Element Method In Frequency Domain Research Articles

Tunable THz flat zone plate based on stretchable single-walled carbon nanotube thin film

Tunable optoelectronics have attracted a lot of attention in recent years because of their variety of applications in next-generation devices. Among the potential uses for tuning optical elements, those allowing consistent parameter control stand out. We present an approach for the creation of mechanically tunable zone plate lenses in the THz range. Our devices comprise single-walled carbon nanotube (SWCNT) thin films of predetermined design integrated with stretchable polymer films. These offer high-performance and in situ tunability of focal length up to 50%. We studied the focusing properties of our lenses using the backward-wave oscillator THz imaging technique, supported by numerical simulations based on the finite element frequency domain method. Our approach may further enable the integration of SWCNT films into photonic and optoelectronic applications and could be of use for the creation of a variety of flexible and stretchable THz optical elements.

Numerical Analysis of the Light Modulation by the Frustule of Gomphonema parvulum: The Role of Integrated Optical Components

Siliceous diatom frustules present a huge variety of shapes and nanometric pore patterns. A better understanding of the light modulation by these frustules is required to determine whether or not they might have photobiological roles besides their possible utilization as building blocks in photonic applications. In this study, we propose a novel approach for analyzing the near-field light modulation by small pennate diatom frustules, utilizing the frustule of Gomphonema parvulum as a model. Numerical analysis was carried out for the wave propagation across selected 2D cross-sections in a statistically representative 3D model for the valve based on the finite element frequency domain method. The influences of light wavelength (vacuum wavelengths from 300 to 800 nm) and refractive index changes, as well as structural parameters, on the light modulation were investigated and compared to theoretical predictions when possible. The results showed complex interference patterns resulting from the overlay of different optical phenomena, which can be explained by the presence of a few integrated optical components in the valve. Moreover, studies on the complete frustule in an aqueous medium allow the discussion of its possible photobiological relevance. Furthermore, our results may enable the simple screening of unstudied pennate frustules for photonic applications.

Metamaterial absorber and antenna ground plane

Metamaterial absorber located near solid metal surface was investigated and antenna design was developed for receiving satellite navigation signals using absorptive ground plane comprises proposed material. The metamaterial structure has been developed, frequency characteristics have been analyzed by finite element method in frequency domain, operating dimensions of elements have been established. Modeling and analysis of radiation pattern for antenna with absorptive ground plane versus the antenna with the classic high impedance ground plane were carried out. Conclusions were drawn on the applicability of the proposed metamaterial structure. Keywords: GNSS Antenna, metamaterial absorber, high impedance ground plane.

Радиопоглощающий метаматериал и экран антенны на его основе

Metamaterial absorber located near solid metal surface was investigated and antenna design was developed for receiving satellite navigation signals using absorptive ground plane comprises proposed material. The metamaterial structure has been developed, frequency characteristics have been analyzed by finite element method in frequency domain, operating dimensions of elements have been established. Modeling and analysis of radiation pattern for antenna with absorptive ground plane versus the antenna with the classic high impedance ground plane were carried out. Conclusions were drawn on the applicability of the proposed metamaterial structure.

Experimental and numerical investigations of mechanical displacements in surface acoustic wave bounded beams

The present paper studies experimentally and numerically the surface acoustic wave (SAW) field on a piezoelectric substrate generated by interdigital transducers (IDT). On the one hand, mechanical displacements produced by the SAW are measured with the help of a laser Doppler vibrometer. On the other hand, mechanical displacements are computed by the two-dimensional finite element method in frequency domain followed by the spatial Fourier transform. Combining these two steps of computations results in the intended two-dimensional distribution of mechanical displacements on the substrate surface. The comparison of experimental and numerical data obtained for a series of different IDTs reveals that it is possible to estimate the shape of the SAW beam and the absolute value of mechanical displacement amplitude using only the basic parameters of the IDT and its electrical admittance measured by a network analyzer.

