Time-harmonic Voltage Research Articles

Analysis of a Strip Antenna Located at a Plane Interface of Uniaxial Metamaterials

A rigorous solution is found to the problem of determining the current distribution and input impedance of a straight strip antenna located at a plane interface of two uniaxial metamaterials. The anisotropy axes of the metamaterials are parallel to each other and to the medium interface. The antenna is oriented perpendicular to these axes and excited by a given time-harmonic voltage. Using the Fourier transform technique, singular integral equations for the antenna current are derived and solved for all possible combinations of the metamaterial parameters. Closed-form representations for the current distribution and input impedance of an infinitely long strip are obtained and their generalization to the case of a finite-length antenna is discussed.

Enhancing the control of boron epoxy cross-ply laminated composite plates through intelligent implementation of PZT sensor and actuator

Piezoelectric materials find diverse applications in structural engineering, particularly in fields like condition monitoring, smart control, and testing. The captivating interplay between their mechanical and electrical properties has garnered significant attention, showcasing immense potential for practical utility. Notably, these materials boast costeffectiveness, lightweight characteristics, compact size, exceptional dynamic capabilities, swift responsiveness, enduring stability, and remarkable energy conversion efficiency. In our research initiative, we delve into a study concentrated on the symmetric surface attachment of two piezoelectric patches or actuators onto composite laminate plates. The goal is to induce a bending effect in the laminate by applying equal-magnitude electric voltages with opposite polarities to these symmetrically positioned piezoelectric actuators. The determination of the bending moment involves the application of principles related to elasticity and piezoelectricity. To scrutinize the displacement and natural frequency of the composite plate influenced by this bending moment, we utilize plate theory and derive analytical solutions. Furthermore, these piezoelectric patches, affixed to the composite laminate plate's surface, double as vibration actuators. We subject the plate to loads to investigate its vibration response in a simply supported rectangular configuration. This excitation is achieved by applying time-harmonic voltages to the piezoelectric patches. Throughout our study, we compute analytical solutions for both deflection and vibration amplitude, presenting numerical results that depict the static deflection and vibration amplitude of the plate. Additionally, a parametric study is conducted to elucidate the influence of piezoelectric actuator size and placement on cross-ply composite laminate plates.

Determination of the Harmonic Losses in an Induction Motor Fed by an Inverter

The advancement, development, improvement, and increased use of power electronic converters led to the efficient speed control of electrical drives. The most famous three-phase induction motor-related control to Pulse-Width Modulation (PWM) technique is used to operate multilevel inverters such as variable-frequency or six-step Voltage Source Inverter (VSI). Switching devices of the inverter are used in the drive systems and act as the main source of harmonics. When the induction motor is fed from the PWM inverter, it will be supplied by low order (5th, 7th, 11th) time harmonic voltage. The motor performance is affected by the presence of these time harmonic components because the additional losses generated in the motor defect its performance, generate pulsating torque, and reduce efficiency. In this work, the analysis of a dynamic model of an induction motor in transient and steady-state operation is developed, considering the effect of time-harmonic voltages generated by the inverter, skin effect, skew effect, temperature rise effect, iron core loss, stray load loss, and magnetic saturation on the motor performance. The performance of the motor is studied by the time-harmonic equivalent circuit and by the fundamental equivalent circuit. The motor performance in terms of efficiency and power factor is compared with the experimental results for both sinusoidal and VSI motor feeds in order to validate the model accuracy.

General Analysis of a Loop Antenna Located on a Uniaxial Metamaterial Cylinder

The general problem of determining the electrodynamic characteristics of a circular loop antenna located coaxially on the surface of a metamaterial cylinder is studied using the integral equation method. The antenna has the form of a perfectly conducting, infinitesimally thin, narrow strip coiled into a ring and is excited by a given time-harmonic voltage. The cylinder is assumed to be filled with a uniaxial metamaterial and surrounded by an isotropic magnetodielectric. Integral equations for azimuthal harmonics of the antenna current are derived and solved in the cases where the normal waves of the metamaterial inside the cylinder have either hyperbolic or nonhyperbolic dispersion. Based on the solutions of these equations, the current distribution and input impedance of the antenna are found in closed form. The behavior of the antenna characteristics as functions of the metamaterial parameters is discussed.

