Vibration Amplitude Distribution Research Articles

Predicting distribution of aeolian vibration amplitude of undamped overhead transmission lines

The most widely accepted estimation procedure of the severity of aeolian vibration is by calculating the maximum oscillation amplitudes of the conductor using Energy Balance Principle (EBP). However, the EBP is based on wind tunnel results where only one frequency is excited, while observations and experimental results show that multiple resonant modes are excited simultaneously. Furthermore, the required number of cycles of each amplitude level is not provided by current EBP-based methods. In this paper, vibration data from an experimental undamped ACSR Bersfort test line in Quebec, Canada, is recorded and analyzed. For each record of aeolian vibrations, amplitudes are fitted to a Rayleigh distribution based on the narrow-band assumption. The number of cycles and Rayleigh parameter are then related to wind conditions through a modified Strouhal frequency and EBP methodology. A statistical model is proposed to relate vibration profiles and wind input while considering wind turbulence intensity. The proposed method performs well and gives accurate estimates of both vibration amplitudes and number of cycles for ACSR Bersfort conductor. Physical and statistical theory is provided for each step of the method in order to extend the application of the method to other types of conductors or different line configurations.

Modernized Resonant Column and Torsional Shearing Apparatus With Multipoint Contactless Displacement Detection System

Abstract In this study, a modification of resonant column/torsional shearing (RC/TS) apparatus was proposed to perform a qualitative analysis of a noncohesive soil specimen vibration during RC tests. An additional multipoint displacement detection system was installed in the RC/TS WF8500 device. In the new measuring system, 48 mini-magnets are attached to the side surface of a cylindrical soil specimen, creating a regular grid of measuring points. Around 48 Hall sensors (Honeywell SS495A1) are used to measure changes in the magnetic field strength due to the movement of the corresponding magnets on the surface of the specimen subjected to dynamic torque. The Hall sensor generates an analog signal that is proportional to the change in the magnetic field. The measurements are collected with a newly developed data acquisition system that consists of a set of analog-to-digital converters and a set of ARM (Advanced RISC (Reduced Instruction Sets Computing) Machine) microcontrollers. The measurement system is controlled with a dedicated software, ControlRec, developed by the authors. The measurements are taken synchronically with and independently from the standard RC test procedure. The new measuring technique allows to observe displacements of the 48 points on the specimens’ surface with over 4 times higher sampling rate than in the original measuring system. As a result, additional effects related to the mechanical wave propagation through soil specimen were observed (local disturbances in distribution of vibration amplitudes or significant displacements near the bottom end of the specimen, which is assumed to be fixed in the standard RC/TS results analysis), that could not be identified using the standard equipment of the device.

High-Frequency Ultrasonic Radiator Power Increase by Means of Summation of Vibrations of Symmetrically Arranged Langevin Transducers

The article focuses on the research of processes of summation of ultrasonic vibrations of individual Langevin transducers symmetrically arranged on a common summator. This design could be used to solve the problem of increasing the power of a high-frequency ultrasonic radiator by means of the summation of the vibrations of individual Langevin transducers. The results of the presented theoretical and experimental investigations supported the possibility of summation of symmetrical diametrical vibrations when they are transformed into longitudinal vibrations. As a result, a new design scheme for high-frequency radiator construction was developed that provides symmetry and uniformity of vibration amplitude distribution of piezoceramic elements. This made it possible to eliminate the damage of piezoceramic elements. The article establishes that an acoustic power (continuous mode) of 1450 W at an efficiency of 78% is achieved when the vibrations from 9 to 11 of symmetrically arranged Langevin transducers at a resonant frequency of 30.05 kHz with an amplitude of 26 µm are summed. The use of this ultrasonic high-frequency radiator with increased power will provide intensification of processes in various areas of industry.

