| 1. |
- Enflo, Bengt, et al.
(författare)
-
Nonlinear standing waves in a closed tub
- 2002
-
Konferensbidrag (refereegranskat)abstract
- Simplified nonlinear evolution equations describing nonsteady-state forced vibrations in an acoustic resonator having one closed end and the other end periodically oscillating are derived. An approach is used based on a nonlinear functional equation. This approach is shown to be equivalent to the version of the successive approximation method developed in 1964 by Chester. It is explained how the acoustic field in the cavity is described as a sum of counterpropagating waves with no cross-interaction. The nonlinear Q-factor and the nonlinear frequency response of the resonator are calculated for steady-state oscillations of both inviscid and dissipative media. The general expression for the mean intensity of the acoustic wave in terms of the characteristic value of a Mathieu function is derived. Some results from a perturbation calculation of the wave profile are given.
|
|
| 2. |
- Enflo, Bengt, et al.
(författare)
-
Nonlinear Standing Waves in a Layer Excited by the Periodic Motion of its Boundary
- 2002
-
Konferensbidrag (refereegranskat)abstract
- Simplified nonlinear evolution equations describing nonsteady-state forced vibrations in an acoustic resonator having one closed end and the other end periodically oscillating are derived. An approach is used based on a nonlinear functional equation. This approach is shown to be equivalent to the version of the successive approximation method developed in 1964 by Chester. It is explained how the acoustic field in the cavity is described as a sum of counterpropagating waves with no cross-interaction. The nonlinear Q-factor and the nonlinear frequency response of the resonator are calculated for steady-state oscillations of both inviscid and dissipative media. The general expression for the mean intensity of the acoustic wave in terms of the characteristic value of a Mathieu function is derived. The process of development of a standing wave is described analytically for three different types of periodic motion of the wall: harmonic excitation, sawtooth-shaped motion and "inverse saw motion".
|
|
| 3. |
- Hedberg, Claes, et al.
(författare)
-
Interaction between low and high-frequency Modes in a Nonlinear System : Gas-Filled Cylinder Covered by a movable Piston
- 2003
-
Ingår i: Nonlinear dynamics. - Dordrecht : Kluwer. - 0924-090X .- 1573-269X. ; 32:4, s. 405-416
-
Tidskriftsartikel (refereegranskat)abstract
- A simple mechanical system containing a low-frequency vibration mode and set of high-frequency acoustic modes is considered. The frequency response is calculated. Nonlinear behaviour and interaction between modes is described by system of functional equations. Two types of nonlinearities are taken into account. The first one is caused by the finite displacement of a movable boundary, and the second one is the volume nonlinearity of gas. New mathematical models based on nonlinear equations are suggested. Some examples of nonlinear phenomena are discussed on the base of derived solutions.
|
|
| 4. |
- Hedberg, Claes, et al.
(författare)
-
Pulse response of a nonlinear layer
- 2001
-
Ingår i: Journal of the Acoustical Society of America. - 0001-4966 .- 1520-8524. ; 110:5, s. 2340-2350
-
Tidskriftsartikel (refereegranskat)abstract
- A simple analytical theory is developed for the description of non-steady state response of a thin nonlinear layer, which differs markedly in its linear properties from the surrounding medium. Such a layer can model the behavior of real inhomogeneities like a cloud of gas bubbles in a liquid, a crack or split plane in a solid, or the contact between two slightly tighted rough surfaces. Both weakly nonlinear pulse and harmonic responses are calculated and the general properties of the spectral and temporal structure of the scattered field are discussed. The exact strongly nonlinear solutions are derived for a special type of stress-strain relationship corresponding to the behavior of real condensed media under strong load. Profiles and spectra shown are in conformity with experimental results. The pulse response on the short delta-pulse shaped incident wave is calculated for arbitrary nonlinear properties of the layer. The possibilities to apply the sets of data on measured characteristics of pulse response in the solution of inverse problems are briefly discussed.
|
|
| 5. |
- Ibragimov, Nail H., et al.
(författare)
-
Principle of an a priori use of symmetries in the theory of nonlinear waves.
- 2004
-
Ingår i: Acoustical Physics. - 1063-7710 .- 1562-6865. ; 50:4, s. 406-419
-
Tidskriftsartikel (refereegranskat)abstract
- The principle of an a priori use of symmetries is proposed as a new approach to solving nonlinear problems on the basis of a reasonable complication of mathematical models. This approach often provides additional symmetries, and hence opens possibilities to find new analytical solutions. The potentialities of the proposed approach are illustrated by applying to problems of nonlinear acoustics.
|
|
| 6. |
- Rudenko, Oleg, et al.
