Frequency Domain Finite Element Model Research Articles

A frequency-domain finite element model for simulating high temperature superconductors using the J-A and T-A formulations

Abstract The AC losses, the current density and the magnetic field are important variables to design devices made of High Temperature Superconductors (HTS). These variables are often numerically computed using a transient finite element analysis even though the interest may lay in the steady-state regime of the device. The need for solving time-dependent variables has led to improve the computation time with efficient finite element models (FEM) relying on different formulations. These transient FEM are computationally slow and demanding in terms of resources. In the present work, an alternative path is taken with the development of a frequency-domain FEM using a phasor representation to alleviate the computation burden. This model does not have the versatility of the transient models. However, it can generate the initial steady-state conditions for a subsequent transient analysis. It is perfectly adapted to study the steady-state regime of HTS devices operated in AC conditions. In this phasor modelling approach, the Root Mean Square (RMS) resistivity of the superconductor is introduced. It is subsequently approximated by an exponential function introducing a factor to ease its implementation in the commercial software COMSOL Multiphysics with the most recent and fastest formulations T-A and J-A. The case studies encompass single BSCCO and REBCO tapes as well as a CORC cable or specifically, in the present work, a CORT (Conductor on Round Tube). The results of the time- and frequency-domain FEM simulations are compared against experimental data. The comparison of the models' results is carried out comparing the current density distributions as well as the AC losses. The comparison against experimental data is only conducted on the AC losses. In the present case, it is used to quantify thoroughly the accuracy of the numerical results compared to the measurements. A reasonable agreement between those results and the experimental data was found. 

Optimization and operation of interdigital transducer to improve signal-to-noise ratio

This study presents a novel optimization method for Lamb wave mode selective transducers, surpassing traditional interdigital transducers (TIDT) by employing non-uniform electrode widths to suppress harmonic components. Utilizing a frequency domain finite element model (FDFEM), the coupling mechanism between the double-sided interdigital transducer (DS-IDT) and the waveguide is analyzed, forming the optimization basis. By discussing key parameters affecting wavelength selection characteristics, an optimization scheme is formulated. Employing a multi-objective genetic algorithm, the strategy focuses on minimizing the ratio of stray to target mode as the cost function, resulting in significant signal-to-noise ratio (SNR) improvements. Compared to TIDTs, SNR gains of at least 4.7 dB at 70 kHz and 8.8 dB at 400 kHz are achieved. Laboratory experiments validate the superior mode selection performance of the optimized interdigital transducer (OIDT) over ordinary piezoelectric wafer (OPW) and TIDT, demonstrating a significant reduction of 48.82 % in stray S0 mode amplitude at 70 kHz and 94.77 % in stray A2 mode amplitude at 400 kHz. This method ensures high SNR for target mode signals, simplifying feature extraction and enhancing structural health monitoring capabilities.

Quantitative monitoring of icing on CFRP laminate with guided wave combining forward modeling and inverse characterization

Aircraft icing is one of the critical factors for flight safety. Timely and accurate monitoring of in-flight ice accretion is essential for flight systems to take immediate and effective action to significantly improve the efficiency of subsequent de-icing processes and ensure flight safety. Since carbon fiber reinforced polymer (CFRP) are now widely used in the aviation industry, the study of ice accretion on the surfaces of CFRP with anisotropic properties is of great importance. In this work, a three-dimensional frequency domain finite element model for icing CFRP laminate is first established, via which the mechanism of mode conversion of ultrasonic guided waves (UGWs) at different ice layer thicknesses is quantitatively analyzed. Then, the time-domain finite element simulation was performed, from which the time–frequency domain spectrogram of the acquired UGW signal is obtained by short-time Fourier transform (STFT). The extracted frequency–time-of-flight (ToF) curve of the signal via STFT shows high agreement with the theoretical results, which confirms the influence of icing on UGW propagation. Finally, numerous experiments with bonded lead zirconate titanate wafers to excite and acquire UGWs are conducted with different ice layer thicknesses and lengths on CFRP. The extracted frequency–ToF curves of UGW signals are used as input to a two-layer feedforward artificial neural network (ANN) to accurately evaluate the length and thickness of the ice layer. The high reliability of this method with ANN is confirmed, which shows the potential of the proposed UGW-based method for quantitative monitoring of icing length and thickness on aircraft CFRP laminate.

