scholarly journals Nonlinear excitation of hypersound vibrations in ferrite plate in conditions of combine influence in two frequencies. Part 1. Resonance on difference frequency

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
V.S. Vlasov ◽  
◽  
D.A. Pleshev ◽  
V.G. Shavrov ◽  
V.I. Shcheglov ◽  
...  
Keyword(s):  
Plate Thickness ◽  
Excitation Level ◽  
Difference Frequency ◽  
Frequency Interval ◽  
Ferrite Plate ◽  
Nonlinear Excitation ◽  
Combine Influence ◽  
Resonance Amplitude ◽  
Resonance Vibrations ◽  
Frequency Excitation

The task about nonlinear excitation of hypersound vibrations in ferrite plate in conditions of combine influence in two frequencies is investigated. As a preliminary task the investigation of only magnetic vibrations by two-frequency excitation is carried out. The possibility of description of forced linear vibrations on the basis of single nonuniform linear second order equation with arbitrary excitation is shown. It is found the analytical solution of task about excitation of oscillator by two signals which frequencies are distinguishes up and down from central frequency on the same frequency interval. It is shown the equivalency of representation of magnetic vibrations in linear regime and model vibrations on the basis of oscillator. It is found that in the general case the vibrations have view as beating which rounding frequency is equal to difference between excitation frequencies. The whole positing of task about excitation of nonlinear magnetoelastic vibrations in normal magnetized ferrite plate by two-frequency excitation is proposed. It is found that in conditions of large nonlinearity when the own elastic resonance of plate is equal to the difference frequency the powerful elastic vibrations are excited. It is found the nonlinear excitation of powerful non-resonance vibrations which take place also in the case of large elastic dissipation. It is shown that the non-resonance vibrations are determined precisely two-frequency character of excitation. It is found that the amplitude of non-resonance vibrations by increasing of plate thickness also is increased. By the small level of excitation, the low of increasing is linear, by middle – quadratic, by large – again approaches to linear with saturation and non-permanent sudden jumps. The character of excitation in conditions of resonance on difference frequency is investigated. It is shown that this resonance has powerful determined nonlinear character because it arises only by enough large excitation level. It is shown that the further increasing of resonance amplitude by the increasing the excitation level is realized by the low which is near to quadratic. But after this increasing when excitation level reaches determined value the resonance amplitude is saturated and remains constant. It is drawn attention to some discrepancy between the realization on nonlinearity by magnetic and elastic systems. For the de-scription of this discrepancy the empirical quadratic dependence is proposed. In brief is proposed some remarks about further development of work.

scholarly journals Nonlinear excitation of hypersound vibrations in ferrite plate in conditions of combine influence in two frequencies. Part 3. Variation of plate thickness

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
V.S. Vlasov ◽  
◽  
D.A. Pleshev ◽  
V.G. Shavrov ◽  
V.I. Shcheglov ◽  
...  
Keyword(s):  
Plate Thickness ◽  
Single Frequency ◽  
Elastic Displacement ◽  
Relaxation Processes ◽  
Ferrite Plate ◽  
Quadratic Character ◽  
Nonlinear Excitation ◽  
Combine Influence ◽  
Elastic Vibrations ◽  
Frequency Excitation