Effect of time harmonic current considering load condition on performance of canned induction motor

Canned induction motors fed by inverters are widely used in pharmaceutical, chemical, and nuclear fields. It is necessary to analyse the effect of time harmonic injected by the inverter on the performance of the canned induction motor. However, the existing researches are to consider the inverter and the motor separately, without analyzing the reverse effect of the induction motor as a nonlinear active load on the time harmonics of the inverter. Therefore, this paper establishes a field-circuit coupling analysis model of the canned induction motor considering the influence of load, and studies the effect of time harmonic current under different load conditions on the electromagnetic field, eddy current loss, and temperature field of the canned induction motor. The paper first uses the analysis method to determine the relationship between the time harmonic voltage of the inverter and the time harmonic current of the motor. Then, the electromagnetic field distribution, eddy current loss, and temperature field distribution of the canned induction motor under different load conditions are calculated. Besides, the laws of time harmonic current on the electromagnetic field, can loss and motor temperature distribution are found. These research results can not only provide a meaningful reference for analysis of the canned induction motor but also provide methods for design optimization and multi-physical field modeling analysis of the canned induction motor.

Electro-thermal excitation of parametric resonances in double-clamped micro beams

We report on a simple yet efficient approach allowing direct electrothermal excitation of parametric resonance (PR) in double-clamped flexible nano- and microscale beams. The application of a time-harmonic voltage between the beam's ends leads to the electric current and Joule's heating of the entire beam, which induces a time-periodic axial stress and results in excitation of the structure lateral vibrations through the PR mechanism. The proposed approach has an advantage, simplifying fabrication and integration and reducing the influence of residual stress, and thermal mismatch, unlike conventional piezoelectric, photothermal, or electrostatic actuation approaches, which require additional piezoelectric layers, light sources, or electrodes in the proximity of a vibrating beam. Single crystal silicon, nominally 500 μm long, 30 μm wide, and 5 μm thick beams were fabricated by deep reactive ion etching and operated at a pressure of ≈1.9 mTorr. The experimental results, consistent with the reduced order and numerical model predictions, demonstrate the feasibility of the suggested excitation scenario, which could be implemented in resonant sensors, timing devices, signal processing, and micro and nanomechanical logical elements.

Theory of a Strip Antenna Located at a Plane Interface of a Uniaxial Magnetic Metamaterial and an Isotropic Medium

Electrodynamic characteristics of an antenna in the form of an infinitesimally thin, perfectly conducting narrow strip located at a plane interface of a uniaxial magnetic metamaterial and an isotropic magnetodielectric medium are studied. The antenna is placed perpendicular to the anisotropy axis of the metamaterial and excited by a time-harmonic external voltage. Singular integral equations for the antenna current are derived for an infinitely long conducting strip. The solutions to such equations are used to find and analyze the current distribution and input impedance of the antenna. Conditions for applicability of an approximate transmission line method for determining the antenna characteristics are established. Within the framework of this method, the obtained results are generalized to the case of a strip antenna with finite length.

A Comparison Between Electrical Capacitance Tomography and Displacement-Current Phase Tomography

We compare electrical capacitance tomography (ECT) and displacement-current phase tomography (DCPT) results for non-invasive imaging of lossy media. ECT is based on mutual capacitance measurements between electrode pairs surrounding the region of interest (RoI), whereas DCPT is a relatively less mature sensing modality that utilizes the phase information inherent in the displacement current measured by such electrode pairs excited by time-harmonic voltages (in the electroquasistatic regime). DCPT and ECT can be implemented using basically the same hardware components and used alongside to provide complementary information for imaging purposes or separately to reconstruct the spatial distribution of the loss tangent or the permittivity within the RoI, respectively. We show that the (nonlinear) relationship between the measured phase in DCPT and the conductivity distribution in the RoI has a more extended linear range than the nonlinear relationship between the measured capacitances in ECT and the permittivity distribution in the RoI. Of note, DCPT does not require electrical contact with the RoI in contrast to electrical impedance tomography. To illustrate the potential of DCPT, we evaluate its performance using both numerical examples and experiment results.