(författare)
-
Enhancements of energy and Q-factor of a nonlinear resonator with increase in its losses
- 2002
-
Ingår i: Doklady Akademii Nauk. - : MAIK Nauka/Interperiodica Publishing, Russia. - 0869-5652. ; 383:1, s. 330-333
-
Tidskriftsartikel (refereegranskat)abstract
- A phenomenon that is paradoxical at first sight is studied: an appropriately-organized energy outflow from a resonator cavity results not in the attenuation of nonlinear vibrations but in their noticeable enhancement. An increase in the resonator Q-factor and in the energy accumulated in it is well pronounced when the frequencies of the higher harmonics generated in a nonlinear medium are close to the natural frequencies of the resonator. An important example of a nonlinear system with the necessary properties is an acoustic resonator with selective losses.
|
|
| 7. |
- Rudenko, Oleg, et al.
(författare)
-
Nonlinear Dynamics of Grains in a Liquid-Saturated Soil
- 2003
-
Ingår i: Nonlinear dynamics. - Dordrecht : Kluwer. - 0924-090X .- 1573-269X. ; 35:2, s. 187-200
-
Tidskriftsartikel (refereegranskat)abstract
- A new kind of nonlinearity of inertial type caused by accelerated motion of interacting particles is described. The model deals with an ensemble of grains immersed into a vibrating fluid. First, the nonlinear vibration of two connected grains is studied. The temporal behaviours of displacement and velocity, as well as spectrum of vibration, are analysed. Numerical simulations are performed. Then an infinite chain of grains is considered and the corresponding differential-difference equation is derived. For the continuum limit the inhomogeneous nonlinear wave equation is solved and temporal profiles are calculated. A new resonant phenomenon is described and the resonant curves are constructed.
|
|
| 8. |
- Rudenko, Oleg, et al.
(författare)
-
Nonlinear response of a layer to pulse action in diagnostics of small inhomogenities
- 2000
-
Ingår i: Doclady, Section Mechanics (Reports of the Russian Academy of Sciences) / Doklady Akademii Nauk. - : MAIK Nauka/Interperiodica Publishing, Russia. - 0869-5652. ; 374 ; 1-3, s. 194-197
-
Tidskriftsartikel (refereegranskat)abstract
- Giant nonlinear respons are observed at acoustic irradiation of microscopic gas bubbles in liquids, cracks and fluid-filled pores in solids; and compressed contact of rough surfaces, and is used in diagnostics of materials of industrial and geological structures. Reconstruction of characteristics of a scattering inhomogeneity requires an analyses of complicated inverse problems. The problem of plane-wave incidence upon a layer is simple and serves a model for more complicated inhomogeneities; its response enables us to reconstruct the spectral composition and field structure of other nonlinear scatterers.
|
|
| 9. |
- Rudenko, Oleg, et al.
(författare)
-
Nonlinear standing waves in a layer excited by periodic motion of its boundary
- 2001
-
Ingår i: Acoustical Physics. - : MAIK NAUKA/INTERPERIODICA PUBL. - 1063-7710 .- 1562-6865. ; 47:4, s. 452-460
-
Tidskriftsartikel (refereegranskat)abstract
- A new analytical approach is developed for the description of standing waves caused by arbitrary periodic vibration of a boundary. The approach is based on the nonlinear evolution equation written for an auxiliary function. This equation offers the possibility to study not only the steady-state acoustic field, but also its evolution in time. One can take into account the dissipative properties of the medium and the difference between one of the resonant frequencies and the fundamental frequency of the driving motion of the wall. An exact non-steady-state solution is derived corresponding to the sawtooth-like periodic vibration of the boundary. The maximal amplitude? values of the particle velocity and the energy of standing waves are calculated. The temporal profiles of standing waves at different points of the layer are presented. A new possibility of pumping a high acoustic energy into a resonator is indicated for the case of a special type of wall motion having the form of an ?inverse saw?. Theoretically, such a vibration leads to an ? explosive instability? and an unlimited growth of the standing wave. For a harmonic excitation, the exact non-steady-state solution is derived as well. The standing wave profiles are described by Mathieu functions, and the energy characteristics by their eigen-values.
|
|
| 10. |
|
|