Digital twin-driven vibration amplitude simulation for condition monitoring of axial blowers in blast furnace ironmaking

ABSTRACT Long-term reliable condition monitoring (CM) of blast furnace blowers is essential to avoid catastrophic failure. Due to variable working conditions, the predefined thresholds in current CM systems influence the accuracy of the monitoring process and can lead to misdiagnoses. In order to overcome this limitation, we propose a digital twin (DT)-based scheme to monitor vibrations found in blowers. Factors believed to impact the distribution of vibration amplitudes are analysed using data collected from a constant speed axial blower operating in an industrial commercial environment and, based on which, a machine learning-based adaptive amplitude simulation model is developed on our on-site private cloud computing platform. Outcomes reveal that different guide vane openings in the manufacturing process can cause changes in amplitudes. By integrating the newly-arriving sensor data, vibration amplitudes can be more accurately predicted in the virtual space. The gap between the simulated and actual value narrowed from ±5 µm to within ±3 µm, from which a dynamic threshold can be defined. The resulting DT model, coupled with the on-site private cloud computing platform, which alleviates the shortage of computational and storage capacity in steel plants, allows for a much more effective CM system.

УЛЬТРАЗВУКОВОЙ ПРЕОБРАЗОВАТЕЛЬ С РАДИАЛЬНО РАСПОЛОЖЕННЫМИ ПЬЕЗОКЕРАМИЧЕСКИМИ ПАКЕТАМИ

This article describes the design of an ultrasonic piezoelectric transducer with increased power. The increase in power is achieved by summing the power of several Langevin converters installed on a single radiating patch. The conducted studies have shown that the main disadvantage of this piezoelectric transducer is the destruction of piezoceramic rings due to the high uneven distribution of oscillation amplitudes in the region of their attachment. Theoretical and experimental studies have made it possible to optimize and eliminate the main drawback of the piezoelectric transducer. In this case, the maximum uniformity of the distribution of vibration amplitudes in the area of attachment of piezoceramic rings was chosen as an optimization criterion.As a result of the research, an optimized design of high-frequency converters has been developed.It has been determined that the installation of 9-11 radially arranged piezoceramic packages provides the minimum non-uniformity of oscillations in the area of piezoring attachment, while the transducer designed for 30 kHz provides acoustic power of at least 1450 W with an efficiency of 78%.

Vibration amplitude mapping by stroboscopic structured light projection

In this work a method to evaluate the distribution of vibration amplitudes of objects was demonstrated, combining for the first time oblique structured light projection, stroboscopic illumination and fringe evaluation. The light pattern was formed by straight and parallel fringes produced by a slightly misaligned Twyman–Green interferometer illuminated by a 40-mW, 650-nm diode laser. Stroboscopic illumination was achieved by driving the laser with a PWM signal with the same frequency than that of the vibrating object. By evaluating the fringes with phase stepping and phase unwrapping procedures, the amplitude mapping of a formica bar and circular rubber membranes was performed. By averaging the fringe position over the light pulse duration a correction ratio between the actual phase and the measured phase was obtained as a function of the pulse duty cycle, and the dependence of the fringe visibility on the duty cycle was studied. The experiments showed that relatively large amplitudes in a range from tens of millimeters up to few millimeters can be measured.

Экспериментальное определение вибрационных характеристик рабочих лопаток турбин помехоустойчивым цифровым спекл-интерферометром

