Study On Characteristics Of Nonlinear Acoustic Based-on Chaotic Theory

With the continuous development and progress of science and technology, nonlinear acoustic theory is more applications to engineering practice, in national defence, medical treatment, industrial and other fields have a wide range of high-power source applications, which also forced nonlinear acoustic theory more in depth research. Nonlinear acoustics as a nonlinear theory in physics, in which many of the problems have the common characteristics of the problem of nonlinear science, chaos theory provides an effective means for study nonlinear problems, we can be to study nonlinear acoustic theory through chaos theory approach.This paper studies the nonlinear time series analysis method, based on nonlinear time series to study the characteristics of nonlinear systems, the different characteristics of nonlinear systems were judged through nonlinear systems chaotic attractor, by phase space reconstruction reconstructed phase space of nonlinear time series, and the selection methods of delay time and embedding dimension were studied, sdudied the method of Lyapunov exponent computation of nonlinear time series, by Lyapunov exponent characteristic of nonlinear time series were judged.In this paper, the vibration characteristics of the nonlinear system and its research methods are discussed, through the system phase diagram, Poincare section, power spectrum, Lyapunov exponent methods analyzed the characteristics of the non-linear system different states, discussed influence of the external excitation parameters on the vibration state of nonlinear systems, and focus on the output power spectrum characteristics of the system states under the different conditions, get the conclusions that the output excitation frequency power of system decreased when system into chaos. To the state of the nonlinear vibration control, in this paper the influence of the nonlinear system parameters on the system characteristics were studied, discussed the influence of the nonlinear coefficient and damping change on characteristics of the system, summarized the law that nonlinear system into chaos under conditions of external excitation and the parameters sensitivity that the system enters chaotic state under the excitation, also discussed the influence of the nonlinear coefficient and damping coefficient on the output power of nonlinear systems. Sdudied the vibration state of nonlinear systems under multi-frequency excitation, amplitude frequency response characteristics of nonlinear systems under multi-frequency excitation were analyzed through multi-scale analysis, compare the vibration state nonlinear system of single-frequency excitation condition with multi-frequency excitation, summarized the influence of joining multi-frequency excitation parameters on the vibration state of the system.The problem of large amplitude acoustic wave propagation in nonlinear acoustic theory was studied, studied the nonlinear propagation of single frequency and multi-frequency large amplitude wave through a nonlinear wave equation, compared propagation law of single frequency plane wave, cylindrical wave and spherical wave, analysed the energy changes of the basis frequency and high frequency wave in the single-frequency large amplitude wave propagation, by the spectral decomposition method studied the nonlinear interaction of large amplitude waves, discussed the influence of different initial phase, frequency and energy on the low-frequency wave energy under two waves nonlinear interaction conditions, and the calculated results of spectral decomposition and Fenlon theoretical results are compared. Studied Finite difference time domain method, and by numerical calculation of nonlinear wave equation studied the problem of large amplitude wave nonlinear propagation, studied the propagations of single-frequency and multi-frequency large amplitude wave through the time domain and frequency domain analysis.Nonlinear propagation problem of large amplitude wave is studied in the dispersion medium, by traveling wave transformation of nonlinear wave equation obtained the equivalent nonlinear system model, through the phase plane analysis method and Melnikov method studied this system, and get the theoretical threshold of the system into chaotic state. By experiment studied the large amplitude wave nonlinear interaction, get the experiment results that low frequency wave energy generated drop in two waves interaction, the sum and difference frequency wave energy were calculated and experimental measured under nonlinear interaction of two waves, obtained the conclusions that the calculation with actual results are more accordant under two waves interaction of large energy. Using the conical spring constructed nonlinear vibration model, through experiment studied the equivalent nonlinear system of nonlinear wave equation using traveling wave transformation, by adjusting the excitation frequency and amplitude studied the vibration state of the nonlinear system, using phase space, Lyapunov exponent and power spectrum methods studied the periodic, doubling period and chaos states.Under the conditions of external excitation the nonlinear vibration characteristics of bubbles were studied, discussed the influence of difference external excitation parameters on the nonlinear vibration of the bubble, and analyzed the vibration characteristics of the bubbles under different states, through the effective medium method nonlinear characteristics of water medium containing the bubbles were studied, using equivalent nonlinear parameter (B/A)n of different water media containing bubbles studied the nonlinear characteristics of the media, get the conclusions that the water medium with bubbles has strong nonlinear characteristics, through experiment the nonlinear coefficients of water medium containing the bubble were measured and calculatedto determine nonlinear system parameters of the actual problem, constructed the equivalent nonlinear system model provides effective way.