Based on the strain invariant relationship and taking the high-order elastic energy into account, a nonlinear wave equation is derived, in which the excitation, linear damping, and the other nonlinear terms are regard...Based on the strain invariant relationship and taking the high-order elastic energy into account, a nonlinear wave equation is derived, in which the excitation, linear damping, and the other nonlinear terms are regarded as the first-order correction to the linear wave equation. To solve the equation, the biggest challenge is that the secular terms exist not only in the fundamental wave equation but also in the harmonic wave equation （unlike the Duffing oscillator, where they exist only in the fundamental wave equation）. In order to overcome this difficulty and to obtain a steady periodic solution by the perturbation technique, the following procedures are taken： （i） for the fundamental wave equation, the secular term is eliminated and therefore a frequency response equation is obtained; （ii） for the harmonics, the cumulative solutions are sought by the Lagrange variation parameter method. It is shown by the results obtained that the second- and higher-order harmonic waves exist in a vibrating bar, of which the amplitude increases linearly with the distance from the source when its length is much more than the wavelength; the shift of the resonant peak and the amplitudes of the harmonic waves depend closely on nonlinear coefficients; there are similarities to a certain extent among the amplitudes of the odd- （or even-） order harmonics, based on which the nonlinear coefficients can be determined by varying the strain and measuring the amplitudes of the harmonic waves in different locations.展开更多
The numerical results obtained by Rayleigh-Plesset （R-P） equation failed to agree with the experimental Mie scattering data of a bubble in water without inappropriately increasing the shear viscosity and decreasing ...The numerical results obtained by Rayleigh-Plesset （R-P） equation failed to agree with the experimental Mie scattering data of a bubble in water without inappropriately increasing the shear viscosity and decreasing the surface tension coefficient. In this paper, a new equation proposed by the present authors （Qian and Xiao） is solved. Numerical solutions obtained by using the symbolic computation program from both the R-P equation and the Qian-Xiao （Q-X） equation clearly demonstrate that Q-X equation yields best results matching the experimental data （in expansion phase）. The numerical solutions of R-P equation also demonstrate the oscillation of a bubble in water depends strongly upon the surface tension and the shear viscosity coefficients as well as the amplitude of driving pressure, so that the uniqueness of the numerical solutions may be suspected if they are varied arbitrarily in order to fit the experimental data. If the bubble＇s vibration accompanies an energy loss such as the light radiation during the contract phase, the mechanism of the energy loss has to be taken into account. We suggest that by use of the bubble＇s vibration to investigate the state equations of aqueous solutions seem to be possible. We also believe that if one uses this equation instead of R-P equation to deal with the relevant problems such as the ＇phase diagrams for sonoluminescing bubbles＇, etc., some different results may be expected.展开更多
Based on Qian's theory,we investigated the reflection and refraction of finite amplitute sound wave on a plane boundary.Under the continuity conditions of the pressure and the normal velocity,some interesting resu...Based on Qian's theory,we investigated the reflection and refraction of finite amplitute sound wave on a plane boundary.Under the continuity conditions of the pressure and the normal velocity,some interesting results are obtained.There exists two kinds of refraction waves.One obeys Snell's law;the other quantitatively agrees to the steeply dipping wave observed by Muir et al.A further analysis shows that a double refraction may occur in an extent of the incident angle when ρ1/ρ2>√C_(02)^(2)/C_(01)^(2)-1.展开更多
The integral of the pulse self-demodulation in acoustic parametric array can be calculated in light of the Fourier convolution theorem.Instead of a rectangular pulse with two discontinuous edges,two kinds of primary e...The integral of the pulse self-demodulation in acoustic parametric array can be calculated in light of the Fourier convolution theorem.Instead of a rectangular pulse with two discontinuous edges,two kinds of primary envelopes are used,the waveforms and their spectra are investigated.An optimal ratio of the primary duration has been found theoretically.Experimental results support this theory.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.11274337)
文摘Based on the strain invariant relationship and taking the high-order elastic energy into account, a nonlinear wave equation is derived, in which the excitation, linear damping, and the other nonlinear terms are regarded as the first-order correction to the linear wave equation. To solve the equation, the biggest challenge is that the secular terms exist not only in the fundamental wave equation but also in the harmonic wave equation （unlike the Duffing oscillator, where they exist only in the fundamental wave equation）. In order to overcome this difficulty and to obtain a steady periodic solution by the perturbation technique, the following procedures are taken： （i） for the fundamental wave equation, the secular term is eliminated and therefore a frequency response equation is obtained; （ii） for the harmonics, the cumulative solutions are sought by the Lagrange variation parameter method. It is shown by the results obtained that the second- and higher-order harmonic waves exist in a vibrating bar, of which the amplitude increases linearly with the distance from the source when its length is much more than the wavelength; the shift of the resonant peak and the amplitudes of the harmonic waves depend closely on nonlinear coefficients; there are similarities to a certain extent among the amplitudes of the odd- （or even-） order harmonics, based on which the nonlinear coefficients can be determined by varying the strain and measuring the amplitudes of the harmonic waves in different locations.
基金Project supported by the National Natural Science Foundation of China (Grant No 10274090)
文摘The numerical results obtained by Rayleigh-Plesset （R-P） equation failed to agree with the experimental Mie scattering data of a bubble in water without inappropriately increasing the shear viscosity and decreasing the surface tension coefficient. In this paper, a new equation proposed by the present authors （Qian and Xiao） is solved. Numerical solutions obtained by using the symbolic computation program from both the R-P equation and the Qian-Xiao （Q-X） equation clearly demonstrate that Q-X equation yields best results matching the experimental data （in expansion phase）. The numerical solutions of R-P equation also demonstrate the oscillation of a bubble in water depends strongly upon the surface tension and the shear viscosity coefficients as well as the amplitude of driving pressure, so that the uniqueness of the numerical solutions may be suspected if they are varied arbitrarily in order to fit the experimental data. If the bubble＇s vibration accompanies an energy loss such as the light radiation during the contract phase, the mechanism of the energy loss has to be taken into account. We suggest that by use of the bubble＇s vibration to investigate the state equations of aqueous solutions seem to be possible. We also believe that if one uses this equation instead of R-P equation to deal with the relevant problems such as the ＇phase diagrams for sonoluminescing bubbles＇, etc., some different results may be expected.
文摘Based on Qian's theory,we investigated the reflection and refraction of finite amplitute sound wave on a plane boundary.Under the continuity conditions of the pressure and the normal velocity,some interesting results are obtained.There exists two kinds of refraction waves.One obeys Snell's law;the other quantitatively agrees to the steeply dipping wave observed by Muir et al.A further analysis shows that a double refraction may occur in an extent of the incident angle when ρ1/ρ2>√C_(02)^(2)/C_(01)^(2)-1.
文摘The integral of the pulse self-demodulation in acoustic parametric array can be calculated in light of the Fourier convolution theorem.Instead of a rectangular pulse with two discontinuous edges,two kinds of primary envelopes are used,the waveforms and their spectra are investigated.An optimal ratio of the primary duration has been found theoretically.Experimental results support this theory.