The paper notes the wide possibilities and high efficiency of vibration diagnostics of parts and assemblies of power units by the method of electronic speckle interferometry (ESI), shows the feasibility of developing and improving methods for obtaining speckle interferograms of vibrating objects. A patented by the authors' scheme of a digital speckle interferometer (DSI) for determining the dynamic parameters of products is presented. The diffuse reference wave greatly simplifies its alignment, mainly the aligned channels of propagation of interfering beams determine the resistance to mechanical and thermal disturbances, and the separate beam splitter and diffuser make it easy to optimize the optical scheme for the object under study. Speckle interferograms are obtained by speckle correlation methods and a developed method for determining the contrast of the dynamic speckle pattern. It does not impose special requirements on the parameters of the video system, does not require the use of a specialized video camera, and allows, by using a rotary platform, to organize a panoramic view of the oscillatory forms of asymmetric structures. The use of this method in combination with the proposed optical scheme provides an express analysis of products in off-bench conditions. The increased noise immunity of the installation allows the determination of the spectrum of frequencies and vibration modes (SFVM) of samples under free boundary conditions, which is rarely realized in interferometry. The paper presents examples of such speckle interferograms, the expediency of obtaining which is important in the resonance study of the elastic properties of the material and vibration resonance flaw detection. The implemented software and hardware solutions increase the resolution and visibility of the band patterns; facilitate their quantitative interpretation and the extraction of numerical information on the distribution of vibration amplitudes. The area of scientific interests and the specificity of the author's developments have determined the preferential adaptation of the proposed device with a complex of software and methodological developments for vibration testing of gas turbine engine (GTE) blades.

Microscopic-Phenomenological Model of Glass Transition and Temperature Dependence of Viscosity—Part I: Foundations of the Model

The glass transition is described as a time- and history-independent singular event, which takes place in an interval dependent on the distribution width of molecular vibration amplitudes. The intrinsic glass transition is not seen as a relaxation phenomenon, but is characterized by a fixed volumetric state at the glass temperature Tg0. The relaxation behavior of the transport properties depends on the distance to Tg0. Free volume is redefined and its generation is the result of the fluctuating transfer of thermal energy into condensed matter and the resulting combined interactions between the vibration elements. This creates vacancies between the elements which are larger than the cross-section of an adjacent element or parts thereof. Possible shifts of molecules or molecular parts through such apertures depend on the size and axis orientation and do not require further energetic activation. After a displacement, additional volume is created by delays in occupying abandoned positions and restoring the energetic equilibrium. The different possibilities of axis orientation in space result in the different diffusive behavior of simple molecules and chain molecules, silicate network formers, and associated liquids. Glass transformation takes place at a critical volume Vg0 when the cross-section of apertures becomes smaller than the cross-section of the smallest molecular parts. The glass transition temperature Tg0 is assigned to Vg0 and is therefore independent of molecular relaxation processes. Tg0 is well above the Kauzmann and Vogel temperatures, usually just a few degrees below the conventionally measured glass temperature Tg(qT). The specific volume at the two temperatures mentioned above cannot be achieved by a glass with an unordered structure but only with aligned molecular axes, i.e. in a crystalline state. Simple liquids consisting of non-spherical molecules additionally alter their behavior above Vg0 at Vgl where the biggest gaps are as small as the largest molecular diameter. Tgl is located in the region of the crystalline melting point Tm. Both regions, above and below Tm, belong to different physical states and have to be treated separately. In the region close to Vg0 respectively Tg0, the distribution of vibration amplitudes has to be taken into account. The limiting volume Vg0 and the formation of apertures larger than the cross-section of the vibrating elements or parts thereof, in conjunction with the distribution width of molecular vibrations as Vg0 is approached, and the spatial orientation of the molecular axes is key to understanding the glass transition.

Influence of inertial links on the distribution of vibration amplitudes of points of the working body of a technological vibrating

Features of problems of dynamics and formation of dynamic states of working bodies of vibrating technological machines are considered. The purpose of the work is to develop a method for constructing mathematical models of vibration machines that provide the ability to evaluate, control and adjust the forms of movement of working bodies by introducing additional links into the structure of the system, forming a closed internal contour. Methods of structural mathematical modeling are used in the construction of original structural formations of their typical elements. The direction of constructive and technical solutions in the implementation of approaches to configure and adjust the structure of the vibration field of the working body is proposed. The method is implemented using the analytical apparatus of the automatic control theory. The features of dynamic states formation based on the application of transfer functions of structural mathematical models of mechanical oscillatory systems are studied. The use of transfer functions of interpartial connections for the formation of vibration fields of working bodies is proposed. Analytical relations are obtained that determine the possibility of implementing specific dynamic modes, including the decoupling of movements by individual coordinates, taking into account the features of the connectivity of movements by characteristic points of the working body, the manifestation of oscillation nodes or modes of dynamic damping. Features of using structural mathematical modeling methods in problems of dynamics of mechanical oscillatory systems with additional connections are discussed. The work is aimed at specialists in the field of theoretical and applied mechanics, machine science and mechanical engineering.