Finite-element/boundary-element transient modelling of hysteresis motors

This paper presents a transient study of hysteresis motor based on the proposed hybrid method of finite element method- boundary element method (FEM-BEM) in which the Jiles-Atherton (J-A) vector hysteresis model of the hard-magnetic material of the rotor is incorporated. The air–gap region is modeled by BEM in order to avoid the discontinuity in the FEM equations due to J-A hysteresis model and the rotor movement and, therefore, the eddy current effect is taken into account in the rotor part, for the first time. To the best of the author’s knowledge, the prior time-dependent numerical models have ignored the torque component caused by eddy currents in the rotor of hysteresis motor, due to difficulty in rotating the mesh in the rotor region and the related convergence problems. The proposed model is employed to study the phenomenon of short period over-excitation in hysteresis motors. A comparison is done between the proposed time-domain model and the frequency-domain finite element model of the hysteresis motor.

Frequency response analysis of concrete seawall including soil-structure-seawater interaction

In this study, a frequency-domain finite element model is proposed to evaluate the seismic response of water-structure-sediment-foundation-backfill coupling system. It includes the seawater as a compressible fluid, seawall as viscoelastic solid, backfilled soil, sediment, and foundation as two-phase poroelastic domains with dynamic behavior described by u-p formulation of Biot’s equations. The dynamic interactions among various domains are fully considered and the PML is adopted as an absorbing boundary condition to truncate the computational domain, absorbing all out-going seismic waves. The dynamic responses in the structure, water and soil are assumed to be generated by the vertical propagating shear or compressional waves from the bedrock substrate under the foundation soil. Both the actions of horizontal and vertical seismic excitations at the bottom of foundation are respectively considered. After verifying the accuracy of PML and coupled model of soil-structure-water system, a series of parametric studies are conducted to investigate the effects of sediment thickness, water depth, foundation stiffness, foundation thickness, inclination of seawall, and properties of backfilled soil including soil permeability, shear modulus, and saturation degree, on the frequency response at the top of seawall.

An accurate frequency-domain model for seismic responses of breakwater-seawater-seabed-bedrock system

A frequency-domain finite element model is proposed to evaluate seismic response of breakwater-seawater-seabed-bedrock system with full consideration of interactions among them. The frequency-domain model contains near field finite element model, accurate absorbing boundary condition (ABC) and seismic wave input. Firstly, the accurate ABC on the truncated boundaries is applied to simulate the far field of infinite domain. Discretizing for wave equation of the fluid-poroelastic-solid media in the depth direction, and using analytical methods in the remaining coordinate direction, the accurate ABC is mathematically derived without introducing any approximate assumptions. Secondly, the equivalent input seismic loads on the ABC are obtained by one-dimension (1D) response of free field. Combining of the proposed ABC, equivalent input seismic loads, and near field finite element equation, the coupled model to evaluate the seismic response of breakwater-water-seabed-bedrock system is obtained. Numerical examples indicate that the proposed model is accurate and efficient. Finally, the proposed model is used to investigate effects of slope angle of breakwater, water depth and seabed soil properties including seabed porosity, permeability coefficient and shear modulus on seismic response of breakwater, and the momentary liquefaction of seabed.

Spin wave generation by surface acoustic waves

Surface acoustic waves (SAW) on piezoelectric substrates can excite spin wave resonance (SWR) in magnetostrictive films through magnetoelastic coupling. This acoustically driven SWR enables the excitation of a single spin wave mode with an in-plane wave vector k matched to the magnetoelastic wave vector. A 2D frequency domain finite element model is presented that fully couples elastodynamics, micromagnetics, and piezoelectricity with interface spin pumping effects taken into account. It is used to simulate SAW driven SWR on a ferromagnetic and piezoelectric heterostructure device with an interdigital transducer configuration. These results, for the first time, present the spatial distribution of magnetization components that, together with elastic wave, exponentially decays along the propagation direction due to magnetic damping. The results also show that the system transmission rate S21(dB) can be tuned by both an external bias field and the SAW wavevector. Acoustic spin pumping at magnetic film/normal metal interface leads to damping enhancement in magnetic films that decreases the energy absorption rate from elastic energy. This weakened interaction between the magnetic energy and elastic energy leads to a lower evanescence rate of the SAW that results in a longer distance propagation. With strong magnetoelastic coupling, the SAW driven spin wave is able to propagate up to 1200 μm. The results give a quantitative indication of the acoustic spin pumping contribution to linewidth broadening.

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.

Design and modeling of an ultra-compact 2x2 nanomechanical plasmonic switch.

