LOCALIZED BENDING VIBRATIONS OF PIEZOCERAMIC TRANSVERSE POLARIZED PLATE

Problem of the piezoceramic plate polarized along the normal of the middle plane of the plate is solved, based on the assumptions of the hypothesis of Kirchhoff, taking into account the components characterizing the electric field. The equations of planar and bending vibrations are obtained. Localized bending vibrations are considered, and the effect of the electric field on the frequency of localized vibrations is investigated.

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Localized Magnetoelastic Bending Vibration of an Electroconductive Elastic Plate

Journal of Applied Mechanics ◽

10.1115/1.2424469 ◽

2006 ◽

Vol 74 (6) ◽

pp. 1071-1077 ◽

Cited By ~ 8

Author(s):

M. Belubekyan ◽

K. Ghazaryan ◽

P. Marzocca ◽

C. Cormier

Keyword(s):

Magnetic Field ◽

External Magnetic Field ◽

Elastic Plate ◽

Plate Theory ◽

Free Edge ◽

Bending Vibrations ◽

Bending Vibration ◽

Conductive Medium ◽

Localized Vibrations ◽

Applied External Magnetic Field

The study of the magnetoelastic vibrations of a flat plate immersed in a uniform applied external magnetic field is presented. Kirchhoff’s plate theory and the model of a perfect conductive medium are used. The conditions for the existence of localized bending vibrations in the vicinity of the free edge of the plate are established. It is shown that the localized vibrations can be detected and eventually can be eliminated by means of an applied magnetic field.

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COMPELLED AXYSIMMETRIC FLEXURAL FLUCTUATIONS OF THICK ROUND RIGID PIEZOCERAMIC PLATE

Vestnik of Samara University Natural Science Series ◽

10.18287/2541-7525-2012-18-6-124-135 ◽

2017 ◽

Vol 18 (6) ◽

pp. 124-135

Author(s):

D.A. Shlyakhin

Keyword(s):

Electric Field ◽

Vibration Frequency ◽

Strain State ◽

Natural Vibration ◽

Nonstationary Problem ◽

Numerical Results ◽

Natural Vibration Frequency ◽

Piezoceramic Plate ◽

Stress Strain ◽

Closed Solution

New closed solution of axisymmetric nonstationary problem of the theory of electroelasticity for thick round piezoceramic plate with rigid of its external radial surface is constructed. Calculated relations are obtained by method of expansion in eigen vector functions in the form of structural algorithm of ﬁnite transformations. Numerical results allow to deﬁne the natural-vibration frequency, the stress-strain state of the testing element, and also the potential and intensity of the induced electric ﬁeld.

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Resolution in photoelectron microscopy

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100086593 ◽

1991 ◽

Vol 49 ◽

pp. 458-459

Author(s):

G. F. Rempfer

Keyword(s):

Electron Microscopy ◽

Electric Field ◽

Ultraviolet Light ◽

Uniform Field ◽

Virtual Image ◽

Lens System ◽

Photoemission Electron Microscopy ◽

Planar Electrode ◽

Electron Lens ◽

Photoemission Electron

In photoelectron microscopy (PEM), also called photoemission electron microscopy (PEEM), the image is formed by electrons which have been liberated from the specimen by ultraviolet light. The electrons are accelerated by an electric field before being imaged by an electron lens system. The specimen is supported on a planar electrode (or the electrode itself may be the specimen), and the accelerating field is applied between the specimen, which serves as the cathode, and an anode. The accelerating field is essentially uniform except for microfields near the surface of the specimen and a diverging field near the anode aperture. The uniform field forms a virtual image of the specimen (virtual specimen) at unit lateral magnification, approximately twice as far from the anode as is the specimen. The diverging field at the anode aperture in turn forms a virtual image of the virtual specimen at magnification 2/3, at a distance from the anode of 4/3 the specimen distance. This demagnified virtual image is the object for the objective stage of the lens system.

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Field-assisted ionization theory for microscopists

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100171833 ◽

1994 ◽

Vol 52 ◽

pp. 820-821

Author(s):

Patrick P. Camus

Keyword(s):

Electric Field ◽

Electron Tunneling ◽

Ionization Probability ◽

Critical Distance ◽

Tunneling Probability ◽

Field Ionization ◽

Radius Of Curvature ◽

Field Evaporation ◽

A Value ◽

Ion Emission

The theory of field ion emission is the study of electron tunneling probability enhanced by the application of a high electric field. At subnanometer distances and kilovolt potentials, the probability of tunneling of electrons increases markedly. Field ionization of gas atoms produce atomic resolution images of the surface of the specimen, while field evaporation of surface atoms sections the specimen. Details of emission theory may be found in monographs.Field ionization (FI) is the phenomena whereby an electric field assists in the ionization of gas atoms via tunneling. The tunneling probability is a maximum at a critical distance above the surface,xc, Fig. 1. Energy is required to ionize the gas atom at xc, I, but at a value reduced by the appliedelectric field, xcFe, while energy is recovered by placing the electron in the specimen, φ. The highest ionization probability occurs for those regions on the specimen that have the highest local electric field. Those atoms which protrude from the average surfacehave the smallest radius of curvature, the highest field and therefore produce the highest ionizationprobability and brightest spots on the imaging screen, Fig. 2. This technique is called field ion microscopy (FIM).

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