Variational Mode Decomposition-Informed Empirical Wavelet Transform for Electric Vibrator Noise Analysis

Electric vibrators find wide applications in reliability testing, waveform generation, and vibration simulation, making their noise characteristics a topic of significant interest. While Variational Mode Decomposition (VMD) and Empirical Wavelet Transform (EWT) offer valuable support for studying signal components, they also present certain limitations. This article integrates the strengths of both methods and proposes an enhanced approach that integrates VMD into the frequency band division principle of EWT. Initially, the method decomposes the signal using VMD, determining the mode count based on residuals, and subsequently employs EWT decomposition based on this information. This addresses mode aliasing issues in the original method while capitalizing on VMD’s adaptability. Feasibility was confirmed through simulation signals and ultimately applied to noise signals from vibrators. Experimental results demonstrate that the improved method not only resolves EWT frequency band division challenges but also effectively decomposes signal components compared to the VMD method.

Online asymmetry estimation for whole angle mode coriolis vibratory gyroscopes by high frequency injection

The whole angle mode gyroscope(WAMG)is considered to be the next generation architecture,but it is suffered from the asymmetry errors to conduct real products.This paper proposes a novel high frequency injection based approach for the error parameters online identification for the WAMG.The significance is that it can separate physical and error fingerprints to enable online calibration.The nonlinear WAMG dynamics are discretized to meet the requirement of numerical precision and computation efficiency.The optimized estimation methods are then constructed and compared to track asymmetry error parameters continuously.In the validation part,its results firstly prove that the proposed scheme can accurately identify constant asymmetry parameters with an overall tracking error of less than 1 ppm and the extreme numerical convergence can reach 10^(-12)ppm.Under the dynamic asymmetry variation condition,the root mean square errors(RMSE)indicate that the tracking accuracy can reach the level of10^(-3),which shows the robustness of the proposed scheme.In summary,the proposed method can effectively estimate the WAMG asymmetry errors online with satisfied performance and practical values.

A Review on Methods for Determining the Vibratory Damping Ratio

This article aims to popularize the methods for determining the vibratory damping ratio, to explain the various mathematical and physical theorems related to the establishment of literal expressions. Vibration damping is an essential parameter to reduce the dynamic responses of structures. The study aimed at its determination is necessary and essential for the safeguard of buildings and human lives during the earthquake. Among the main methods studied in this article, the free vibration attenuation method seems to be easy to implement but requires a state-of-the-art device to capture the responses. In addition to this device, the other methods require other equipment for the vibration of the system and the transformation of the responses in the frequency domain.

Output Waveform Analysis of an Electro-hydraulic Vibrator Controlled by the Multiple Valves

The existing research of the electro-hydraulic vibrator mainly focuses on system stability, working frequency width and output waveform distortion. However, this high frequency performance of the electro-hydraulic vibrator is difficult to be improved greatly due to fast insufficiently frequency response of the servo valve itself and limited compensation capability of the control structure in the vibrator system. In this paper, to realize high frequency vibration, an improved two-dimensional valve （here within defined as a 2D valve） as a main control component is adopted to the parallel connection with a servo valve to control the electro-hydraulic vibrator, Because the output waveforms of this electro-hydraulic vibrator are incapable to be verified through timely feedback as in the conventional electro-hydraulic servo system, the analysis to the output waveform becomes crucial to the design and control of the electro-hydraulic vibrator. The mathematical models of hydraulic actuation mechanism and the orifice area of the parallel valves connection are established first. And then the vibration process is divided into two sections in terms of the direction of the flow, the analytical expression of the excited waveform is solved. Based on relationships exist between working states and the control parameters the analytical results, the vibration boundary positions and the are derived. Finally an experimental system was built to validate the theoretical analysis. It is verified that this electro-hydraulic vibration system could achieve high working frequency, up to 2 000 Hz. The excited waveform is similar to the sinnsoidal waveform. And the ascent and decent slopes of the waveforms are somewhat asymmetrical. This asymmetry is not only caused by the change of the direction of the elastic force but also dependent on the bias position of the vibration. Consequentky the distortion of effective working waveform is less tha~ 10%. This electro-hydraulic vibrator controlled by the multiple valves could not only greatly enhance the working frequency but also precisely control the vibration characteristic variables such as waveform shape.