A 2x2 Mach-Zehnder optical switch design with a footprint of 0.5 μm x 2.5 μm using nanomechanical gap plasmon phase modulators [Nat. Photonics 9(4),267-273(2015)] is presented. The extremely small footprint and modest optical loss are enabled by the strong phase modulation of gap plasmons in a mechanically actuated 17 nm air gap. Frequency-domain finite-element modeling at operating wavelength 780 nm shows that the insertion loss is ≤ 8.5 dB, the extinction ratio is > 25 dB, and crosstalk for all ports is > 24 dB. A design optimization approach and its dependence on geometrical parameters are discussed.

Validation of finite element computations for the quantitative prediction of underwater noise from impact pile driving

The acoustic radiation from a pile being driven into the sediment by a sequence of hammer strikes is studied with a linear, axisymmetric, structural acoustic frequency domain finite element model. Each hammer strike results in an impulsive sound that is emitted from the pile and then propagated in the shallow water waveguide. Measurements from accelerometers mounted on the head of a test pile and from hydrophones deployed in the water are used to validate the model results. Transfer functions between the force input at the top of the anvil and field quantities, such as acceleration components in the structure or pressure in the fluid, are computed with the model. These transfer functions are validated using accelerometer or hydrophone measurements to infer the structural forcing. A modeled hammer forcing pulse is used in the successive step to produce quantitative predictions of sound exposure at the hydrophones. The comparison between the model and the measurements shows that, although several simplifying assumptions were made, useful predictions of noise levels based on linear structural acoustic models are possible. In the final part of the paper, the model is used to characterize the pile as an acoustic radiator by analyzing the flow of acoustic energy.

Analysis of Reflection Powers from a Perfectly Matched Layer for Elastic Waves in the Frequency Domain Finite Element Model

Analysis of Reflection Powers from a Perfectly Matched Layer for Elastic Waves in the Frequency Domain Finite Element Model

Analysis of Reflection Powers from a Perfectly Matched Layer for Elastic Waves in the Frequency Domain Finite Element Model

A perfectly matched layer (PML) is useful for truncating the computation region of scattering problems in a finite element analysis (FEA). The approximation of the open region with thick layer and discretization of it with finite elements generates reflection waves from PML boundary. However, reflection powers generated by finite element discretization have not been quantified for elastic waves. In this paper, we explain the reflection from PMLs by discretized wave number analysis of elastic plane-wave scattering, and demonstrate that the results of discretized wave number analysis give satisfactory approximations of FEA.

Efficient frequency-domain finite element modeling of two-dimensional elastodynamic scattering

A frequency-domain finite element technique is presented that enables the complete characterization of a finite-sized scatterer using a minimum number of separate model executions and a relatively small spatial modeling domain. The technique is implemented using a commercial finite element package. A certain forcing profile is applied at a set of points surrounding the scatterer to cause a uni-modal plane wave to be incident on the scatterer from a specified direction. The scattered field is recorded and decomposed first into modes and then into far-field scattering coefficients in different directions. The data obtained from the model are represented in a scattering matrix that describes the far-field scattering response for all combinations of incident and scattering angles. The information in the scattering matrix can be efficiently represented in the Fourier domain by another matrix containing a finite number of Fourier coefficients. It is shown how the complete scattering behavior in both the near- and far-field can be extracted from the matrix of Fourier coefficients. Modeling accuracy is examined in various ways, including a comparison with the analytical solution for a circular cavity, and guidelines for the selection of modeling parameters are given.

A general method for the frequency domain FE modeling of rotating electromagnetic devices

In this paper, we present a general method to include time periodic movement in the frequency domain finite-element simulation of rotating electromagnetic (EM) devices. For the particular case of a two-dimensional (2-D) finite-element (FE) model of a rotating machine, it only requires elementary manipulations of the static moving band stiffness matrix, calculated for a number of discrete rotor positions in a fundamental period. As an application example, the no-load operation of an induction motor has been simulated. The harmonic balance results agree well with those obtained with time stepping.

Tides in the Tongan Region of the Pacific Ocean

Tidal levels and currents in the Tongan region of the Pacific were simulated using a two-dimensional frequency-domain finite element model. The eight major diurnal and semidiurnal tidal constituents were modeled successfully, using open boundary conditions taken from a global tidal model based on the Topex/Poseidon satellite altimeter. Comparison of model results with observations from the single tide gauge site in the area were later used to adjust the boundary conditions. The validity of omitting horizontal eddy viscosity from the finite element model was checked by running an equivalent finite difference model. The results show that although the submarine Tongan ridge does not appear to trap tidal energy, there are residual tidal currents and possible recirculations which are capable of influencing biological productivity around Tonga. The model results are reduced to a simple method for predicting tidal heights in outlying areas, based only on the tidal calendar for the capital, Nuku'alofa.