Investigation of the nonlinear phenomena of a Langevin ultrasonic transducer caused by high applied voltage

2021 ◽  
pp. 095440622110093 ◽  
Author(s):  
Shibo Zhang ◽  
Yang Li ◽  
Sisi Li ◽  
Yongbo Wu ◽  
Jiang Zeng
Keyword(s):  
Nonlinear Model ◽  
Longitudinal Vibration ◽  
Ultrasonic Transducer ◽  
Linear Functions ◽  
Vibration Velocity ◽  
System Response ◽  
Nonlinear Phenomena ◽  
Amplitude Curve ◽  
Nonlinear Phenomenon ◽  
Physical Point

In the field of power ultrasound, Langevin ultrasonic transducers (LUTs) usually operate at a large displacements output power by applying high voltages. However, empirically, a LUT exhibits nonlinearities such as amplitude jumping and peak hysteresis for high voltages in actual operations. The nonlinearities would reduce the efficiency and output accuracy of an LUT. In this research, the burst-mode method was used to measure the longitudinal vibration velocity of the LUT, which gradually decreased with time after the excitation voltage was turned off. The equivalent mechanical losses and equivalent spring constants were determined using the velocity attenuation rate and resonant frequency and they were found to be the linear functions of velocity, helping to develop a novel nonlinear model. This model contained two quadratic nonlinear terms based on the linear model. Furthermore, the developed nonlinear model was analyzed using the Lagrangian method as well as the multiscale method, which confirmed that the model was effective in describing the nonlinear behavior. It was also found that the frequency-amplitude curve bent when the nonlinear term was taken into account, which resembled the nonlinear phenomenon tested experimentally. From a physical point of view, this bending was meaningful because it led to the formation of multi-valued response regions with jumping phenomena. Additionally, according to the obtained results, the maximum value of the system response was independent of the degree of nonlinearity of the system.

FEM Modeling of Vibro-Impact Response of Metal Plates Excited by a High-Power Ultrasonic Transducer

2012 ◽  
Vol 197 ◽  
pp. 278-282
Author(s):  
Zhao Jiang Chen ◽  
Shu Yi Zhang ◽  
Zhi Liang Zhang
Keyword(s):  
Contact Force ◽  
High Power ◽  
Ultrasonic Transducer ◽  
Vibration Velocity ◽  
Nonlinear Phenomena ◽  
Fem Modeling ◽  
Frequency Spectra ◽  
Metal Plates ◽  
Power Ultrasonic ◽  
Subharmonic Vibration

When thin metal plates are excited by a high-power ultrasonic transducer, superharmonic and high-order subharmonic vibration phenomena of the plates are observed in our experiments. However, the nonlinear mechanism in the system is still not fully understood. In this paper, a finite element model is established based on the experimental conditions and numerical simulations are performed to explore the generation mechanism of the nonlinear vibration. By comparing the waveforms and frequency spectra of the vibration velocity of the plate to these of the contact force between the ultrasonic horn tip and the plates, it can be found that waveform distortion of the contact force is the main reason for generating the superharmonic vibration, while the intermittent contact-impact between the horn tip and the plate is the reason for subharmonic vibration in the plate. The FEM simulation results can explain reasonably the observed experimental phenomena, which are useful to help to improve the effects of the nonlinear phenomena occurred in ultrasonic processing.

scholarly journals Experimental travelling waves identification in mechanical structures

2017 ◽  
Vol 24 (1) ◽  
pp. 152-167
Author(s):  
Izhak Bucher ◽  
Ran Gabai ◽  
Harel Plat ◽  
Amit Dolev ◽  
Eyal Setter
Keyword(s):  
Energy Flux ◽  
Power Flow ◽  
Reactive Power ◽  
Mechanical Energy ◽  
Travelling Waves ◽  
Electrical Power ◽  
Normal Modes ◽  
Standing Waves ◽  
Amplitude Curve ◽  
Physical Point

Vibrations are often represented as a sum of standing waves in space, i.e. normal modes of vibration. While this can be mathematically accurate, the representation as travelling waves can be compact and more appropriate from a physical point of view, in particular when the energy flux along the structure is meaningful. The quantification of travelling waves assists in computing the energy being transferred and propagated along a structure. It can provide local as well as global information about the structure through which the mechanical energy flows. Presented in this paper is a new method to quantify the fraction of mechanical power being transmitted in a vibration cycle at a specific direction in space using measured data. It is shown that the method can detect local defects causing slight non-uniformity of the energy flux. Equivalence is being made with the electrical power factor and electromagnetic standing waves ratio, commonly employed in such cases. Other methods to perform experiment based wave identification in one-dimension are compared with the power flow based identification. Including a signal processing approach that fits an ellipse to the complex amplitude curve and Hilbert transform for obtaining the local phase and amplitude. A new representation of the active and reactive power flow is developed and its relationship to standing waves ratio is demonstrated analytically and experimentally.