An exact PML to truncate lattices with unstructured-mesh-based adaptive finite element method in frequency domain for ground penetrating radar simulation

We present a new approach of unstructured grid adaptive finite element in the frequency domain (AFEFD) based on exact perfect matching layer (EPML) boundary condition for Ground penetrating radar (GPR) simulation. The discrete equations of transverse magnetic mode are derived by using the unstructured Delaunay mesh coupled with linear interpolation basis functions. For the trade off between the computational efficiency and the accuracy of simulation, an h-type adaptive finite element method (AFEM) is employed and, in particular, with less layer thickness and fewer parameters setting, an EPML boundary condition is developed to truncate the AFEM lattices. In addition, the Zienkiewicz-Zhu posterior error estimation, the mesh refinement scheme and the implementation process of AFEM are also elaborated in detail. To testify the validity and practicability of this methodology, a homogeneous medium model of line current radiation field with analytical solution and a complex model of lining fracture disease are considered. The results of frequency-domain slices, transformed time-domain forward profile, together with wavefield snapshots demonstrated that the reflections, diffractions and other codas caused by non-physical factors at the boundary are effectively absorbed, subsequently, the absorbing performance of simulation with AFEM in frequency domain is greatly improved. More importantly, the proposed methodology can automatically control its mesh density according to the features of the complex object, which significantly economize the computing resource of simulation when AFEM is employed.

FE analysis of surface acoustic wave transmission in composite piezoelectric wedge structures

The paper numerically investigates the transmission of harmonic surface acoustic waves (SAWs) across the perfectly bonded and perfectly sliding contacts between two 90°-wedges, at least one of which possessing piezoelectric properties. The finite element method in frequency domain is used. The structures are constructed of lithium niobate, fused quartz, silicon and gallium arsenide. The SAW is always incident from lithium niobate. The dependences of the transmission coefficient on the combination of materials and the orientation of the lithium niobate, as well as on the height of the step at the interface between the two parts of the structure are computed and analyzed. This step can appear in the process of fabrication of the composite substrate. The obtained results demonstrate that SAWs are able to transmit fairly efficiently across a wedge-like contact. Therefore such structures can be useful, in particular, in cases when it is advantageous to generate a SAW in one strongly piezoelectric material and observe its action, e.g., due to the transmitted surface normal displacement in another material like in SAW-driven microfluidics.

Optimized tapered dipole nanoantenna as efficient energy harvester.

In this paper, a novel design of tapered dipole nanoantenna is introduced and numerically analyzed for energy harvesting applications. The proposed design consists of three steps tapered dipole nanoantenna with rectangular shape. Full systematic analysis is carried out where the antenna impedance, return loss, harvesting efficiency and field confinement are calculated using 3D finite element frequency domain method (3D-FEFD). The structure geometrical parameters are optimized using particle swarm algorithm (PSO) to improve the harvesting efficiency and reduce the return loss at wavelength of 500 nm. A harvesting efficiency of 55.3% is achieved which is higher than that of conventional dipole counterpart by 29%. This enhancement is attributed to the high field confinement in the dipole gap as a result of multiple tips created in the nanoantenna design. Furthermore, the antenna input impedance is tuned to match a wide range of fabricated diode based upon the multi-resonance characteristic of the proposed structure.

Numerical assessment of the vibration control effects of porous liners on an over-the-wing propeller configuration

An over-the-wing position of propellers comes with noise shielding and significantly reduced sound emission to the ground. A drawback of this configuration may be the additional impact due to the passing propeller blades on the airfoil’s surface inducing structure-borne sound in the wing. This structural sound propagates within the wing and the fuselage and can radiate further into the cabin as airborne sound. In order not to trade the advantage of reduced noise transmission to the ground with higher sound pressure levels within the cabin, a remedy is proposed, which consists in placing a poroelastic liner on the wing’s surface below the rotor where the blade tips move closely to the airfoil’s skin. In this work, a numerical approach to assess the effects of porous liners for an over-the-wing propeller configuration is presented. A simplified generic channelwing structure is exposed to pressure fluctuations on its surface which are caused by an over-the-wing propeller. Porous liners are applied to the wing’s surface where the blade tips pass in close proximity. Structural vibrations are determined using the finite element method in frequency domain. Surface data is obtained from CFD computations. The porous material is represented by Biot’s theory.

