Mathematical model of contact excitation of ultrasonic waves by a disk piezoelectric transducer

2017 ◽  
Author(s):  
Margarita Romanyuk ◽  
Oleg Petrischev ◽  
Ganna Vlasyuk
Keyword(s):  
Mathematical Model ◽  
Piezoelectric Transducer ◽  
Ultrasonic Waves

scholarly journals Ultrasonic Waves in Bubbly Liquids: An Analytic Approach

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1309
Author(s):  
P. R. Gordoa ◽  
A. Pickering
Keyword(s):  
Mathematical Model ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Acoustic Waves ◽  
Elliptic Functions ◽  
Coupled System ◽  
Ultrasonic Waves ◽  
Partial Differential ◽  
Special Cases ◽  
Spherical Bubbles

We consider the problem of the propagation of high-intensity acoustic waves in a bubble layer consisting of spherical bubbles of identical size with a uniform distribution. The mathematical model is a coupled system of partial differential equations for the acoustic pressure and the instantaneous radius of the bubbles consisting of the wave equation coupled with the Rayleigh–Plesset equation. We perform an analytic analysis based on the study of Lie symmetries for this system of equations, concentrating our attention on the traveling wave case. We then consider mappings of the resulting reductions onto equations defining elliptic functions, and special cases thereof, for example, solvable in terms of hyperbolic functions. In this way, we construct exact solutions of the system of partial differential equations under consideration. We believe this to be the first analytic study of this particular mathematical model.

Influence of a delamination on Lamb wave excitation by a nearby piezoelectric transducer

2020 ◽  
pp. 1045389X2091997 ◽  
Author(s):  
Alisa N Shpak ◽  
Mikhail V Golub ◽  
Inka Mueller ◽  
Artem Eremin ◽  
Jens Kathol ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Piezoelectric Transducer ◽  
Lamb Wave ◽  
Lamb Waves ◽  
Boundary Integral ◽  
Experimental Investigations ◽  
Wave Excitation ◽  
Damage Scenarios ◽  
Active Sensor ◽  
Piezoelectric Wafer

This article presents the results of theoretical and experimental investigations of characteristic changes of Lamb wave excitation and scattering by a strip-like horizontal delamination in a layered elastic waveguide for Lamb waves induced by a piezoelectric wafer active sensor. The boundary integral equation method is used to describe wave propagation in an infinite layered waveguide with a delamination, while the frequency domain spectral element method is employed to model the dynamic behaviour of the piezoelectric wafer active sensor, which allows to simulate debonding between the piezoelectric wafer active sensor and the waveguide. Experimental investigations of the dynamic interaction of the piezoelectric wafer active sensor with a layered plate containing a horizontal delamination is conducted for several damage scenarios, showing a good agreement with the results obtained using the developed mathematical model. The obtained mathematical model is employed to analyse alteration of the piezo-induced Lamb waves including modes’ decomposition due to delamination. The conversion and/or conservation of the Lamb waves on account of a delamination is investigated. The electro-mechanical impedance of the piezoelectric transducer and the stress intensity factors of a delamination are analysed in dependence on the delamination location.

Condition monitoring of mechanical seals: Detection of film collapse using reflected ultrasonic waves

2000 ◽  
Vol 214 (9) ◽  
pp. 1187-1194 ◽  
Author(s):  
D Anderson ◽  
J Jarzynski ◽  
R. F. Salant
Keyword(s):  
Steady State ◽  
Piezoelectric Transducer ◽  
Ultrasonic Waves ◽  
Mechanical Seal ◽  
Mechanical Seals ◽  
Reflected Waves ◽  
Bench Tests ◽  
State Tests ◽  
Lubricating Film ◽  
Film Collapse

A method for detecting the collapse of the lubricating film in a mechanical seal has been developed. A piezoelectric transducer is placed behind the non-rotating seal face and is used to generate ultrasonic waves, which propagate towards the interface between the two seal faces. The same transducer is used to detect the reflected waves, whose amplitude is a measure of the degree of contact between the faces. The results of bench tests, steady-state tests and transient tests show that the method is effective.

Modelling of an Electric Circuit’s Type Influence on Dynamic Flexibility of System with Passive Vibration Damping

2014 ◽  
Vol 1036 ◽  
pp. 511-516 ◽  
Author(s):  
Marek Płaczek
Keyword(s):  
Mathematical Model ◽  
Approximate Method ◽  
Piezoelectric Transducer ◽  
Electric Circuit ◽  
Vibration Damping ◽  
Mathematical Tool ◽  
Exact Methods ◽  
One Dimensional ◽  
Mathematical Algorithm ◽  
Vibrating Systems

Paper presents a proposal of mathematical algorithm used for analysis of influence of type of selected passive electric circuit on dynamic flexibility of system with piezoelectric transducer used for shunting vibration damping. Mathematical model of one-dimensional, vibrating system with shunted piezoelectric transducer is proposed and using approximate method the systems dynamic flexibility is calculated. Influence of type of used passive electric circuit on the systems dynamic flexibility are analysed. The purpose of this work is to obtain a functional mathematical tool that can be used to design such kind of systems obtaining the best efficiency of their work. In order to make it possible it is necessary to know the influence of type and parameters of elements of chosen passive electric circuit on the systems characteristic. In order to realize the assumed aims, the discrete-continuous mathematical model of the considered system is created. It is not possible to use an exact methods to analyse such kind of one-dimensional, vibrating systems with piezoelectric transducers, this is why the approximate method is used.

Quantitative Evaluation of an Internal Flaw of a Structural Component Using Electromagnetic Acoustic Transducers

2001 ◽  
Author(s):  
Shinichi Maruyama ◽  
Toshihiko Sugiura ◽  
Akihiro Inoue ◽  
Masatsugu Yoshizawa
Keyword(s):  
Mathematical Model ◽  
Nondestructive Evaluation ◽  
Ultrasonic Waves ◽  
Local Optimum ◽  
Electromagnetic Acoustic Transducers ◽  
Acoustic Transducers ◽  
Time Period ◽  
Internal Flaw ◽  
Inspection Process ◽  
The Mathematical Model

Abstract Electromagnetic acoustic transducers (EMATs) can transmit and detect ultrasonic waves in a conductive specimen out of any contact with it. This process can be given theoretical modeling and formulation based on elastodynamics and electromagnetics. It suggests a possibility of quantitative nondestructive evaluation using EMATs. This research deals with a numerical method of flaw identification from a receiver signal obtained by EMATs. Experimental results of the receiver signals agree well with numerical ones, which verified the mathematical model of the inspection process. Flaw identification is formulated as a problem of parameter optimization. To avoid being trapped in a local optimum, initial parameters were successfully evaluated from the height and the time period of peaks in the receiver signals. Flaw parameters were identified from the receiver signals obtained by numerical simulations and experiments, which verified the method of flaw identification presented here.

Sign in / Sign up

Export Citation Format

Share Document