摘要:

The fundamental system is transformed to three nonlinear equations of the interacting components, a rightwards propagating, leftwards propagating and stationary one, by a projecting technique. The dynamics is determined by small nonlinear, dispersive and viscous terms. Finally the system is reduced to one equation of Korteweg-de Vries type. It is shown that the evolution is described by an integrable KdV-MKdV equation on a class of initial conditions specified by the projection. A soliton solution is presented. ©2000 American Institute of Physics.

ISSN:0094-243X    

DOI:10.1063/1.1309274

出版商:AIP    

年代:1900

数据来源: AIP

摘要:

Waves in a liquid containing bubbles, distributed in it with densityn(r),and waves in an elastic structure coupled with a number of oscillators are analyzed, with the principal question being the influence of nonlinearity on the form of the wave. This form (a soliton, for example) is very sensitive to a change of nonlinear parameter of the structure. The change occurs when the structure alters its local elastic properties during its operation (when fractures originate, for example). Stationary nonlinear waves in media with resonant dispersion (MRD) are nonstandard compared with nonlinear waves in media with weak dispersion – KdV solitons and cnoidal waves. The governing equation, the Resonant Dispersion Equation (RDE), is formulated. Its solutions have important differences compared with those of KdV and Burgers Equations. They include solitons with vertical fronts and shock waves of a complicated form. These forms are very sensitive to the nonlinear and dissipative parameters of the structure. ©2000 American Institute of Physics.

ISSN:0094-243X    

DOI:10.1063/1.1309275

出版商:AIP    

年代:1900

数据来源: AIP

摘要:

Propagation of sound in a bubbly fluid can, if dissipation is neglected, be described by Korteweg de Vries’ equation. This can be solved with the inverse scattering transform. Korteweg de Vries’ equation is studied as an initial value problem with an N-wave as initial condition. The inverse scattering method, leading to Marchenko’s linear integral equation, is used. From the solution of Marchenko’s equation the scattering potential, which also is the solution of Korteweg de Vries’ equation, is obtained. In Marchenko’s equation, the reflection coefficient of the scattering problem is found as a factor in two integrals. With anN-wave as initial condition, this reflection coefficient becomes non-zero and the two integrals are integrated numerically. To get the scattering potential, the Marchenko integral equation is solved by iteration. Already in the first step solution, the scattering potential att=0coincides well with the given initial condition of the Korteweg de Vries equation. This solution decays quickly to the right of the front, which is moving to the right, and is oscillating and more slowly decaying to the left. By comparison with an asymptotic matching solution, the decay to the right can be shown to be exponential. ©2000 American Institute of Physics.

ISSN:0094-243X    

DOI:10.1063/1.1309276

出版商:AIP    

年代:1900

数据来源: AIP

摘要:

The dynamics of the sinusoidally driven cavitation bubble oscillator influenced by external random signals, modelled by white noise and an Ornstein-Uhlenbeck process, is studied. By numerical simulations it is shown that chaotic oscillations of cavitation bubble oscillators can be stabilized to periodic oscillations. Shift of bifurcation points and destruction of period-doubling cascades were observed as a result of the action of noise. They are discussed from the point of view of experimental time series. ©2000 American Institute of Physics.

ISSN:0094-243X    

DOI:10.1063/1.1309277

出版商:AIP    

年代:1900

数据来源: AIP

摘要:

This paper reports the results of the experiments to verify the theoretical findings so far made that shock formation of nonlinear acoustic waves propagating in an air-filled tube can be suppressed, if a suitable array of Helmholtz resonators is connected with the tube axially, and that an acoustic solitary wave may be generated, if dissipative effects are negligible. The experiments observe evolutions of the pressure disturbances propagating in the tube without the array and in the one with the array connected, respectively. By connecting the array, it is found that shock formation is really suppressed and that a localized pulse emerges in place of the shock. Its pressure profile and propagation speed are compared with those of the solitary wave predicted in theory. ©2000 American Institute of Physics.

ISSN:0094-243X    

DOI:10.1063/1.1309278

出版商:AIP    

年代:1900

数据来源: AIP

摘要:

The fundamental properties, especially some unique features of parametrically excited standing solitons, are briefly summarized, also providing comparison with some simple cases of KdV solitons, by leaving the mathematical and computational details to references quoted. ©2000 American Institute of Physics.

ISSN:0094-243X    

DOI:10.1063/1.1309279

出版商:AIP    

年代:1900

数据来源: AIP

摘要:

Strong shock waves in a bubbly liquid are examined by using a simple numerical model based on the K-dV-Burgers equation. In this model, two kinds of coefficients of the equation are switched with each other depending upon the relative magnitude of the peak amplitude to a certain threshold. Irregular behavior is numerically found both in the oscillatory wave trains behind the shock front and in the evolution of the shock front itself. Since such irregularity is enhanced when the nonlinearity increases, the wave behavior is considered to be chaotic. ©2000 American Institute of Physics.

ISSN:0094-243X    

DOI:10.1063/1.1309280

出版商:AIP    

年代:1900

数据来源: AIP

摘要:

The “Rasping Noise” is an abnormal exhaust noise that occurs in small cars equipped with two boxes exhaust systems. It is an intermittent metallic noise that irritates the ear because of its high frequency components. It occurs during rapid acceleration or deceleration in cold conditions. Pressure signals are picked up in a critical exhaust line at Rasping conditions. Order and wavelet analysis are found to be efficient and completing tools in studying an eventual occurrence of discontinuities or shock waves in such a critical exhaust line. ©2000 American Institute of Physics.

ISSN:0094-243X    

DOI:10.1063/1.1309281

出版商:AIP    

年代:1900

数据来源: AIP

摘要:

The nonlinear equations of hydrodynamic type featuring effects of nonlinear self-action and interactions of nonlinear acoustic hydrodynamic-type fields are considered. These equations, complemented by the continuity equation, describe the evolution of a passive and active tracer in moving continuous media. It is shown that the solutions of the mentioned nonlinear equations with arbitrary initial conditions are reduced to the solutions of a system of linear diffusion equations. It allows to investigate in detail the dynamic and statistical characteristics of nonlinear interaction of acoustic waves in a model polytropic gas, and also to analyze behavior of density fields and effects of diffusion and transport of particles in nonlinear fields of hydrodynamic type. ©2000 American Institute of Physics.

ISSN:0094-243X    

DOI:10.1063/1.1309282

出版商:AIP    

年代:1900

数据来源: AIP

摘要:

Recently, considerable attention has been focused on the application of nonlinear acoustic properties for the non-destructive evaluation of materials. Normally a number of separate pieces of instrumentation must be combined to make these ultrasonic measurements. Selecting, matching, and controlling a number of instruments can be challenging. The principles of operation of a single instrument, under computer control, designed to make a variety of measurements are given. The unit transmits high power (up to 5 kilowatts) radio frequency bursts from 0.2 MHz to 20 MHz and receives signals from 50 kHz to 80 MHz. A unique variation of superheterodyne receiver circuitry allows the receiver to be tuned to frequencies different than the transmit ones and still maintain the coherency required for simultaneous phase and amplitude measurements. Quadrature phase sensitive detection, analog integration, and signal conditioning allow the examination of very small signals in the presence of large ones. In many cases the ratio may exceed 100 dB. Generation of any number of harmonics within the receiver bandwidth may be monitored. In addition, a second high power RF burst transmitter allows for the study of nonlinear mixing phenomena. A variety of data is presented. ©2000 American Institute of Physics.

ISSN:0094-243X    

DOI:10.1063/1.1309283

出版商:AIP    

年代:1900

数据来源: AIP