Темьянов Б.К., Евдокимов Ю.К. «Обратная операторная задача для частотно-импедансной модели неоднородной акустической среды: численная и экспериментальная реализации» Нелинейный мир, 13, № 4, с. 19-25 (2015)

Рассмотрен алгоритм решения обратной коэффициентной задачи для уравнения Риккати одномерной акустической среды. Проведены численное моделирование рассматриваемого алгоритма при различных значениях подключенного акустического сопротивления и экспериментальная проверка полученного алгоритма. Показано, что погрешность восстановления функции неоднородности образца существенно зависит от погрешности вносимой измерением адмиттанса. Existing methods of ultrasonic inspection reveal defects in the studied objects in the form of sharp violations of homogeneity of the mechanical properties of sensed medium. In this paper, a numerical simulation and experimental implementation of the algorithm of continuously varying parameters reconstruction using the input complex conductivity (admittance) in the one-dimensional approximation were considered. The most difficult stage of numerical simulation was the solving Fredholm integral equation of the first kind with the use of regularization on the basis of the generalized discrepancy principle that determines the optimal value of the regularization parameter in accordance with a right side error of the integral equation. The error of the right side was simulated by random variable with known root-mean-quare value. The values of the regularization parameter chosen in accordance with the generalized discrepancy principle using simulated right part error do not coincide with the optimum values. Despite this, the iterative structure of the algorithm with additional conditions, allows us to operate even with large differences between the chosen and the optimal values of the regularization parameter. An additional condition is the condition of not exceeding 100% accuracy of the solution at each iteration. In this case the obtained approximation will tend to the exact solution. Test regularization modeling showed that if the matched load is connected to the end of line error rate on the iteration does not exceed 100% in a wide range of values of the regularization parameter that determines high accuracy of the algorithm in this case. If a short circuit or idle running at the end of a line error value at iteration acquire much higher values, which leads to large errors in the solution. Given this fact, further reasoning were only the case of the connection of the matched load in the end of medium. Two functions of heterogeneity in the form of quadratic polynomials defining the distribution of continuously varying parameters of the sensed medium were considered using which the input admittance was calculated with the measurement error of 0.1% and 1%. The reconstruction errors for the case monotonically increasing function heterogeneity reached the values of the 0,2% and 0.5%, respectively, at different levels of the input admittance measurement error. For the case of a monotonically decreasing function of heterogeneity error solutions were somewhat higher: 0.2% and 0.7%, respectively. The optimal values of frequency ranges of measurements have also been identified. Experimental realization of the algorithm was carried out on the basis of hardware-software complex of ultrasonography TOMOSCAN FOCUS LT. The main operating element of this complex is the ultrasonic phased array (UPA) is a set of piezoelectric elements in a polymeric insulating matrix. UPA is contacted with a test sample through a special wedge. One of the main stages of the experimental implementation was the measuring of the input admittance. The estimation of the input admittance was carried out on the results of measurements of the reflection coefficient of the border prism – the measurement object. For a more precise operation of the algorithm, all subsequent pulses after the first were cut off, so the connection of the matched load by the end of the line was simulated. Measurement error admittances were high enough; the standard deviation of the measured values relative to the average is 9%. The maximum standard deviation of the reconstructed functions heterogeneity relative to the average value does not exceed 7%. According to the results of the reconstruction we can conclude that the method restores the structure of the sample with high values of the errors introduced by the measurement of the input admittance.

Кияшко С.В., Афенченко В.О., Назаровский А.В. «Генерация спиральных волн при параметрическом возбуждении в кювете с неоднородной границей» Нелинейный мир, 13, № 4, с. 76-80 (2015)

Экспериментально исследован процесс генерации спиральных волн при параметрическом возбуждении капиллярных волн, возникающих на поверхности слоя вязкой жидкости, помещенного в кювету с неоднородной границей. Для неоднородности в виде уступа найдены области параметров, при которых генерируется устойчивая спиральная волна. Выяснено, что наиболее эффективна неоднородность с высотой уступа, близкой к длине волны возбуждающихся спиральных структур. In the present paper we report results of experimental study of the process of arising of standing spiral waves on the surface of vis-cous liquid layer in an oscillating field of gravity. Parametric pumping creates instability and growth of wave amplitude is limited by the nonlinear dependence of viscous losses on amplitude. Only roll structures of standing waves may exist in a highly viscous liquid because of strong competition. However, spiral waves do not occur in ordinary conditions; instead, parallel rolls in a rectangular cell and circular standing waves in a round cell are formed. This is explained by the fact that, when pump is switched on, strongly damping shear waves appear at the vertical boundary of the cell, that serve as initial perturbations for excitation of standing roll waves. In a round cell, these perturbations repeat the shape of the cell, thus resulting in the onset of stationary regime in the form of circular rolls. However, if there is nouniformity such as a ledge in the wall, then the excitation front will contain a defect that will move to the cen-ter of the cell, which may give rise to a spiral wave. In the current work the process of spiral wave generation in the presence of nonuniformities at the boundary and in the case of perturbations on the liquid surface is studied in experiment. We took highly viscous silicon oil (viscosity 100 times more than water viscosity) as an operating liquid. Vertical vibrations of the cell were produced by means of a vibration table. In the course of the experiment we varied the amplitude and oscillation frequency f∼41–81 Hz of the cell, as well as liquid depth (4–8 mm). Images of the patterns formed by capillary waves were recorded by a digital video camera and were fed to the computer for further processing. Experiments on studying spiral wave generation in the presence of nonuniformity at the boundary were conducted as follows. A tri-angular ledge was placed at the boundary of a circular cell. After that, sinusoidal voltage was supplied to the amplifier input at fixed liquid depth and with fixed frequency of external signal. Near the walls, there appeared regions of capillary ripples containing defects, with the boundaries parallel to the walls of the cell. Further, the fronts of these regions propagated to the center of the cell, the am-plitude of the standing field balanced, and a spiral structure were established. We investigated generation of spiral waves as a function of parameters of nonuniformity at the boundary. It was revealed that the most effective is nonuniformity with ledge height close to the wavelength of excited spiral waves. It was shown that in the presence of several ledges at the boundary, multi-arm spiral waves with preset number of arms and arm direction may be generated. Regions of the parameters at which a stable spiral structure is formed were found.

Черкашин Ю.Н., Еременко В.А., Чумаков О.С. «Динамика нелинейного волнового пучка с переменным коэффициентом нелинейности» Нелинейный мир, 13, № 4, с. 55-59 (2015)

Показана проблема генерации и распространения нелинейных волновых пучков в динамично неоднородной среде. В отличие от традиционной постановки рассмотрены задачи с акцентом на физически значимые эффекты в решении проблемы генерации нелинейных волн. Отмечено, что эти эффекты связаны с изменением коэффициента нелинейности вдоль трассы распространения. Выявлено, что при достаточно плавных изменениях коэффициента нелинейности структура пучка сохраняется (адиабатичность). Односолитонное или многосолитонное решения сохраняют свою структуру с меняющимися шириной и амплитудой пучка при сохранении энергии. Обнаружено, что при резком изменении коэффициента нелинейности меняется характер решения, а «правило квантования», стимулирует преобразование односолитонных и многосолитонных решений друг в друга. При нарушении «правила квантования» часть энергии высвечивается. Показано, что увеличение коэффициента нелинейности при наличии посторонних волновых полей в окрестности солитона приводит к значительному росту амплитуды уединенной волны, вызывая фактически образование «волны-убийцы».