Design for Vibrator Field Experiment Based-on Vibrator-earth System

Source-generated energy in seismic vibrator records high frequency harmonic behavior. Conventional vibrator-earth coupling model was set up on the linear system. Some assumptions in the application of linear theory to the vibrator problem play an insignificant role in the overall coupling structure. Obviously, non-linear behaviors can be modeled using a “hard-spring” form of the Duffing equation. Model dedicates that a qualitatively similar harmonic component is present for a broad range of possible mathematical descriptions. After some qualitative analysis about the non-linear system, some conclusion can be drawn. Firstly, The design of the vibrator weight should be abided by two points as followed: In order to avoid decoupling for the vibrator to the earth, the weight should be greater than the peak of the driving force amplitude as to keep the resultant force pointing to the earth’s core. On the other hand, for the limited energy output, the vibrator overweight may damage the system high-frequency ability.Secondly, as the driving force frequency approaching to the ground hard-spring inherent frequency, the energy transmission was found to climb its peak from the system energy absorbed curve. At last, due to the non-linear coupling model system, its load curve would come into unstable frequency range, which might limit the application of the Vibroseis conventional sweeping pattern-linear sweep. A new sweeping pattern was listed: the driving signal was the pseudo-random sequence modulated by a fixed frequency cosine signal satisfying with the exploration precision and absorbing efficiency. The synthesized signal was ready to be realized by the electromagnetic driven system. Even the side-lobes noise of its auto-correlation function was restrained well. The theory coming from the Vibrator-earth coupling model was applied to the design of the Portable High-frequency Vibrator System (PHVS), and the good result was obtained. By the analysis of the vibrator base plate signal, the model was proved to be true. The exploration research on PHVS made a first step on its following optimal design.

Vibration Measurement of Pedestrian Bridge Using Double Magnetic Suspension Vibrator Based on Wavelet Analysis

Aiming at the problem of pedestrian bridge vibration measurement,a vibration measurement system of pedestrian bridge with dual magnetic suspension vibrator structure was designed according to absolute vibration measurement principle. The relationship between the magnetic repulsion force of vibrator and its displacement was obtained by the experimental method and the least square fitting method. The vibration equations of two magnetic suspension vibrators were deduced respectively,and the measurement sensitivity of the system was deduced. The amplitude-frequency characteristic of the system was studied. A simulation model of vibrator measurement system with double magnetic suspension vibrator was established. The analysis shows that the sensitivity of the vibration measurement system with double magnetic suspension vibrator is higher than that with single magnetic suspension vibrator. The four vibration waveforms were measured,that is,no one passes through a pedestrian bridge,there are cars running under the pedestrian bridge,single pedestrian passes through the pedestrian bridge and multiple pedestrians pass through the pedestrian bridge. The multi-scale one-dimensional wavelet decomposition function was used to analyze the vibration signals. The vibration characteristics were obtained using one dimension wavelet decomposition function under four different conditions. Finally,the vibration waveforms of four cases were reconstructed. The measured results show that the vibration measurement system of pedestrian bridge with double magnetic suspension vibrator structure has high measurement sensitivity. The design has a certain value to monitor a pedestrian bridge.

Simulation Analysis and Experiment on Piezoelectric Cantilever Vibrator

Piezoelectric cantilever bimorph vibrator is the core component of piezoelectric inertial actuators.Piezoelectric cantilever bimorph vibrator with lumped mass at the end is studied,and a dynamic model is constructed by the proposed method of transforming symmetric electrical signal excitation to equivalent harmonic force excitation.Combining the theory and test,the single-degree-of-freedom damp vibration system consisting of the vibrator is analyzed and the full response is provided.Dynamical system modeling and simulation are conducted by software Matlab/Simulink.The output response of deflection,velocity,acceleration,driving force are solved using the input signal of equivalent harmonic force.Based on the data of theory,simulation and experiments,the deflection of vibrator is analyzed and compared under the excitation of sine wave signal.Result shows that the dynamic deflection results of vibrator from theory,simulation and experiments agree well with each other.The proposed modeling and analysis approaches of the single-degree-of-freedom damp vibration system consisting of the vibrator,have some reference significance for further research of piezoelectric inertial actuators.