Magnonic crystals—Prospective structures for shaping spin waves in nanoscale

We have investigated theoretically band structure of spin waves in magnonic crystals with periodicity in one- (1D), two- (2D) and three-dimensions (3D). We have solved Landau–Lifshitz equation with the use of plane wave method, finite element method in frequency domain and micromagnetic simulations in time domain to find the dynamics of spin waves and spectrum of their eigenmodes. The spin wave spectra were calculated in linear approximation. In this paper we show usefulness of these methods in calculations of various types of spin waves. We demonstrate the surface character of the Damon–Eshbach spin wave in 1D magnonic crystals and change of its surface localization with the band number and wavenumber in the first Brillouin zone. The surface property of the spin wave excitation is further exploited by covering plate of the magnonic crystal with conductor. The band structure in 2D magnonic crystals is complex due to additional spatial inhomogeneity introduced by the demagnetizing field. This modifies spin wave dispersion, makes the band structure of magnonic crystals strongly dependent on shape of the inclusions and type of the lattice. The inhomogeneity of the internal magnetic field becomes unimportant for magnonic crystals with small lattice constant, where exchange interactions dominate. For 3D magnonic crystals, characterized by small lattice constant, wide magnonic band gap is found. We show that the spatial distribution of different materials in magnonic crystals can be explored for tailored effective damping of spin waves.

Development of a simplified heat transfer model of hollow blocks by using finite element method in frequency domain

Hollow blocks or bricks are widely used due to the good thermal insulation, lightweight, acoustic insulation, etc. This paper presents the development of a simplified heat transfer model of hollow block for simple and efficient heat flow calculation. This model is developed based on parameter identification in frequency domain by using finite element method in frequency domain. Firstly, the frequency domain finite element model (FDFEM) of the hollow block is developed by using finite element method in frequency domain to obtain the theoretical frequency characteristics of this structure. Then, the heat transfer function model in the form of s-polynomial (i.e., the s-polynomial heat transfer function model) is identified by using a parameter identification procedure based on the calculated theoretical frequency thermal characteristics. Finally, the simplified heat transfer model, i.e., the Conduction Transfer Function (CTF) coefficients, of this hollow block are derived from the identified s-polynomial heat transfer function model. A case study is presented for the prediction of the dynamic heat transfer of this hollow block by using the simplified heat transfer model. The predicted dynamic heat transfer of this block is validated by experimental data.

The mathematical modeling of the electric field in the media with anisotropic objects

We present a numerical scheme for modeling the electric field in the media with tensor conductivity. This scheme is based on vector finite element method in frequency domain. The numerical computations of the electric field in the anisotropic medium are done. The conductivity of the anisotropic medium is positive defined dense tensor in general case. We consider the electric field from anisotropic layer, inclined anisotropic layer and some anisotropic objects in isotropic half-space.

A finite element frequency domain method for 2D photonic crystals

In this paper we propose a new finite element frequency domain (FEFD) method to compute the band spectra of 2D photonic crystals without impurities. Exploiting periodicity to identify discretization points differing by a period, it increases the effectiveness of the algorithm and reduces significantly its computational complexity. The results of an extensive experimentation indicate that our method offers an effective alternative to the most quoted methods in the literature.

Cellular handsets antenna modeling by vector finite element method

An algorithm of electromagnetic fields simulation and calculation of cellular handsets antenna parameters by vector finite element method in frequency domain is presented. The algorithm is based on discretization of the electric field equation by Galerkin method using basis functions of various order. Incorporation of lumped elements and ports into finite element model is provided. Fast frequency sweep is used for accelerating solution process in a wide frequency band. Comparison of simulation and experimental results proves high accuracy and reliability of the developed computer code.

Using spectral element method for analyzing continuous beams and bridges subjected to a moving load

Spectral element method in frequency domain is employed to analyze continuous beams and bridges subjected to a moving load. The formulation is developed for an Euler beam under a moving load with an arbitrary amplitude and velocity. It is shown that the procedure is simplified for a moving load with a constant amplitude and velocity. Static Green’s function is used as a modifying function to improve the moment and shear force results. It is further shown that while modifying function is used in conjunction with spectral element method, fewer elements will be required to achieve proper results. The numerical examples show the accuracy of the method.