THEORY OF A STRIP LOOP ANTENNA LOCATED ON THE SURFACE OF AN AXIALLY MAGNETIZED PLASMA COLUMN

We study the current distribution and input impedance of a circular loop antenna in the form of an inflnitesimally thin, perfectly conducting narrow strip coiled into a ring. The antenna is located on the surface of an axially magnetized plasma column surrounded by a homogeneous isotropic medium. The current in the antenna is excited by a time-harmonic voltage creating an electric fleld with the azimuthal component in a gap of small angular opening on the strip surface. The emphasis is placed on the solution of the integral equations for the azimuthal harmonics of the antenna current in the case where the magnetoplasma inside the column is nonresonant. The properties of the kernels of the integral equations are discussed and the current distribution in the antenna is obtained. It is shown that the presence of a magnetized plasma column can signiflcantly in∞uence the electrodynamic characteristics of the antenna compared with the case where it is located in the surrounding medium or a homogeneous plasma medium the parameters of which coincide with those inside the column.

CURRENT DISTRIBUTION AND INPUT IMPEDANCE OF A STRIP LOOP ANTENNA LOCATED ON THE SURFACE OF A CIRCULAR COLUMN FILLED WITH A RESONANT MAGNETOPLASMA

We study the electrodynamic characteristics of a strip loop antenna located on the surface of a circular column fllled with a resonant magnetoplasma and surrounded by a homogeneous isotropic background medium. The antenna current is excited by a time-harmonic voltage creating an electric fleld with the azimuthal component in a narrow gap on the strip surface. It is shown that the current distribution and input impedance of such an antenna are strongly in∞uenced by the presence of an inflnite number of propagating quasielectrostatic modes that are guided by a column containing a resonant magnetoplasma.

Unsteady electroosmosis in a microchannel with Poisson–Boltzmann charge distribution

The present study is concerned with unsteady electroosmotic flow (EOF) in a microchannel with the electric charge distribution described by the Poisson-Boltzmann (PB) equation. The nonlinear PB equation is solved by a systematic perturbation with respect to the parameter λ which measures the strength of the wall zeta potential relative to the thermal potential. In the small λ limits (λ<<1), we recover the linearized PB equation - the Debye-Hückel approximation. The solutions obtained by using only three terms in the perturbation series are shown to be accurate with errors <1% for λ up to 2. The accurate solution to the PB equation is then used to solve the electrokinetic fluid transport equation for two types of unsteady flow: transient flow driven by a suddenly applied voltage and oscillatory flow driven by a time-harmonic voltage. The solution for the transient flow has important implications on EOF as an effective means for transporting electrolytes in microchannels with various electrokinetic widths. On the other hand, the solution for the oscillatory flow is shown to have important physical implications on EOF in mixing electrolytes in terms of the amplitude and phase of the resulting time-harmonic EOF rate, which depends on the applied frequency and the electrokinetic width of the microchannel as well as on the parameter λ.

Dynamic characteristics of axially-symmetrical annular corrugated shell piezoelectric transducers

ABSTRACT The coupled extensional and exural vibrations of an annular corrugated shell piezoelectric transducer consisting of multiple circularly-annular surfaces smoothly connected along the interfaces were investigated in the paper. Only a time-harmonic voltage is applied across two electrodes of the piezoelectric shell as the external loading. A theoretical solution was obtained using the classical shell theory. Based on the solution, basic vibration characteristics of resonant frequencies, mode shapes were calculated and examined.

In-plane P-SV waves from a piezoelectric strip actuator: exact versus effective boundary condition solutions

A piezoelectric strip of finite width and thickness is placed on top of an isotropic elastic half space. It operates in actuator mode, and a time harmonic voltage is thus applied across it. The piezoelectric material is of type 6 mm oriented so that a two-dimensional (2-D) in-plane (P-SV) problem results. By Fourier series expansions, the problem is solved exactly, and this result is compared to the case when the piezoelectric strip is replaced by an effective boundary condition, which is derived by series expansions in the thickness coordinate in the piezoelectric strip. At low frequencies, the results agree very well, and this corresponds to the situation often met in practice. In general, the effective boundary condition should be much easier to apply, for example when a finite element method (FEM) program is used.

Antiplane shear waves from a piezoelectric strip actuator: exact versus effective boundarycondition solutions

A piezoelectric strip of finite width and thickness is placed on top of anisotropic elastic half-space. It operates in actuator mode and a time harmonicvoltage is thus applied across it. The piezoelectric material is of type6mm oriented so that a 2D antiplane (scalar) problem results. By Fourier series expansions theproblem is solved exactly and this result is compared to the case when the piezoelectricstrip is replaced by an effective boundary condition, which is derived by series expansionsin the thickness coordinate in the piezoelectric strip. At low frequencies the results agreevery well and this corresponds to the situation usually met in practice. In general, theeffective boundary condition should be easier to apply and it is in particular noted that thisis the case when using a FEM program where the option of a piezoelectric material isusually not available.

