free. However, more complex forms are possible such as the Nikolaevskii equation and the KuramotoSivashinsky equation incorporating linear excitation. We analyse a situation when the phase equation is based on nonlinear excitation. We derive conditions on the values of the parameters leading to the situation and show that the values satisfying the conditions exist.

show abstract

Dynamics of Viscoelastic Media with Internal Oscillators

Cited by 26 publications

References 6 publications

Non-linear Evolution of P-waves in Viscous–Elastic Granular Saturated Media

Non-linear Evolution of P-waves in Viscous–Elastic Granular Saturated Media

Range of validity and intermittent dynamics of the phase of oscillators with nonlinear self-excitation

Phase equation with nonlinear excitation for nonlocally coupled oscillators

Contact Info

Product

Resources

About