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The present work extends a recent two-dimensional analytical model for sound generation and transmission in an axial-flow outlet guide vanes row, by taking into account vane camber and stagger, as well as cut-on/cut-off or cut-off/cut-on transitions of inter-vane channel modes. It is aimed at demonstrating that such transitions may have a significant role in turbomachinery aeroacoustics, typically by changing the balance of upstream and downstream scattered waves. The model is based on a mode-matching procedure and generates a uniformly valid description of the sound field. Previous implementations neglecting the vane curvature have shown significant limitations at high frequencies compared to numerical simulations performed with a finite element method code. The extension presented in this paper introduces curvature by a slowly-varying duct formalism. Comparison with numerical simulations show substantial improvements at the cost of a reasonably higher computation time., Ce travail étend un modèle analytique bidimensionnel développé récemment pour la génération et la transmission du bruit au travers d’aubes de redresseur, par la prise en compte de la cambrure et du calage des aubes, ainsi que des transitions de modes coupé/passant ou passant/coupé dans les canaux inter-aubes. L’objectif est de démontrer qu’un tel phénomène de transition peut jouer un rôle significatif sur l’aéroacoustique des turbomachines, en modifiant la répartition des ondes diffractés à l’amont et à l’aval des aubes. Le modèle est basé sur la technique de raccordement modal et fournit une description uniformément valide du champ sonore. De précédentes implémentations négligeant la courbure des aubes ont montrées des limitations importantes à haute fréquence en se comparant à des résultats issus de simulations numériques par méthode des éléments finis. L’extension présentée dans ce travail introduit la courbure par une approche lentement variable. Les comparaisons avec la simulation numérique montrent une nette amélioration des résultats au prix d’une augmentation raisonnable du temps de calcul.

Аналіз електроенцефалограм є невід’ємна складова діагностики неврологічних захворюваннях. З огляду на їхню просторово-часову залежність традиційні підходи у клінічній практиці пов’язані із аналізом амплітуд сигналів із визначеним інтервалом його дискретизації. При цьому зовсім не враховуються залежності сигналів у просторі, що притаманне реальним змінюванням електроенцефалограм. Мета роботи полягає у розробці підходу, що надає можливість під час аналізу електроенцефалограм здорових і хворих пацієнтів урахувати просторову і часову залежність цих сигналів для підвищення якості діагностування. На ґрунті аналізу підходів до спектрального аналізу нестаціонарних медичних сигналів, зокрема, електроенцефалограм, запропоновано застосування системи ортонормованих вейвлет - функцій Морле, які, на відміну від інших розповсюджених вейвлет-функцій, здатні забезпечити отримання спектрів сигналів, що аналізуються, як у часі, так й у просторовому вимірі. Отримано спектральне подання ЕЕГ-сигналів із застосуванням вейвлет-функцій Морле. Виконано кратномасштабний аналіз електроенцефалограм для здорових і хворих пацієнтів, що надає можливість підвищити якість спектрального аналізу сигналів у просторово-часовому вимірі. Застосування вейвлет-функцій до аналізу ЕЕГ-сигналів пацієнтів, хворих на епілепсію надало можливість суттєво підвищити якість діагностики шляхом відокремлення низькочастотних і високочастотних компонент сигналу із застосуванням методів фільтрації завад. Аналіз ЕЕГ-сигналів із застосуванням вейвлет-перетворень є ефективний метод надійної ідентифікації біоелектричного стану головного мозку як здорових пацієнтів так і хворих на епілепсію. Моніторинг та аналіз пацієнта упродовж тривалішого часу може надати більше інформації про розвиток епілепсії. Вейвлет-перетворення у сполученні із штучними нейронними мережами надає можливість реалізувати класифікатор на грунті розподілу енергії складових сигналу ЕЕГ. Визначення активності окремих компонентів сигналів ЕЕГ, а також матеріальність процесів, що мають місце у джерелах цих хвиль, може стати предметом подальших досліджень. The analysis of electroencephalograms is an integral part of the diagnosis of neurological diseases. Given their spatial-temporal dependence, traditional approaches in clinical practice are associated with the analysis of signal amplitudes with a defined interval of its discretization. At the same time, the dependence of signals in space, which is inherent in real changes of electroencephalograms, is not taken into account at all. The purpose of the work is to develop an approach that makes it possible to take into account the spatial and temporal dependence of these signals during the analysis of electroencephalograms of healthy and sick patients to improve the quality of diagnosis. Based on the analysis of approaches to the spectral analysis of non-stationary medical signals, in particular, electroencephalograms, it is proposed to use a system of orthonormal wavelets - Morle functions, which, unlike other widespread wavelet functions, are capable of obtaining the spectra of the analyzed signals, both in time and in the spatial dimension. A spectral presentation of EEG signals was obtained using Morle wavelet functions. Multiple-scale analysis of electroencephalograms for healthy and sick patients was performed, which provides an opportunity to improve the quality of spectral analysis of signals in the space-time dimension. The application of wavelet functions to the analysis of EEG signals of patients with epilepsy made it possible to significantly improve the quality of diagnosis by separating low-frequency and high-frequency components of the signal using noise filtering methods. The analysis of EEG signals using wavelet transformations is an effective method of reliable identification of the bioelectrical state of the head brains of both healthy patients and patients with epilepsy. Monitoring and analyzing the patient over a longer period of time can provide more information about the development of epilepsy. Wavelet transformation in combination with artificial neural networks provides an opportunity to implement a classifier based on the energy distribution of the components of the EEG signal. Determining the activity of individual components of EEG signals, as well as the materiality of the processes taking place in the sources of these waves, may become the subject of further research.

