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Интеллектуальная Система Тематического Исследования НАукометрических данных |
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Calculation of the field of the high intensive focused ultrasound beam using the modular nonlinearity modelтезисы доклада
- Автор: Gusev V.A.
- Сборник: Abstracts of International conference Days on diffraction 2022
- Тезисы
- Год издания: 2022
- Место издания: PDMI St. Petersburg
- Первая страница: 29
- Последняя страница: 30
- Аннотация: One of the important problems of nonlinear acoustics is the calculation of the field of high intensive focused beams in the focal region. For this problem, it is not possible to find an exact analytical solution and one has to resort to approximate or numerical calculations. Numerical calculations make it possible to calculate the field amplitude for specific values and parameters of the radiating system. However, in this case, it is necessary to enumerate a large array of realizations to solve the problem of optimizing the field at the focus and obtain the maximum amplitude. A wide class of approximate methods that make it possible to obtain analytical solutions for high-intensity acoustic fields is associated with the approximation of nonlinear geometric acoustics and ray methods. However, these approaches do not allow one to correctly describe the field in the focal region. Asymptotic methods suitable for describing the field at the focus are mainly developed for linear problems and require further development for application in the nonlinear case. One of the possible ways to obtain analytical and qualitative dependences for the field in the focal region of a high intensive focused beam is associated with the use of the modular nonlinearity model. The idea is that the term containing the classical quadratic nonlinearity is replaced by the term containing the modular type nonlinearity. In this case, the qualitative behavior of the nonlinear term is generally preserved. Two significant differences can be identified. First, in a quadratic-nonlinear medium, a discontinuity in the profile is formed smoothly and at some distance from the emitter. In a medium with modular nonlinearity, a discontinuity forms immediately. Secondly, at small amplitudes in a quadratically nonlinear medium, there is a smooth transition to a linear regime, which is absent in a medium with modular nonlinearity. Both of these differences are not very significant when calculating the field at the focus of a high intensive beam, since the main interest is the structure of the field near the beam axis with a large amplitude. In this case, at the initial stage of beam propagation, approximate solutions of equations with quadratic nonlinearity are suitable, which are then used as boundary conditions for solving model equations with modular nonlinearity. The paper proposes model equations with modular nonlinearity suitable for describing the field in the focal region of a high intensive focused beam. It is shown that the temporal profile of the wave is distorted asymmetrically due to diffraction distortions. The peak negative pressure decreases, and the range of negative pressures itself increases. Peak positive pressure, on the contrary, increases, and the interval decreases. According to the model of modular nonlinearity, the wave propagates at different speeds in the intervals of positive and negative polarity. This leads to the formation of areas of ambiguity, in which a discontinuity is drawn according to the rule of equal areas. As a result, a discontinuous profile is formed. The combined effect of diffraction and nonlinear distortions leads to the formation of short pulses of positive polarity with a large amplitude and rather long intervals with a flat negative polarity profile without strongly pronounced peaks of negative polarity. The dynamics of the profile distortion is described by exact analytical expressions, which allow one to proceed to the solution of the problem of optimizing the radiating system in order to obtain the maximum amplitude at the focus.
- Добавил в систему: Гусев Владимир Андреевич