Vol 69, No 6 (2023)

In physics, in particular, acoustics, time is traditionally considered as a continuous coordinate. Some exception is signal processing, where sampling is necessary for calculations on computers. But all acoustic problems are formulated and solved using time-continuous models described by differential equations and their solutions in the form of continuous time functions. Meanwhile, these problems can be formulated and solved in an equivalent way using discrete-time models described by finite-difference equations and their solutions in the form of time series. As the experience of some other fields of science, for example, control theory, shows, the discrete approach has a number of advantages over the continuous approach, the use
of which greatly facilitates the solution of many problems. This paper aims to partially fill the gap in acoustics that exists here and is aimed at creating the theoretical foundations of a discrete-time approach to solving acoustic problems. The paper is limited to the consideration of one oscillatory system widely used in acoustics— a linear structure with N degrees of freedom consisting of lumped inertial, elastic and dissipative elements, to which, in particular, the finite element method leads. For several continuous models of this system, equivalent
discrete-time models are constructed in the paper, finite-difference equations are derived and their solutions are obtained. The criterion of equivalence of continuous and discrete models in the paper is the mathematically exact equality of the corresponding solutions at all discrete points in time. Based on this criterion, analytical relations have been established between the parameters of continuous and discrete models and their equations, which make it possible to build its discrete-time model based on a continuous model of the system
and, conversely, to build its continuous model based on a known discrete model. Special attention is paid in the paper to the forced vibrations of the system under the action of kinematic excitation, which is important in many acoustic problems, whereas in the literature only force excitation is considered. The paper also discusses
one of the most useful properties of discrete modeling—the simplicity of constructing discrete models based on experimentally measured signals. A corresponding example is given. Note that the term “ARMAmodel” is an abbreviation for “autoregressive and moving average model”, generally accepted in control theory, systems theory and other fields of science.

A methodology is proposed for high-precision local measurement of the group velocity of longitudinal waves in solid samples with millimeter thickness. Achievement of the required accuracy involves laser thermo-optical excitation of submicrosecond ultrasonic video pulses and ultrawideband piezoelectric recording of acoustic signals reflected from the test sample. Plane-parallel samples made of duralumin, quartz, and steel with a thickness of 2–6 mm are studied. To achieve the required accuracy in measuring the group velocity
of ultrasound, the signal shape is mathematically processed with compensation for diffraction of the ultrasonic beam as it propagates through the sample. The possibility of ensuring the uncertainty in measuring the group velocity of ultrasound in the 1–15 MHz frequency range at a level of 0.1% in samples with millimeter
thickness is demonstrated.

The acoustic properties of suspensions based on pure glycerol and diamond powder with a particle size of 1–2 μm and different concentrations were studied using a resonator with a longitudinal electric field. A disk resonator made of langasite with round electrodes on both sides of the plate with a frequency of 4.1MHz, operating on a longitudinal acoustic wave, was completely immersed in a liquid container with the studied suspension. Based on the measured frequency dependences of the real and imaginary parts of the
electric impedance of the resonator using an equivalent electromechanical circuit, the longitudinal elastic modulus and longitudinal viscosity coefficient of the samples were determined. Comparison of the experimental dependences of the longitudinal elastic modulus, viscosity coefficient, and longitudinal acoustic wave
velocity on the volume concentration of diamond particles in the suspension with the calculated dependences demonstrated good agreement.

Представлен конечно-элементный метод расчета гидродинамического шума, возбуждаемого турбулентными пульсациями жидкости в присутствии упругого тела. Традиционный подход к решению этой задачи на основе прямого решения уравнения Лайтхилла требует большого объема вычислений. Показано, что ситуация существенно упрощается при расчете компонент шума на относительно низких частотах, которые отвечают длинам волн, превышающим размеры турбулентной области. В этом случае шумовое поле удается выразить через давление турбулентных пульсаций на поверхности упругого тела, найденное в приближении несжимаемой жидкости. Статья подготовлена по материалам доклада, представленного на IX Российской конференции “Вычислительный эксперимент в аэроакустике и аэродинамике”, г. Светлогорск, 26 сентября–1 октября 2022 г.

A new method for separating acoustic and pseudosound pressure fluctuations is proposed, based on analysis of signals at a pair of closely located points, so that the total size of the measurement zone is much smaller than the correlation scale of pseudosound perturbations. It is suggested that hydrodynamic fluctuations
propagate at a velocity significantly lower than the sound velocity and obey the “frozen-in” perturbation model, which makes it possible, in real time or during data postprocessing, to convert the spatial derivative of the signal into a temporal derivative, which, after time integration, yields an estimate for pseudosound perturbations
at the measurement point. A theoretical model of the approach and test results using model examples and numerical simulation data are presented.

Physical and mathematical numerical models have been developed to predict the effective acoustic properties of sound-absorbing honeycomb structures at sound pressure levels of 100 and 130 dB with normal sound wave incidence. The sound absorption coefficients and patterns of acoustic interactions of cells installed at the end of a cylindrical duct with normal sound wave incidence on them were studied by numerical mathematical and physical modeling. The sound absorption efficiency of single and groups of resonators of various shapes and sizes is estimated, and unique combinations of cells in groups are identified, taking into account their acoustic interactions. Representative samples of fragments of sound-absorbing structures were 3D-printed; laboratory tests of the samples were carried out with an interferometer with a normal sound wave incidence on the cells at a sound pressure level of 130 dB.