Phase Shift Strategies in Phase Shifting Time Averaging Interferometry

Classical time-averaging interferometry technique is widely used for MEMS/MOEMS dynamic behavior investigations. It provides useful information on resonant vibration frequencies and mode shapes in the form of Bessel fringe images. To evaluate the information on objects’ vibration amplitude distribution, one needs to further process Bessel fringe images (besselograms). Among different available approaches to besselograms processing, Temporal Phase Shifting is of particular interest since it provides the most accurate results. However, it requires an additional cumbersome correction routine via specially designed look-up-tables fitted to the calculation algorithm used. In this paper, we numerically investigate the possibility of reducing Bessel images argument (phase) evaluation error by different phase shifting strategies. Two different 5 step algorithms are investigated for that purpose. Additionally, a quick and robust correction procedure based on evaluated phase distribution is presented. It allows us to speed up the calculations significantly. Moreover, such an approach is much less susceptible to noise in comparison to a look-up-table solution.

A fault diagnosis method using Interval coded deep belief network

The rolling bearing, though a widely used component in rotating machinery, is also failure-prone. There are some difficulties in extracting valuable fault features from the vibration signal generated by the rolling bearing operation. Based on the interval coded deep belief network, an improved method for fault diagnosis is introduced to deal with the existing problems. Interval code is an encoding method to characterize fault features by using bearing vibration amplitude distribution. This method can also reduce the complexity of the original data and integrate input dimension. The deep belief network can remove the dependence from manual feature extraction and quickly extract the fault features from coding results. This proposed method is employed in the fault diagnosis experiments of rolling bearing to evaluate the performance. From the obtained experiment results, it can be concluded that the interval coded deep belief network boosts performance, which can eliminate the limitation of the input data dimension in the traditional deep learning model.

Residual stress relief of welded aluminum alloy plate using ultrasonic vibration

Ultrasonic vibratory stress relief (UVSR) is a novel method for residual stress relieving of metal parts. In this paper, the UVSR method was applied to treat a random-sized plate, which is not designed to match with the resonant frequency of the ultrasonic transducer. The UVSR system includes an ultrasonic generator, a 20 kHz ultrasonic transducer and specially designed fixtures to exert ultrasonic vibration to the treated parts. Based on the experimental results, the average stress relief ratio reached 53% and the final residual stress distribution interval was reduced by 57. The vibratory stress introduced by the ultrasonic vibration was obtained accurately by matching the FE model with the measured vibration amplitude distribution. It is found that local yield stress, instead of macroscopic yield stress, should be used as the threshold of residual stress relieving. Moreover, if the local yield stress of a material is constant, the local yield stress of 6082 aluminum alloy is reduced by at least 27% during the UVSR. Finally, it is found that the residual stress relief rate in one direction is proportional to the vibratory stress introduced in that direction.

Full-field vibration profilometry using time-averaged interference microscopy aided by variational analysis.

