Based on the Burgers equation and Manley-Rowe equation, the derivation about nonlinear interaction of the acoustic waves has been done in this paper. After nonlinear interaction among the low-frequency weak waves and ...Based on the Burgers equation and Manley-Rowe equation, the derivation about nonlinear interaction of the acoustic waves has been done in this paper. After nonlinear interaction among the low-frequency weak waves and the pump wave, the analytical solutions of acoustic waves＇ amplitude in the field are deduced. The relationship between normalized energy of high-frequency and the change of acoustic energy before and after the nonlinear interaction of the acoustic waves is analyzed. The experimental results about the changes of the acoustic energy are presented. The study shows that new frequencies are generated and the energies of the low-frequency are modulated in a long term by the pump waves, which leads the energies of the low-frequency acoustic waves to change in the pulse trend in the process of the nonlinear interaction of the acoustic waves. The increase and decrease of the energies of the low-frequency are observed under certain typical conditions, which lays a foundation for practical engineering applications.展开更多
In order to study the dynamic characteristics of the single-frequency signal through the nonlinear control system,the system control mode,the outer excitation patterns of the model and the amplitude are investigated b...In order to study the dynamic characteristics of the single-frequency signal through the nonlinear control system,the system control mode,the outer excitation patterns of the model and the amplitude are investigated by using the methods of the nonlinear dynamical analysis. The time-domain diagram,power spectrum,phase diagram and the largest Lyapunov exponent obtained from the process of the signal propagate through different control module are given. The researches on different control systems demonstrate that: after single-frequency signal goes through the nonlinear controller,it is still non-chaotic although the output contains more frequency components; but with the feedback and the external perturbation,the output is a continuous broadband spectrum and the result shows that there is chaos. The energy of the input signal reduces with some appropriate parameters. Therefore,the control system of the nonlinear feedback is a good way to broaden the spectrum of output with inputting a single-frequency signal.展开更多
基金financially supported by the Scientific Research Fund of Heilongjiang Provincial Education Department(Grant No.12541132)the Natural Science Youth Foundation of Heilongjiang Province of China(Grant No.QC2015082)
文摘Based on the Burgers equation and Manley-Rowe equation, the derivation about nonlinear interaction of the acoustic waves has been done in this paper. After nonlinear interaction among the low-frequency weak waves and the pump wave, the analytical solutions of acoustic waves＇ amplitude in the field are deduced. The relationship between normalized energy of high-frequency and the change of acoustic energy before and after the nonlinear interaction of the acoustic waves is analyzed. The experimental results about the changes of the acoustic energy are presented. The study shows that new frequencies are generated and the energies of the low-frequency are modulated in a long term by the pump waves, which leads the energies of the low-frequency acoustic waves to change in the pulse trend in the process of the nonlinear interaction of the acoustic waves. The increase and decrease of the energies of the low-frequency are observed under certain typical conditions, which lays a foundation for practical engineering applications.
基金Sponsored by Basic Research Development Program(Grant No.7131107)the National Natural Science Foundation of China(Grant No.51206101)
文摘In order to study the dynamic characteristics of the single-frequency signal through the nonlinear control system,the system control mode,the outer excitation patterns of the model and the amplitude are investigated by using the methods of the nonlinear dynamical analysis. The time-domain diagram,power spectrum,phase diagram and the largest Lyapunov exponent obtained from the process of the signal propagate through different control module are given. The researches on different control systems demonstrate that: after single-frequency signal goes through the nonlinear controller,it is still non-chaotic although the output contains more frequency components; but with the feedback and the external perturbation,the output is a continuous broadband spectrum and the result shows that there is chaos. The energy of the input signal reduces with some appropriate parameters. Therefore,the control system of the nonlinear feedback is a good way to broaden the spectrum of output with inputting a single-frequency signal.