Исследованы акустические характеристики экранов Т-образного профиля на основе конечно-элементного моделирования. Установлено, что эффективность уменьшения уровня звука данным экраном связана не только с дифракцией, но также и с интерференцией звука на передней и задней кромках экрана. Показано, что интерференция звука на задней кромке экрана, в отличие от интерференции звука на передней кромке, влияет на звуковое поле только на небольших расстояниях от задней поверхности экрана. Проанализировано влияние на эти процессы частоты звука и геометрических размеров экрана.

A new method for estimating formant frequency tracks of the vocal tract for arbitrary speech segments is proposed. The method uses the ratio of two Fourier transforms of a speech signal with special exponential-type windows depending on some parameter. This ratio is used for specific points in time and is considered as a function of frequency and parameter. By analyzing, for several parameter values, the distribution of minimum points (in terms of frequency) for the phase of this ratio and/or a similar distribution of extreme points for its amplitude, it is possible to estimate formant frequencies from the peaks of these distributions. A mathematical study is presented that substantiates this approach. A series of numerical experiments were carried out on the processing of synthetic and real speech signals, which confirmed the performance capabilities of the proposed formant evaluation method. In particular, in experiments with synthesized vowels, it was found that the error in estimating their resonance frequencies is small and stable with respect to additive noise up to a signal-to-noise ratio of 5 dB. For real speech, the method makes it possible to calculate the formant frequency tracks for both sounds with vocal excitation and for voiceless fricatives, aspirated plosives, and whispered speech.

Abstract—A laser scanning vibrometer was used to measure the amplitudes and phases of the vibrational velocity of shear waves excited by a one-dimensional source in the form of a narrow rectangular bar in a gellike medium. The vibrations of 26 plates reflecting the laser beam and located inside an optically transparent
phantom along a segment with a length of 84.5 mm at a distance of 20 mm from the source were measured.
The angular distributions of the amplitude and phase of shear waves at discrete frequencies from 59 to 500 Hz were measured in continuous mode. In pulsed mode, the vibrator excited a pulse in the medium with a duration
of 1.5 periods of the 300 Hz frequency. The amplitudes and phases of shear waves were calculated by fast
Fourier transform of the time profile of the vibration velocity of the plates with a duration of 50 ms. The angular amplitude distributions measured in the pulsed and continuous modes are qualitatively the same. At all frequencies, the distributions are symmetrical with respect to the vertical axis. The maximum oscillation amplitude is observed at angles close to ±45°. The velocity of shear waves, calculated from the measured phase distributions, increases from 2 to 2.5 m/s with a change in frequency from 50 to 500 Hz. It is shown that this velocity behavior is well described by a relaxation model of the medium with one relaxation time equal to 0.3 ms. Shear wave attenuation depends on frequency and exceeds 1 cm-1 for waves with frequencies above
250 Hz. The maximum attenuation per wavelength is observed near the relaxation frequency of the medium in the 300–400 Hz range. The results can be used to optimize devices for measuring the elasticity of soft tissues.

Разработка компактных гидроакустических низкочастотных излучателей высокой удельной мощности связана со сложностями, обусловленными противоречивыми требованиями к габаритам, КПД, излучаемой мощности, ширине рабочей полосы частот, технологичностью изготовления. Для компактных излучателей габариты корпуса ограничивают возможность совмещения резонансов активного элемента и механической колебательной системы, что затрудняет их разработку. Компактный гидроакустический преобразователь продольно-изгибного типа с излучающей поверхностью сложной формы – “3D НЧИ” – разработан для масштабного моделирования и проверки теоретических расчетов такой конструкции, и при сравнительно малых размерах обладает высокой эффективностью. В работе приведены полученные при помощи лазерной виброметрии результаты измерений в воздухе колебательных характеристик двух различных по размеру и вариантам гофрирования титановых корпусов “3D НЧИ” и собранных излучателей. Предложенные конструктивные решения преобразователя с максимальными габаритными размерами менее 100 мм и весом примерно 1 кг обеспечивают чувствительность по напряжению около 1 Па м/В в рабочей полосе частот и основной резонанс в диапазоне 1–2 кГц. “3D НЧИ” обладает высоким значением коэффициента механической трансформации и использования присоединенной массы, а также имеет ряд других преимуществ по сравнению с аналогичными разработками. Показано, что различия в размерах двух представленных излучателей на 10–12% и геометрии излучающих оболочек (12 и 16 волн гофрирования) приводят к различию измеренных в воздухе резонансных частот (4.0 и 3.5 кГц соответственно). При этом излучатель большего размера обладает меньшим разбросом значений механического коэффициента трансформации по гребням и впадинам корпуса, а также более плотным распределением спектральных компонент за пределами основной полосы частот.