Full-field vibration testing is indispensable in characterization of micro-electro-mechanical components. Time-averaged interference (TAI) microscopy is a very capable and accurate vibration profilometry technique. It employs natural all-optical multiplexing of required information, i.e., recorded interferogram is amplitude-modulated by the Bessel pattern, which in turn encodes spatial distribution of vibration amplitude in its underlying phase function. We propose a complete end-to-end numerical scheme for efficient and robust vibration amplitude map demodulation based on the variational data-analysis paradigm. First, interferogram is variationally pre-filtered and complex analytic-interferogram is generated, exploiting the Hilbert spiral transform. The amplitude term of analytic-interferogram is accessed for Besselogram, i.e., TAI amplitude modulation distribution. Next, the Besselogram is variationally pre-filtered and complex analytic-Besselogram is calculated applying the Hilbert spiral transform. Finally, the phase term of the analytic-Besselogram is determined, unwrapped and post-filtered to achieve spatial distribution of vibration amplitude. Proposed approach is verified using simulated interferograms and corroborated upon experimental vibration testing. Reported method compares favorably with the reference Hilbert-Huang transform-based method. The improvement was gained by adding two new steps to the calculation path: (1) additional removal of the interferogram's residual background and noise and (2) variational based vibration amplitude map error correction method.

Vibration optimization of an infinite circular AT-cut quartz resonator with ring electrodes

• The thickness-shear vibrations of an infinite circular AT-cut quartz resonator with ring electrodes were studied theoretically. • The influences of electrode geometry and electrode/plate mass ratios on the vibration profiles were investigated in detail. • A nearly uniform displacement distribution and mass sensitivity of the resonator was achieved by optimization. • The obtained results may provide a fundamental reference to the design and optimization of QCR sensors for microweighing. This paper presents the thickness-shear (TSh) vibration modes of an infinite circular AT-cut quartz resonator with ring electrodes. By application of 2D scalar differential equations derived by Tiersten and Smythe, we obtain the resonant frequencies and vibration amplitude distributions of thickness-shear modes in the resonator. The theoretical results have been verified in commercial FEM software COMSOL. Through numerical examples, we illustrate that the distribution of displacement fields in the center part of the ring electrode is adjustable. Furthermore, we optimize the size of the electrodes and the mass ratio of the electrode to the plate, in order to achieve a nearly uniform displacement distribution and mass sensitivity of the resonator. These results can be a theoretical guidance for design and optimization of sensors based on quartz resonators.

Hilbert–Huang transform based advanced Bessel fringe generation and demodulation for full-field vibration studies of specular reflection micro-objects

The Hilbert-Huang transform working principle is used to develop advanced single-frame and two-frame Bessel fringe pattern generation and demodulation algorithms especially tailored to enhance full-field vibration studies using time-averaged interferometry. The Bessel fringe pattern, named as the Besselogram, is understood as calculated amplitude modulation/contrast variation map of the time-averaged interferogram intensity distribution. Proposed Besselogram processing techniques are computationally fast and robust to fringe pattern imperfections and environmental disturbances encountered in interferometric studies of vibrating micro-objects. The advanced fast adaptive bidimensional empirical mode decomposition scheme is employed to filter interferograms, Bessel fringes and their phase maps. Reported Bessel fringe pattern analysis method possesses unique ability to determine both vibration phase and amplitude distribution maps from a single time-averaged interferogram. Comprehensive numerical simulations corroborate advantageous features of proposed methods. Experimental evaluation performed for two resonant modes of a silicon micro-membrane is enclosed for completeness of the analysis.

Ultrasound source using a rectangular vibrating plate combined with rigid walls

Ultrasound sources that use a stripe-mode rectangular vibrating plate radiate strong ultrasound waves in the air. In this study, we investigated the design strategy for combining the vibrating plate with rigid walls and evaluated the intense ultrasound waves radiated by the sound source. First, we examined the design method for a rectangular transverse vibrating plate with both ends fixed and the vibration amplitude distribution of the vibrating plate. Second, we measured the sound pressure distribution in the formation of the standing wave field. Finally, we clarified the relationship between the input power and sound pressure of the standing wave field antinodes.