A FEM-BEM interactive coupling for modeling the piezoelectric health monitoring systems

In this research, finite element and boundary element methods are coupled together to model the interaction of a piezoelectric ceramic working as an actuator with an elastic material. Piezoelectric-elastic material's interaction occurs in smart structures. This work is aimed at determining the actuation effects being transferred from the actuators to the host and the resulting overall structural response. To obtain the amount of these actuations, the system of the host structure and an actuator has been modeled by using coupled finite element boundary element method in frequency domain. The host structure, which is assumed as an isotropic elastic solid region is modeled as a half space. The piezoelectric ceramic region is modeled by the 3-D finite element method, while the elastic half space with boundary element method. Finite element model of piezoelectric ceramic and boundary element model of the elastic half space are coupled together at their interface such that the vibrations of the piezo-actuator induce vibrations in the elastic half space. A couple of examples are given to show the induced displacement field around the piezo-actuator on the surface of the elastic medium. The results show that high jump in magnitude of horizontal displacements at the corners of the actuator attached to the structure occurs, which is an indication of high stress concentration, of the shear stress type at the corners. This stress concentration sometimes causes complete debonding of the actuator from the base structure. By using the suggested BEM-FEM coupled model for actuators with different dimensions or material properties much useful information concerning the amount of actuation and load transfer can be obtained. The presented work is a step towards modeling of structural health monitoring systems.

Effects of open trench siding on vibration-screening effectiveness using the two-dimensional boundary element method

The two-dimensional boundary element method in frequency domain is used to investigate the screening effectiveness of the open trench–wall barrier system on reducing vibration generated by a footing. Sheet piles or diaphragm walls are on both sides of the open trench as a vibration barrier in this study. The results showed that screening effectiveness of the open trench without siding is greater than that of the open trench–wall barrier system, which is essential for stabilizing the excavation surface in practice. The trench depth of the barrier system appears to govern the screening efficiency of the barrier, and increase in depth results in better vibration-screening effectiveness. The influence of the open trench width, the embedded length of the trench wall and the distance between the vibration source and the barrier are proven to be insignificant. The screening effectiveness of an open trench barrier with walls increases with the frequency of the vibration.

Adaptive finite element frequency domain method for eddy current problems

In the present paper, adaptive finite element methods are studied for time-harmonic eddy current problems in the case of three-dimensional isotropic and linear materials. We adopt the formulation based on the magnetic field and a magnetic scalar potential in this paper, since it needs the least number of unknowns. Reliable and efficient a posteriori error estimates are obtained and the efficiency of the adaptive algorithm is demonstrated by numerical and engineering experiments.

Three-dimensional analysis of the screening effectiveness of hollow pile barriers for foundation-induced vertical vibration

The study applies the three-dimensional boundary element method in frequency domain to investigate the screening effectiveness of circular piles in a row for a massless square foundation subject to harmonic vertical loading. Four types of piles were studied: steel pipe piles, concrete hollow piles, concrete solid piles and timber piles. A parametric study was undertaken to examine the effects of pile dimensions, operational frequency, and source distance on the screening effectiveness. The results showed that screening effectiveness of steel pipe piles is generally better than that of solid piles, and that a concrete hollow pile barrier can be ineffective due to its stiffness. The influence of pile length on screening effectiveness is more significant than that of pile spacing and the distance between the vibrating foundation and the pile barrier.

Grounding Performance Analysis of the Substation Grounding Grids by Finite Element Method in Frequency Domain

Based on finite-element method (FEM) of 1-D conductor element coupled with 3-D soil element, we take into account the frequency dependent characteristic of the discretized elements to analyze the grounding performance of the substation grounding grids. Compared with A-V formulation of 3-D FEM, the proposed method can greatly save the CPU time, and the frequency can be considered during FEM modeling. In comparison with the method of moment (MoM) and the measured results, the presented method is proved to be correct and effective. Furthermore, we can calculate the H-field generated by the substation grounding grids with both currents in the underground conductors and leakage currents flowing in the soil. The results show slight difference between FEM and MoM, which can be explained by the fact that the leakage currents in the soil are not taken into account for MoM