Comparative results of evaluating the smoothness of automatic transmission gear shifting during car operation

2020 ◽  
Keyword(s):  
Longitudinal Vibration ◽  
Automatic Transmission ◽  
Quality Criteria ◽  
Technical Condition ◽  
Vibration Velocity ◽  
Vibration Acceleration ◽  
Passenger Cars ◽  
Shift Quality ◽  
Vibroacoustic Diagnostics ◽  
Comparative Results

The authors have studied the process of gear shifting, smoothness of it and peculiarities of automatic gearbox functioning of during car operation. The article describes the urgency of the problem of jerks and vibrations when changing gears. When assessing the smoothness of gear shifting, the method of technical state vibroacoustic diagnostics is applied. The method is based on the recorded parameters of vibration velocity, vibration acceleration, vibration movement with their further conversion (fast Fourier transform) into a spectralsignal. The procedure of longitudinal vibration acceleration measurements on cars in operation is described. A comparative analysis of the smoothness of gear shifting in an automatic transmission was carried out using the example of modern passenger cars. Keywords car; car operation; automatic gearbox; technical condition; gearbox malfunction; smoothness; jerks; jolts; gear shift quality criteria; vibration acceleration

scholarly journals Nonlinear Phenomena in Cournot Duopoly Model

Systems ◽  
2018 ◽  
Vol 6 (3) ◽  
pp. 30
Author(s):  
Pavel Pražák ◽  
Jaroslav Kovárník
Keyword(s):  
Demand Function ◽  
Deterministic Chaos ◽  
Linear Functions ◽  
Nonlinear Phenomena ◽  
Cournot Duopoly ◽  
Limit Values ◽  
Economic Agents ◽  
Duopoly Model ◽  
Sensitive Dependence ◽  
Stackelberg Duopoly

The economic world is very dynamic, and most phenomena appearing in this world are mutually interconnected. These connections may result in the emergence of nonlinear relationships among economic agents. Research discussions about different markets’ structures cannot be considered as finished yet. Even such a well-known concept as oligopoly can be described with different models applying diverse assumptions and using various values of parameters; for example, the Cournot duopoly game, Bertrand duopoly game or Stackelberg duopoly game can be and are used. These models usually assume linear functions and make analyses of the behavior of the two companies. The aim of this paper is to consider a nonlinear inverse demand function in the Cournot duopoly model. Supposing there is a sufficiently large proportion among the costs of the two companies, we can possibly detect nonlinear phenomena such as bifurcation of limit values of production or deterministic chaos. To prove a sensitive dependence on the initial condition, which accompanies deterministic chaos, the concept of Lyapunov exponents is used. We also point out the fact that even though some particular values of parameters are irrelevant for the above-mentioned nonlinear phenomena, it is worth being aware of their existence.

scholarly journals Characteristic Analysis of longitudinal vibration Sucker Rod String With Variable Equivalent Stiffness

2018 ◽  
Vol 153 ◽  
pp. 06009 ◽  
Author(s):  
Jian Lv ◽  
Mingming Xing
Keyword(s):  
Longitudinal Vibration ◽  
Step Function ◽  
Load Force ◽  
System Response ◽  
Equivalent Stiffness ◽  
Function Form ◽  
Characteristic Analysis ◽  
Response Curves ◽  
Sucker Rod ◽  
Force Excitation

Considering the influence of variable equivalent stiffness on system response, the equivalent stiffness is defined as a step function, and a mathematical model of nonlinear longitudinal vibration of sucker rod string (SRS) is built. The dynamic response under displacement and load force excitation is solved by fourth-order Runge-Kutta method with zero initial condition. The results show the steady-state responses under the displacement and load force excitation of different function forms are different. The response curves of both displacement and velocity under the displacement and load force excitation of cosine function form have larger fluctuation than it under the displacement and load force excitation of sine function form. Therefore, the characteristic analysis of SRS plays an important role in understanding the influence of the excitation form and sensitive parameters on steady response.

scholarly journals Adaptive Model-Free Coupling Controller Design for Multi-Axis Motion Systems