Polynomial chaos expansion method in estimating probability distribution of rotor-shaft dynamic responses

Abstract The main purpose of the study is an assessment of computational efficiency of selected numerical methods for estimation of vibrational response statistics of a large multi-bearing turbo-generator rotor-shaft system. The effective estimation of the probability distribution of structural responses is essential for robust design optimization and reliability analysis of such systems. The analyzed scatter of responses is caused by random residual unbalances as well as random stiffness and damping parameters of the journal bearings. A proper representation of these uncertain parameters leads to multidimensional stochastic models. Three estimation techniques are compared: Monte Carlo sampling, Latin hypercube sampling and the sparse polynomial chaos expansion method. Based on the estimated values of the first four statistical moments the probability density function of the maximal vibration amplitude is evaluated by the maximal entropy principle method. The method is inherently suited for an accurate representation of the probability density functions with an exponential behavior, which appears to be characteristic for the investigated rotor-shaft responses. Performing multiple numerical tests for a range of sample sizes it was found that the sparse polynomial chaos method provides the best balance between the accuracy and computational effectiveness in estimating the unknown probability distribution of the maximal vibration amplitude

Noise suppression in curved glass shells using macro-fiber-composite actuators studied by the means of digital holography and acoustic measurements

The paper presents methods and experimental results of the semi-active control of noise transmission in a curved glass shell with attached piezoelectric macro fiber composite (MFC) actuators. The semi-active noise control is achieved via active elasticity control of piezoelectric actuators by connecting them to an active electric shunt circuit that has a negative effective capacitance. Using this approach, it is possible to suppress the vibration of the glass shell in the normal direction with respect to its surface and to increase the acoustic transmission loss of the piezoelectric MFC-glass composite structure. The effect of the MFC actuators connected to the negative capacitance shunt circuit on the surface distribution of the normal vibration amplitude is studied using frequency-shifted digital holography (FSDH). The principle of the used FSDH method is described in the paper. The frequency dependence of the acoustic transmission loss through the piezoelectric MFC-glass composite structure is estimated using measurements of the specific acoustic impedance of the curved glass shell. The specific acoustic impedance is measured using two microphones and a laser Doppler vibrometer (LDV). The results from the LDV measurements are compared with the FSDH data. The results of the experiments show that using this approach, the acoustic transmission loss in a glass shell can be increased by 36 dB in the frequency range around 247 Hz and by 25 dB in the frequency range around 258 Hz. The experiments indicate that FSDH measurements provide an efficient tool that can be used for fast and accurate measurements of the acoustic transmission loss in large planar structures.

Effects of Geometric Nonlinearity on Free and Forced Vibration Analysis of Moderately Thick Annular Functionally Graded Plate

This article deals with the nonlinear free and forced vibration of moderately thick annular functionally graded material plates. The thickness is assumed to be constant. Material properties are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. The formulations are based on the first-order shear deformation plate theory and von Kármán-type equation. Steady-state free and forced vibration analysis is investigated and results for linear and nonlinear vibration of isotropic annular plate are compared with those in the literature. Results reveal that the vibration frequencies are dependent on vibration amplitude and volume fraction distribution has a significant effect on the nonlinear vibration and dynamic response of the functionally graded plate.

Harmonic Motion Microwave Doppler Imaging: A Simulation Study Using a Simple Breast Model

A hybrid method for tissue imaging using dielectric and elastic properties is proposed and investigated with simple bi-layered breast model. In this method, local harmonic motion is generated in the tissue using a focused ultrasound probe. A narrow-band microwave signal is transmitted to the tissue. The Doppler component of the scattered signal, which depends on the dielectric and elastic properties of the vibrating region, is sensed. A plane-wave spectrum technique is used together with reciprocity theorem for calculating the response of a vibrating electrically small spherical tumor in breast tissue. The effects of operating frequency, antenna alignment and distance, and tumor depth on the received signal are presented. The effect of harmonic motion frequency on the vibration amplitude and displacement distribution is investigated with mechanical simulations using the finite element method. The safety of the method is analyzed in terms of microwave and ultrasound exposure of the breast tissue. The results show that the method has a potential in detecting tumors inside fibro-glandular breast tissue.