The task about nonlinear excitation of hypersound vibrations in ferrite plate in conditions of combine influence in two frequencies is investigated. As a most important parameter which is varied it is proposed the relative thickness of plate which is determined as relation of real thickness to the thickness which correspond to elastic resonance on the difference of excitation frequencies. It is established the necessity of choosing of character value of constant field which is determined by enough effective excitation of elastic vibrations. The system of nonlinear equations of motion of magnetization and elastic displacement is described. For solving of this system, the numerical Rounge-Cutta method is applied. The results of this calculation are the time-evolvent of vibrations, dependencies magnetic end elastic vibrations amplitudes and the spectra of vibrations in permanent conditions after end of relaxation processes. It is found the multi-regime character of elastic vibrations which takes place by variation of plate thickness. In the character of development of elastic vibrations in time by the increasing of plate thickness it is found four regimes: regime №1 – regular beatings, regime №2 – established resonance, regime №3 – displacement of center of established vibrations, regime №4 – gigantic oscillations. The intervals of thickness values which are necessary, or realization of these regimes are determined. The properties of each regimes taken separately are investigated. It is found that the regime №1 is realized when the thickness of plate is more less then the thickness of resonance on differential frequency. In this case the elastic vibrations in generally repeats the vibrations of magnetization which are realized as beating between two frequencies of excitation. The regime №2 takes place when the plate thickness is near to resonance on differential frequency. When thickness is corresponds to resonance on differential frequency it is found large raising of resonance character. In the vibrations of elastic displacement, the constant component is discovered. The regime №3 takes place when the plate thickness is exceeded of resonance on several (from two to seven) times. The vibrations of magnetization in this regime are the same as in regimes №1 and №2. The elastic displacement has two components: oscillatory on differential frequency and constant which value by increasing of thickness smoothly is increased. The displacement of center of oscillatory component by thickness is increased has quadratic character. The regime №4 takes place by plate thickness exceeds resonance thickness on the order and more. The vibrations of magnetization maintain the character of beating which are the same as in regimes №1, №2 and №3. The vibrations of elastic displacement are characterized by extremely large amplitude which is more then the amplitude in regime №3 on order and more and has extremely large period which is more then period of differential frequency vibrations on two-three order and more. The amplitude of vibrations and its period by the thickness is increases also increase by linear meaning. The some quality opinions about the nature of observed phenomena are proposed. It is established the specific character of two-frequency excitation in comparison to single-frequency excitation. As the possible task it is proposed the plan of singing the part of solution as dependence of vibration amplitude from plate thickness has quadratic character with necessary appreciation of two-frequency excitation. The mechanical analogy for vibrations of hard rod which is compressed on both ends by approaching forces is proposed. This analogy allows to interpret the displacement of vibrations center and gigantic oscillations regime.

scholarly journals Nonlinear excitation of hypersound vibrations in ferrite plate in conditions of combine influence in two frequencies. Part 2. Variation of constant field

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
V.S. Vlasov ◽  
◽  
D.A. Pleshev ◽  
V.G. Shavrov ◽  
V.I. Shcheglov ◽  
...  
Keyword(s):  
Large Amplitude ◽  
Small Amplitude ◽  
Magnetic Characteristics ◽  
Constant Field ◽  
Nonlinear Excitation ◽  
Combine Influence ◽  
Elastic Vibrations ◽  
Frequency Excitation ◽  
Fractal Character ◽  
Elastic Characteristics