Temperature dependence of mode coupling effect in piezoelectric vibrator made of[001]c-poled Mn-doped 0.24PIN-0.46PMN-0.30PT ternary single crystals with high electromechanical coupling factor

The influence of temperature on mode coupling effect in piezoelectric vibrators remains unclear.In this work,we discuss the influence of temperature on two-dimensional(2D)mode coupling effect and electromechanical coupling coefficient of cylindrical[001]c-poled Mn-doped 0.24PIN-0.46PMN-0.30PT piezoelectric single-crystal vibrator with an arbitrary configuration ratio.The electromechanical coupling coefficient kt decreases with temperature increasing,whereas k33 is largely invariant in a temperature range of 25℃-55℃.With the increase of temperature,the shift in the‘mode dividing point’increases the scale of the poling direction of the piezoelectric vibrator.The temperature has little effect on coupling constantΓ.At a given temperature,the coupling constantΓof the cylindrical vibrator is slightly greater than that of the rectangular vibrator.When the temperature changes,the applicability index(M)values of the two piezoelectric vibrators are close to 1,indicating that the coupling theory can be applied to piezoelectric vibrators made of late-model piezoelectric single crystals.

Low-frequency ride comfort of vibratory rollers equipped with cab hydro-pneumatic mounts

Based on the advantages of hydraulic and pneumatic mounts,a new hydro-pneumatic mount(HPM)is proposed to improve the low-frequency ride comfort of vibration rollers.Through the experiment of the vibratory roller,a nonlinear vehicle dynamic model working on off-road soil grounds is then established to assess the HPM's ride comfort in the low-frequency region.Two indices,the power spectral density(PSD)acceleration and root mean square(RMS)acceleration of the operator vibration and cab shaking,are chosen as objective functions in both the frequency and time regions.The research results show that when the cab isolations are equipped with the HPM,the RMS values of the operator's seat,cab's pitch and roll angles are reduced by 35%,42%and 53%;and the maximum PSD of the operator's seat,cab's pitch and roll angles are decreased by 39%,59%and 65%,respectively.Consequently,the characteristics of the nonlinear damper and high-static stiffness of HPM can greatly reduce the operator vibration and cab shaking in the low-frequency region when compared to the vibratory roller's cab using the rubber mounts.

Dynamical Examinations of Vibrator Models, Describing Some Non Elastic Properties of Crystals

On the base of a vibrator atomic model the mechanical and thermal properties of the object are analyzed. The potential energy of the vibrator is represented by means of positive term with coordinate deflection in second power and negative term with deflection in fourth power. With the use of dynamical procedure of calculation, which permits to calculate mean deflection and root mean square amplitude of vibrations, the dependence of applied force from mean amplitude and temperature is calculated. This dependence shows a maximum (or minimum, when the direction of force is reversed), the height of which diminishes with rising temperature. When the force reaches the value of the maximum, the object does not elastic counteract to the force, and gliding begins. It is also considered a vibrator with positive term, containing the deflection in second power and a term, where the deflection treats in third power (Boguslawski vibrator). Exact calculations of the dependence of the force from the temperature in adiabatic process, where the entropy is maintained constant, shows that it is represented by means of a curve with a maximum, so that stretching leads to cooling till the point of maximum is reached.

The Analysis of a Vibrator Oil-stirring Phnomenon and Study on a New Structure

The deep vibrator is an important equipment of foundation improvement. It works through eccentric masses with high-speed. But the traditional eccentric structure will stir the oil around it, and it will result in the loss of motor power. The paper analyzed the stirring phenomenon, and got the level and specific data of stirring and swirling through fluent software. After principle analysis, a new type of anti-churning eccentric structure was put forward, which can effectively avoid stirring phenomenon. Otherwise, the new structure will also not produce irregular vibration because of swirling, then it can work with a better performance. In addition, the contrast of dynamic performance between a traditional and new structure was carried out in the paper and proved that the new structure has a better working performance. Modeling data in the paper is from surveying and mapping, so the conclusion can be taken as guidance for vibrator designing.

Adding body load modifies the vibratory sensation of the foot sole and affects the postural control

Background: Heavy backpacks are often used by soldiers and firefighters. Weight carrying could reduce the speed and efficiency in task completion by altering the foot sole sensitivity and postural control.Methods: In fifteen healthy subjects, we measured the changes in sensitivity to vibrations applied to the foot sole when standing upright or walking after load carrying(30% body weight). The participants were asked to judge different vibration amplitudes applied on the 2 nd or 5 th metatarsal head and the heel at two frequencies(25 and 150 Hz) to determine the vibration threshold and the global perceptual representation(Ψ)of the vibration amplitude(Φ)given by the Stevens power function(Ψ=k×Φ~n). Any increase in negative k value indicated a reduction in sensitivity to the lowest loads. Pedobarographic measurements, with computation of the center of pressure(COP) and its deviations, were performed during weight carrying.Results: The 25-Hz vibration threshold significantly increased after weight carrying when standing upright or walking.After standing with the added loads, the absolute negative k value increased for the 25 Hz frequency. After walking with the added loads, the k coefficient increased for the two vibration frequencies. Weight carrying significantly increased both the CoP surface and CoP lateral deviation.Conclusions: Our data show that weight carrying reduces the sensory pathways from the foot sole and accentuates the center of pressure deviations.