Vibration analysis of angle-ply laminated composite plates with an embedded piezoceramic layer.

An optical full-field technique, called amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI), is used in this study to investigate the force-induced transverse vibration of an angle-ply laminated composite embedded with a piezoceramic layer (piezolaminated plates). The piezolaminated plates are excited by applying time-harmonic voltages to the embedded piezoceramic layer. Because clear fringe patterns will appear only at resonant frequencies, both the resonant frequencies and mode shapes of the vibrating piezolaminated plates with five different fiber orientation angles are obtained by the proposed AF-ESPI method. A laser Doppler vibrometer (LDV) system that has the advantage of high resolution and broad dynamic range also is applied to measure the frequency response of piezolaminated plates. In addition to the two proposed optical techniques, numerical computations based on a commercial finite element package are presented for comparison with the experimental results. Three different numerical formulations are used to evaluate the vibration characteristics of piezolaminated plates. Good agreements of the measured data by the optical method and the numerical results predicted by the finite element method (FEM) demonstrate that the proposed methodology in this study is a powerful tool for the vibration analysis of piezolaminated plates.

Induced vibrations of piezolaminated elastic beams

The forced induced vibrations of a piezolaminated elastic beam, being driven by time harmonic voltages applied to the actuators on top and bottom surfaces, is analysed using an exact elasticity solution. The analysis is carried out using the method of Fourier series and the solution is exact within the assumptions of linear elasticity and plane strain deformation. Numerical results are computed for various configurations of sandwich and laminated beams, including an aluminum beam with actuators fixed to top and bottom surfaces. To show the capability of the elasticity solution, the static shape of laminated beams due to the piezoelectric induced strains are calculated and compared with approximate existing results.

The vibration of a simply supported rectangular elastic plate due to piezoelectric actuators

An analysis of a simply supported rectangular elastic plate forced into bending vibrations by the application of time harmonic voltages to piezoelectric actuators attached to its bottom and top surfaces is performed by using the equations of linear elasticity. The actuators have been modeled as thin surface films and mixed edge conditions are employed to simulate simple supports.

A Study of the Electromagnetic Vibration of a Capacitor Induction Motor Caused by Time-Harmonic Voltages.

In recent years, distortion of power source voltage waveform has become noticeable, as electrical appliances with rectifier circuits have been widely used. Connecting capacitor induction motor (CRM) to such distorted supply, or controlling CRM by simple controller with switching device such as triacs, harmonic voltage is supplied to CRM. In that case, CRM produces electromagnetic vibrations caused by not only the fundamental voltage but also time-harmonic voltages in the distorted voltage. In addition, CRM produces electromagnetic vibration due to backward magnetic field. Thus, it is difficult to clarify the relationship between electromagnetic vibration of CRM and harmonic voltages.In this paper, the causes of the electromagnetic vibration of CRM operating under distorted wave supply voltage are discussed. First, a general equation of dominant electromagnetic force waves is shown considering not only forward magnetic fields but also backward magnetic fields. Using the general equation, causes of dominant electromagnetic vibration are clarified. Next, by means of discussing in details of some examples of the dominant vibration, the relationship between the vibration and harmonic voltages becomes evident. Furthermore, the relationship between the vibration and backward magnetic field is clarified.

The cylindrical bending vibration of a laminated elastic plate due to piezoelectric actuators

We analyze the forced cylindrical bending vibrations of a laminated elastic plate with actuators at the top and bottom surfaces and forced into vibrations by applying time harmonic voltages to the actuators. The actuators are modeled as thin films and mixed edge conditions are employed to simulate simple supports. The analysis is performed by using the method of Fourier series and the solution is exact within the assumptions of linear elasticity and plane strain deformations. Numerical results are computed for an aluminum plate with actuators affixed to its two major surfaces.

A theory of electroded thin thermopiezoelectric plates subject to large driving voltages

We first reduce existing equations for nonlinear thermoelectroelasticity to the case of large electric fields, small strains, and infinitesimal temperature variations. These equations are then specialized to the case of thin plates with completely electroded major surfaces, and it is shown that in this case the charge equation of electrostatics is satisfied trivially to the lowest order. An example is given to illustrate the effect of heat conduction on the response of a thin electroded plate subjected to time harmonic voltages on the two major surfaces.