With the 3:1 internal resonance , the primary and secondary resonances of an axially moving thin circular cylindrical panel are investigated in the present work. The governing equation and the compatibility equation are established based on the Donnell's nonlinear shell theory and solved to obtain the nonlinear steady-state responses by combining the Galerkin method and the method of multiple scales. The analytical solutions are verified by numerical solutions based on the Runge-Kutta Method. The governing equation includes both the quadratic nonlinearity and the cubic nonlinearity, so the perturbation solutions need to consider three time scales. The quadratic nonlinearity causes the softening behavior of the system. Natural frequencies and the 3:1 internal resonance condition are obtained by the linear analysis. Under the primary resonance , the internal resonance causes the coupling of the first two modes to complicate the nonlinear dynamic response. The response for the second mode possesses an extra bulge or peak due to the internal resonance. The quadratic nonlinearity results in the zero frequency drift and the second-order harmonic. Under the secondary resonance, the exciting force only arouses the second mode. Results are shown to examine the effects of the internal resonance, the exciting force and viscous damping coefficients on the nonlinear dynamic response of an axially moving thin circular cylindrical panel.

In ultrasonic guided wave inspections, incident waves propagate as a finite-bandwidth wave packet. During propagation, the shape of the wave packet is distorted because of dispersion even if there are no viscous or scattering effects. Although the presence of distortion is well known, how the wave packet is distorted has not been sufficiently investigated. We use the method of multiple scales (MMS), a perturbative scheme, to investigate the dispersion of the Lamb waves comprising the finite-bandwidth wave packet. Solutions obtained by the MMS to order O ( e 2 ) show that the shape of an input wave-packet remains invariant during propagation along the waveguide. The wave packet propagates with a group velocity obtained from a classical analysis. The O ( e 3 ) -order MMS solutions exhibit a symmetric distortion of the shape, whereas the O ( e 4 ) -order MMS solutions feature symmetric and anti-symmetric distortion. For the derivation of the O ( e 3 ) - and O ( e 4 ) -order MMS solutions, the Fourier transform of the wave-packet shape is introduced. The proposed MMS solutions were verified by comparing them with the numerical time-domain solutions constructed from the classical frequency-domain solutions. The strength of the distortion depends on propagation mode, input frequency, and shape of the input wave packet. Because the wave-packet distortion induces a shift and reduction of the peak, the propagation velocity is different from the group velocity. For long-distance inspections, the proposed method provides the precise propagation velocity and details of the propagation-mode selection.

In the present work, vibration suppression of a single degree of freedom nonlinear spring-mass primary (main) system subjected to simultaneous external harmonic and parametric excitation by using traditional and non-traditional active nonlinear vibration absorber (ANVA) is carried out. The traditional and non-traditional ANVA consists of a PZT (lead zirconate titanate) stack actuator in series with a nonlinear spring and a damper. In the traditional ANVA, the damper is connected to the main system whereas, in non-traditional ANVA, the damper is connected to the base of the main system. The governing nonlinear equations of motion for the system have been derived using weighted modal matrix approach considering novel actuation force by time delay in displacement, velocity and acceleration feedback of the main system by the PZT stack actuator and the nonlinear spring in series combination. The method of multiple scales (MMS) is used to obtain the reduced equations which are solved using Newton’s method. The responses of the system for the primary, principal parametric and simultaneous primary and principal parametric resonance conditions have been studied. The results are compared with those obtained by using the harmonic balance method (HBM), numerical method and with previous literature. From these results, two resonating peaks in the frequency response of the main system are shown by using the reduced equation of the MMS which was not reported in earlier literature. It is shown that for the active case the vibration of the undamped main system is completely reduced at the specified operating frequency for both the linear and nonlinear systems. Also, for a wider range of operating frequencies, the vibration of the main system is reduced by actively tuning the absorber for various mass ratios. Further, the efficacy of the active force is observed in reducing the instability regions and improving the critical value of excitations in the trivial state.

In the commented paper, the authors considered a two-dimensional airfoil with nonlinear stiffness and damping, and derived the amplitude modulation equation (AME) of the system limit cycle oscillation around its bifurcation. Based on the variation equation of the AME, they conducted the stability analysis. Unfortunately, the obtained variation equation associated with the AME is incorrect.

A novel dual proof mass accelerometer is proposed by introducing mode localization in two electrostatically coupled resonators. The levering mechanism is utilized to amplify the inertial force applied axially to the two weakly coupled resonators. The dynamic model considering the electrostatic and mechanical nonlinearities is established and solved by the method of multiple scales, and also is validated by the harmonic balance method (HBM) coupled with the asymptotic numerical method (ANM). The linear and nonlinear sensitivities depicted as the difference of relative shift of amplitude ratio are investigated as well as the main influencing factors. It has been found that linear sensitivity is up to 4 orders of magnitude higher than that expressed by the difference of relative frequency shift. Also, the nonlinear sensitivity is further increased by 1.47 times comparing to the linear sensitivity. Moreover, the resolution is also greatly improved when the sensor is driven beyond its critical amplitude. Finally, the effect of the electrostatic coupling on the sensing performances is explored, and the optimal coupling voltage is theoretically identified at the limit of mode aliasing.