Development of a vehicle-track interaction model to predict the vibratory benefits of rail grinding in the time domain

Imperfections in the wheel-rail contact are one of the main sources of generation of railway vibrations. Consequently, it is essential to take expensive corrective maintenance measures, the results of which may be unknown. In order to assess the effectiveness of these measures, this paper develops a vehicle-track interaction model in the time domain of a curved track with presence of rail corrugation on the inner rail. To characterize the behavior of the track, a numerical finite element model is developed using ANSYS software, while the behavior of the vehicle is characterized by a unidirectional model of two masses developed with VAMPIRE PRO software. The overloads obtained with the dynamic model are applied to the numerical model and then, the vibrational response of the track is obtained. Results are validated with real data and used to assess the effectiveness of rail grinding in the reduction of wheel-rail forces and the vibration generation phenomenon.

A soft-sensing model on hydraulic excavator's backhoe vibratory excavating resistance based on fuzzy support vector machine

In order to measure the backhoe vibratory excavating resistance of a hydraulic excavator fast and precisely,the influences of vibratory excavating depth,angle,vibratory frequency,amplitude,bucket inserting velocity and soil type on the vibratory excavating resistance were analyzed.Simulation analysis was carded out to establish the bucket inserting velocity,amplitude and vibratory frequency considered as secondary variables and excavating resistance as primary variable.A fttzzy membership function was introduced to improve the anti-noise capacity of support vector machine,which is a soft-sensing model on the hydraulic excavator＇s backhoe vibratory excavating resistance based on fuzzy support vector machine.The simulation result reveals that its maximum relative training and testing error are nearly 0.68% and-0.47%,respectively.It is concluded that the model has quite high modeling precision and generalization capacity,and it can measure the vibratory excavating resistance accurately,reliably and fast in an indirect way.

Structural Dynamics in Biology: A Bridge Given by Implicit Vibratory Crossed Models

This article proposes a synthesis and contribution at three levels: generation of dynamic equations of shell structures interacting with fluids, reduction of implicit resolution, and cross-applications to aerospace tanks and living systems. The synthesis of the equations is proposed around the four principles of thermodynamics at the level of discrete, structural and digitized systems. The implicit approach envisages an innovative analysis in terms of condensation and digitization, with in particular a perspective towards singular and integral methods. Some illustrations are proposed, in the field of performed research models and also in the fields of educational applications in biodynamics. The proposed bridge links, on one hand, the analytical Lagrange-Feynman’s approach, and on the other hand experimental results obtained in laboratory and numerical experiments obtained with multiphysics software. Finally, the realized models concern conservative and dissipative models for the active and passive control of complex systems, in a unified approach.

Vibration harmonic suppression technology for electromagnetic vibrators based on an improved sensorless feedback control method

To realize low harmonic distortion of the vibration waveform output from electromagnetic vibrators,we propose a vibration harmonic suppression technology based on an improved sensorless feedback control method.Without changing the original driving circuit,the alternating current(AC)equivalent resistance of the driving coil is used to obtain high-precision vibration velocity information,and then a simple and reliable velocity feedback control system is established.Through the study of the effect of different values of key parameters on the system,we have achieved an effective expansion of the velocity characteristic frequency band of low-frequency vibration,resulting in an enhanced harmonic suppression capability of velocity feedback control.We present extensive experiments to prove the effectiveness of the proposed method and make comparisons with conventional control methods.In the frequency range of 0.01-1.00 Hz,without using any sensors,the method proposed in this study can reduce the harmonic distortion of the vibration waveform by about 40%compared to open-loop control and by about 20%compared to a conventional sensorless feedback control method.