The task about nonlinear excitation of hypersound vibrations in ferrite plate in conditions of combine influence in two frequencies is investigated. The thickness of plate is chosen so as the frequency of its elastic resonance was equal to difference of two components of alternating field. The most attention is given to properties of excited elastic vibrations by changing the value of applied constant field. The system of nonlinear motion equations of magnetization and elastic displacement is described. For solving of this system, the numerical method Runge-Cutta is applied. The results of this calculation are the time-evolvent of vibrations, dependencies magnetic end elastic vibrations amplitudes and also the spectra of vibrations in permanent conditions after end of relaxation processes. The influence of constant field value on character of vibrations is investigated. The comparison of amplitude-frequency characteristics of magnetic and elastic vibrations in linear and nonlinear regimes by the thickness of plate correspond to resonance on central and different frequencies is carried out. It is shown that by thickness which correspond to resonance on different frequency the characteristic has large indented skirting. It is found the large variety of dependencies of elastic vibrations character from field. In condition of stabilization so as after the completion of relaxation establishment processes it is found five more character regimes of vibrations: regime №1 – small-amplitude chaos; regime №2 – regular vibrations; regime №3 – non-symmetrical doubling of period; regime №4 – symmetrical doubling of period; regime №5 – irregular beating. For each of regimes the evolution of vibrations along time are obtained and the corresponding frequency spectra are found. The localization of regimes along the value of constant field by difference excitation level is investigated. It is found that the region of large-amplitude regimes (№2–№5) is limited in both sides by regions of small-amplitude regime №1. It is found that inside of region where large-amplitude regimes take place the most extended regime is generalized regime with doubling of period which is the sum of regimes №3 and №4 which occupies about 79%. The next on prevalence it the regime №5 – irregular beating which occupies 13% of whole region. The most exceptional is the regime №2 – regular vibrations which occupies only 8% from whole interval. It is found the extremely large critical intending of dependence of elastic vibrations amplitude from constant field. It is found that the structure of amplitude-field characteristic is very sensual to excitation level and plate thickness and the degree of sensitivity reach part of percent. From the comparison of localization on field by magnetic and elastic characteristics it is found that elastic characteristics as a whole are displaced down along field relatively magnetic characteristics. In this case the low-field falling of elastic characteristics is localized on the same falling of magnetic characteristics but the high-field falling of elastic characteristics is localized slightly lower of the field value which correspond to ferromagnetic resonance on central frequency. It is found that the reason of this displacement in this case is elastic resonance of plate on difference frequency. The card of regimes on the plane "alternating field – constant field” along broad interval of varying of both fields is constructed. It is found that by the constant field the large-amplitude regimes on the card occupy the “curved-linear trapezium” which axis lies along the coordinate “alternating field” and transverse width along coordinate “constant field” by increasing of alternating field is increased. It is found that outside of both sides by constant field of this “trapezium” the low-amplitude regime №1 – “small-amplitude chaos” is exited. The middle of “trapezium” occupies the strip directed along coordinate “alternating field” which is filled by regime №5 – “irregular beating”. Along both sides from this strip also right until the boundaries of “trapezium” the regimes №3 and №4 – “doubling of period” are excided. The reasons and necessary conditions of chaotic character of elastic vibrations are investigated. It is found that the necessary condition of chaos is excitation simultaneous in two frequencies. It is found that the large indented jumping character of dependence elastic vibrations amplitude from constant field has as first-reason the chaotic character magnetic vibrations. The character of jumps in dependence elastic vibrations amplitude from constant field is investigated. It is shown that by two-frequencies excitation the increasing of step along field causes large increasing of indenting of characteristics. It is found that the same behavior of amplitude-field dependencies of vibrations reveals its fractal character. The some comments about nature of jumps are proposed. It is found that jumps are determined by non-permanent character exactly magnetic vibrations which are shown only by two-frequency excitation on enough large level and have fractal character. As an analogy is mentioned that the line (skirting) of elastic vibrations field dependence on the plane “amplitude-field” is similar to chaotic trajectory of time-evolvent of vibrations on the plane “amplitude-time” for different oscillators which show chaotic vibrations. It is mentioned that the same behavior of trajectories on the plane “coordinate-potential” take place in cases when potential has dynamic character. The supposition is proposed that in investigated here task about two-frequency excitation of magnetostriction transducer may by constructed the function which can play the role of dynamic potential.

scholarly journals Uncertainty Assessment of CFD Investigation of the Nonlinear Difference-Frequency Wave Loads on a Semisubmersible FOWT Platform

2020 ◽  
Vol 13 (1) ◽  
pp. 64
Author(s):  
Lu Wang ◽  
Amy Robertson ◽  
Jason Jonkman ◽  
Yi-Hsiang Yu
Keyword(s):  
Low Frequency ◽  
Uncertainty Assessment ◽  
Difference Frequency ◽  
Offshore Wind ◽  
Wave Loads ◽  
Wave Excitation ◽  
Wave Load ◽  
Frequency Wave ◽  
Floating Offshore Wind Turbines ◽  
Frequency Excitation