2020 ◽  
Vol 10 (10) ◽  
pp. 3592
Author(s):  
Bo-Sheng Chen ◽  
Ching-Hung Lee
Keyword(s):  
Controller Design ◽  
Uncertain System ◽  
Contour Error ◽  
Nonlinear Phenomena ◽  
Nonlinear Phenomenon ◽  
Adaptive Model ◽  
Model Free ◽  
Fuzzy Neural ◽  
Adaptive Coupling ◽  
The Stability

In this study, we introduce an adaptive model-free coupling controller while using recurrent fuzzy neural network (RFNN) for multi-axis system to minimize the contour error. The proposed method can be applied to linear or nonlinear multi-axis motion control systems following desired paths. By the concept of cross-coupling control (CCC), multi-axis system is transferred into a nonlinear time-varying system due to the time-dependent coordinate transformation; tangential, normal, and bi-normal components of desired contour. Herein, we propose a model-free adaptive coupling controller design approach for multi-axis linear motor system with uncertainty and nonlinear phenomena. RFNN establishes the corresponding adaptive coupling controller to treat the uncertain system with nonlinear phenomenon. The stability of closed-loop system is guaranteed by the Lyapunov method and the adaptation of RFNN is also obtained. Simulation results are introduced in order to illustrate the effectiveness.

Domains and Types of Aeroelastic Instability of Slender Beam

2007 ◽  
Author(s):  
Jirˇi´ Na´prstek
Keyword(s):  
Stability Boundary ◽  
Stability Loss ◽  
Stability Domain ◽  
Theoretical Explanation ◽  
Point Of View ◽  
System Response ◽  
Physical Point ◽  
Model Response ◽  
Gyroscopic Forces ◽  
The Stability

Slender structures exposed to a cross air flow are prone to vibrations of several types resulting from aeroelastic interaction of a flowing medium and a moving structure. Aeroelastic forces are the origin of nonconservative and gyroscopic forces influencing the stability of a system response. Conditions of a dynamic stability loss and a detailed analysis of a stability domain has been done using a linear mathematical model. Response properties of a system located on a stability boundary together with tendencies in its neighborhood are presented and interpreted from physical point of view. Results can be used for an explanation of several effects observed experimentally but remaining without theoretical explanation until now.

Variational Modal Identification of Conservative Nongyroscopic Systems

1989 ◽  
Vol 111 (2) ◽  
pp. 160-171 ◽  
Author(s):  
L. Silverberg ◽  
S. Kang
Keyword(s):  
Longitudinal Vibration ◽  
Modal Identification ◽  
System Response ◽  
Bending Vibration ◽  
Free System ◽  
Dirac Delta ◽  
Vibration Problem ◽  
Identification Method ◽  
Delta Functions ◽  
Admissible Functions

A new modal identification method for Conservative Nongyroscopic Systems is proposed. The modal identification method is formulated as a variational problem in which stationary values of a functional quotient are sought. The computation of the functional quotient is carried out using a set of admissible functions defined over the spatial domain of the system. Measurements of the free system response at discrete points are carried out using any combination of displacements, velocities, and/or accelerations. Three types of admissible functions have been considered—global functions, spatial Dirac-delta functions, and finite element interpolation functions. The variational modal identification method is applied to a pure bending vibration problem, to a pure longitudinal vibration problem, and to a combined bending and longitudinal vibration problem. The effectiveness of the variational modal identification method using different sets of admissible functions is examined.

Nonlinear Model Tracking in Application to Failed Nondestructive Evaluations

2011 ◽  
Author(s):  
Timothy A. Doughty ◽  
Natalie S. Higgins ◽  
Nicholas G. Etzel
Keyword(s):  
Natural Frequency ◽  
Nonlinear Model ◽  
Equation Model ◽  
False Alarms ◽  
Parameter Estimates ◽  
Nonlinear Phenomena ◽  
Time Data ◽  
Monitoring Method ◽  
Cantilevered Beam ◽  
Nondestructive Evaluations

The nondestructive health monitoring method of Nonlinear Model Tracking (NMT) is introduced and tested under various conditions. The study involves the fatigue and failure of a slender cantilevered beam subject to harmonic nonstationary base excitation around the beam’s second natural frequency. A nonlinear differential equation model for the system is assumed and parameters for the model are estimated using Continuous Time System Identification populated with healthy system stimulus and response data. Updated with real time data sets from the system in operation, the method tracks changes in parameter estimates. The NMT method indicates with repeatability the onset of plasticity, crack initiation and growth well in advance of system failure. Additionally, the NMT method is shown to not give false alarms when system behavior varies in a way that is associated with nonlinear phenomena. Linear methods based on tracking the system’s natural frequency are shown to misidentify the onset of failure for fully healthy systems.

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