Influence of overhanging tool length and vibrator material on electromechanical impedance and amplitude prediction in ultrasonic spindle vibrator

This study presents the development of an ultrasonic transducer with a radius horn for an ultrasonic milling spindle(UMS)system.The ultrasonic transducer was intended to have a working frequency of approximately 30 kHz.Two different materials were considered in the study:stainless steel(SS 316L)and titanium alloy(Ti-6Al-4V).Titanium alloy gave a higher resonance frequency(33 kHz)than stainless steel(30 kHz)under the same preload compression stress.An electromechanical impedance simulation was carried out to predict the impedance resonance frequency for both materials,and the effect of the overhanging toolbar was investigated.According to the electromechanical impedance simulation,the overhanging toolbar length affected the resonance frequency,and the error was less than 3%.Harmonic analysis confirmed that the damping ratio helps determine the resonance amplitude.Therefore,damping ratios of 0.015-0.020 and 0.005-0.020 were selected for stainless steel and titanium alloy,respectively,with an error of less than 1.5%.Experimental machining was also performed to assess the feasibility of ultrasonic-assisted milling;the result was a lesser cutting force and better surface topography of Al 6061.

Dynamics and vibration reduction performance of asymmetric tristable nonlinear energy sink

With its complex nonlinear dynamic behavior,the tristable system has shown excellent performance in areas such as energy harvesting and vibration suppression,and has attracted a lot of attention.In this paper,an asymmetric tristable design is proposed to improve the vibration suppression efficiency of nonlinear energy sinks(NESs)for the first time.The proposed asymmetric tristable NES(ATNES)is composed of a pair of oblique springs and a vertical spring.Then,the three stable states,symmetric and asymmetric,can be achieved by the adjustment of the distance and stiffness asymmetry of the oblique springs.The governing equations of a linear oscillator(LO)coupled with the ATNES are derived.The approximate analytical solution to the coupled system is obtained by the harmonic balance method(HBM)and verified numerically.The vibration suppression efficiency of three types of ATNES is compared.The results show that the asymmetric design can improve the efficiency of vibration reduction through comparing the chaotic motion of the NES oscillator between asymmetric steady states.In addition,compared with the symmetrical tristable NES(TNES),the ATNES can effectively control smaller structural vibrations.In other words,the ATNES can effectively solve the threshold problem of TNES failure to weak excitation.Therefore,this paper reveals the vibration reduction mechanism of the ATNES,and provides a pathway to expand the effective excitation amplitude range of the NES.

A Review on Vibration Control of Multiple Cylinders Subjected to FlowInduced Vibrations

The fatigue damage caused by flow-induced vibration(FIV)is one of the major concerns for multiple cylindrical structures in many engineering applications.The FIV suppression is of great importance for the security of many cylindrical structures.Many active and passive control methods have been employed for the vibration suppression of an isolated cylinder undergoing vortex-induced vibrations(VIV).The FIV suppression methods are mainly extended to the multiple cylinders from the vibration control of the isolated cylinder.Due to the mutual interference between the multiple cylinders,the FIV mechanism is more complex than the VIV mechanism,which makes a great challenge for the FIV suppression.Some efforts have been devoted to vibration suppression of multiple cylinder systems undergoing FIV over the past two decades.The control methods,such as helical strakes,splitter plates,control rods and flexible sheets,are not always effective,depending on many influence factors,such as the spacing ratio,the arrangement geometrical shape,the flow velocity and the parameters of the vibration control devices.The FIV response,hydrodynamic features and wake patterns of the multiple cylinders equipped with vibration control devices are reviewed and summarized.The FIV suppression efficiency of the vibration control methods are analyzed and compared considering different influence factors.Further research on the FIV suppression of multiple cylinders is suggested to provide insight for the development of FIV control methods and promote engineering applications of FIV control methods.

Snap-through behaviors and nonlinear vibrations of a bistable composite laminated cantilever shell:an experimental and numerical study

The snap-through behaviors and nonlinear vibrations are investigated for a bistable composite laminated cantilever shell subjected to transversal foundation excitation based on experimental and theoretical approaches.An improved experimental specimen is designed in order to satisfy the cantilever support boundary condition,which is composed of an asymmetric region and a symmetric region.The symmetric region of the experimental specimen is entirely clamped,which is rigidly connected to an electromagnetic shaker,while the asymmetric region remains free of constraint.Different motion paths are realized for the bistable cantilever shell by changing the input signal levels of the electromagnetic shaker,and the displacement responses of the shell are collected by the laser displacement sensors.The numerical simulation is conducted based on the established theoretical model of the bistable composite laminated cantilever shell,and an off-axis three-dimensional dynamic snap-through domain is obtained.The numerical solutions are in good agreement with the experimental results.The nonlinear stiffness characteristics,dynamic snap-through domain,and chaos and bifurcation behaviors of the shell are quantitatively analyzed.Due to the asymmetry of the boundary condition and the shell,the upper stable-state of the shell exhibits an obvious soft spring stiffness characteristic,and the lower stable-state shows a linear stiffness characteristic of the shell.