Current mid-fidelity modeling approaches for floating offshore wind turbines (FOWTs) have been found to underpredict the nonlinear, low-frequency wave excitation and the response of semisubmersible FOWTs. To examine the cause of this underprediction, the OC6 project is using computational fluid dynamics (CFD) tools to investigate the wave loads on the OC5-DeepCwind semisubmersible, with a focus on the nonlinear difference-frequency excitation. This paper focuses on assessing the uncertainty of the CFD predictions from simulations of the semisubmersible in a fixed condition under bichromatic wave loading and on establishing confidence in the results for use in improving mid-fidelity models. The uncertainty for the nonlinear wave excitation is found to be acceptable but larger than that for the wave-frequency excitation, with the spatial discretization error being the dominant contributor. Further, unwanted free waves at the difference frequency have been identified in the CFD solution. A wave-splitting and wave load-correction procedure are presented to remove the contamination from the free waves in the results. A preliminary comparison to second-order potential-flow theory shows that the CFD model predicted significantly higher difference-frequency wave excitations, especially in surge, suggesting that the CFD results can be used to better calibrate the mid-fidelity tools.

scholarly journals Numerical solution of Rayleigh-Lamb frequency equation for real, imaginary and complex wavenumbers

2018 ◽  
Vol 157 ◽  
pp. 08011 ◽  
Author(s):  
Michal Šofer ◽  
Petr Ferfecki ◽  
Pavel Šofer
Keyword(s):  
Numerical Solution ◽  
Guided Waves ◽  
Lamb Waves ◽  
Plate Thickness ◽  
Ultrasonic Inspection ◽  
Wave Mode ◽  
Frequency Equation ◽  
Frequency Interval ◽  
Large Structures ◽  
Complete Procedure

Guided waves, especially Lamb waves or shear-horizontal waves, are widely used types of waves for ultrasonic inspection of large structures. Well known property of guided waves is their dispersive character, which means that the propagation velocity of the particular wave mode is not only a function of physical properties of the material, in which the wave propagates or the wave´s frequency, but also depends on the geometry of the structure in itself. Dispersion curves provide us the information related to the dependency between the wavenumber and the frequency of the particular mode and can be obtained by a numerical solution of Rayleigh-Lamb frequency equation. A solution of Rayleigh-Lamb frequency equation forms for a given frequency and plate thickness a set of a finite number of real and pure imaginary wavenumbers and an infinite number of complex wavenumbers. Proposed paper presents a complete procedure of how to obtain all three kinds of wavenumbers for a given geometry and frequency interval. The main emphasis is placed on the effectiveness of the procedures, which are used for finding the roots of dispersion equation for all three kinds of wavenumbers.

Difference-frequency ultrasound generation from microbubbles under dual-frequency excitation

2010 ◽  
Vol 19 (9) ◽  
pp. 094302 ◽  
Author(s):  
Ma Qing-Yu ◽  
Qiu Yuan-Yuan ◽  
Huang Bei ◽  
Zhang Dong ◽  
Gong Xiu-Fen
Keyword(s):  
Difference Frequency ◽  
Dual Frequency ◽  
Frequency Excitation ◽  
Frequency Ultrasound

scholarly journals Bainitic Ferrite Plate Thickness Evolution in Two Nanostructured Steels

Materials ◽  
2021 ◽  
Vol 14 (15) ◽  
pp. 4347
Author(s):  
Victor Ruiz-Jimenez ◽  
Jose A. Jimenez ◽  
Francisca G. Caballero ◽  
Carlos Garcia-Mateo
Keyword(s):  
Driving Force ◽  
Room Temperature ◽  
Plate Thickness ◽  
Bainitic Ferrite ◽  
Isothermal Transformation ◽  
Bainitic Transformation ◽  
Transformation Rate ◽  
Continuous Change ◽  
Ferrite Plate

Bainitic ferrite plate thickness evolution during isothermal transformation was followed at the same holding temperatures in two nanostructured steels containing (in wt.%) 1C-2Si and 0.4C-3Si. A dynamic picture of how the bainitic transformation evolves was obtained from the characterization of the microstructure present at room temperature after full and partial transformation at 300 and 350 °C. The continuous change during transformation of relevant parameters influencing the final scale of the microstructure, YS of austenite, driving force of the transformation and evolution of the transformation rate has been tracked, and these variations have been correlated to the evolution of the bainitic ferrite plate. Instead of the expected refinement of the plate predicted by existing theory and models, this study revealed a thickening of the bainitic ferrite plate thickness as the transformation progresses, which is partially explained by changes in the transformation rate through the whole decomposition of austenite into bainitic ferrite.

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