Frequency Domain Finite Element Method Research Articles

Quantitative assessment of delamination in composites using multiple local-defect-resonance modes

Accurately visualizing the geometry and dimensions of internal delamination in fiber-reinforced polymer (CFRP) composites is a challenging endeavor. In this paper, we develop a method to identify and characterize delamination in composites by the integration of multiple local defect resonance (LDR) modes. The proposed method was validated by using T300/M914 CFRP plates containing three distinct defect geometries, employing both numerical simulations and experimental measurements. The approach commences with the application of a frequency-domain finite element method for LDR frequency determination, emphasizing improved computational efficiency. This technique is further corroborated through the use of the defect-to-background ratio (DBR) method, which identifies LDR frequencies in both numerical simulations and experimental testing. The integration of multiple LDR modes (IMLDR) at various frequencies enables precise imaging of delamination defects of diverse geometries and sizes. Experimental results closely align with the numerical findings, confirming that the integrated imaging results accurately correspond to artificial defects. This method furnishes precise descriptions of damage location, geometry, and dimensions. The obtained results indicate that the proposed IMLDR-based technique significantly enhances the accuracy and reliability of delamination imaging in composites. Consequently, it offers an effective approach for quantitatively assessing delamination damage in composites.

Finite Element Method study on VLF propagable modes coupling and interference in the anisotropic earth‐ionosphere waveguide

AbstractIn this paper, the coupled‐mode theory is incorporated into the improved frequency‐domain finite element method (FEM) to simulate very low frequency (VLF) propagable modes coupling and interference in the anisotropic Earth‐ionosphere waveguide. The matrix equation of the electric field is solved using parallel lower‐upper factorization technique to speed up the calculation. The method used to determine the propagation constants for different propagable modes is given. After the FEM is validated by comparing simulated results with the measured data, effects of variable geomagnetic information on the attenuation rate, relative phase velocity, mode coupling, and multiple‐mode interference of VLF electromagnetic wave in the anisotropic waveguide are investigated. This work provides an efficient way for improving the prediction accuracy of the VLF communication, positioning, navigation, and timing systems.

An Efficient Goal-Oriented Adaptive Finite Element Method for Accurate Simulation of Complex Electromagnetic Radiation Problems

A goal-oriented adaptive frequency domain finite element method for solving electromagnetic radiation problems including complex structures is presented in this paper. Compared with the traditional adaptive finite element method, the goal-oriented method can flexibly control the refined regions according to the parameters of interest; therefore it has better convergence and has made significant progress in scattering problems and eigenvalue problems. To simulate complex antennas, this paper proposes an error indicator with high accuracy and low computational cost, and it uses the adjoint problem to weight element residuals without additional degrees of freedom. Moreover, high-quality mesh refinement algorithms adapted to this indicator are developed using a suitable point insertion strategy for multiscale structures. By simulating two practical antennas, comparisons with the traditional goal-oriented FEM and the well-developed <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">h</i> -adaptive finite element method in commercial software demonstrate the accuracy and efficiency of the proposed method.

Using Computer Technique for Developing Method for Vibration Damage Estimation Under Combined Random and Deterministic Loading

Abstract This paper is focusses on developing a novel method for vibration damage estimation for military helicopters, fighter aircrafts and any other aircraft exposed to combined stochastic and deterministic loading. The first stage of the research focused on frequency domain damage prediction, which is the legacy method proposed by Bishop and developed by Sweitzer, Schlesinger, Woodward, Kerr, Murthy, Datta and, Atkins. The mentioned frequency domain-based method is used in commercial software, e.g., MSC CAE Fatigue. Frequency domain damage prediction is based on superposition of spectral moments and Dirlik method of Rainflow Cycle Counting algorithm in frequency domain. The first phase of the research showed the legacy algorithm based on transfer function developed using FEM (Finite Element Method) method in Abaqus environment and is very conservative. The second stage of the research aims to develop a novel method which allowing for more robust and accurate damage estimation. For this purpose, the Monte Carlo method for retrieving random signal in the time domain from signal in frequency domain was used. To obtain the system transfer function, – the 1 g load harmonic system response was obtained using FEM analysis. It was subsequently scaled linearly by the PSD input curve for random loading and sine wave, or sine sweep function for deterministic loading to calculate the cumulative system response of the linear system. The research allows the development of a novel method to precisely estimate vibration damage using combined time and frequency domains approach, based on effective frequency domain FEM analysis of the linear system. The new proposed method can be also used for precise replication of test conditions via considering signal clipping and frequency resolution used for real testing.

High-temperature characterization of interdigitated transducers on gallium arsenide and surface acoustic wave analysis via interdigitated transducer modeling

Interdigitated transducer devices may provide an advantageous platform to study stress-enhanced interfacial phenomena at elevated temperatures, and an appropriate device design requires a thorough understanding of temperature-dependent material properties. In this study, the scattering parameter response for a surface acoustic wave resonator is simulated using a frequency-domain finite element method from 20 to 177 °C. Experimental device measurements are taken for the interdigitated transducer device fabricated on semi-insulating GaAs 100 oriented in the 110 direction, and the results are in good agreement with the simulation. Surface acoustic wave analysis provides the magnitude of bulk stress values and surface displacement over the experimental temperature range produced by a standing surface acoustic wave. The computational analysis combined with experimental verification suggests that such devices, when optimized for the maximum magnitude, can produce strain levels that could influence chemical potential associated with crystalline growth, atomic diffusion, and catalytic reactions. The modeling results demonstrate an interdigitated transducer's potential as an experimental platform to study the impact of strain on temperature-sensitive surface and bulk phenomena in piezoelectric materials.

Finite element method study on VLF propagation in the fine Earth‐ionosphere waveguide

AbstractA fast and highly efficient frequency‐domain finite element method (FEM) is developed to simulate propagation characteristics of very low frequency (VLF) waves in the fine Earth‐ionosphere waveguide structure containing the transition period between day and night. The FEM is accelerated by embedding the GPU‐based parallel LU factorization method. We present an approach for determining the waveguide structure with the VLF transmitter and receiver locations. After validating the method, effects of the time‐ and location‐varying electric density on the amplitude and phase of the VLF wave are investigated. The electric density of the International Reference Ionosphere (IRI) is revised by coupling with the solar zenith angle. Numerical results simulated using the revised IRI model show excellent agreement with the measured data for the VLF wave from Novosibirsk to Qingdao. This work provides a promising way to research VLF electromagnetic properties of the Earth‐ionosphere waveguide and improve the prediction accuracy of VLF navigation and communication.

Tuning SERS Signal via Substrate Structuring: Valves of Different Diatom Species with Ultrathin Gold Coating.

The discovered light modulation capabilities of diatom silicious valves make them an excellent toolkit for photonic devices and applications. In this work, a reproducible surface-enhanced Raman scattering (SERS) enhancement was achieved with hybrid substrates employing diatom silica valves coated with an ultrathin uniform gold film. Three structurally different hybrid substrates, based on the valves of three dissimilar diatom species, have been compared to elucidate the structural contribution to SERS enhancement. The comparative analysis of obtained results showed that substrates containing cylindrical Aulacoseira sp. valves achieved the highest enhancement, up to 14-fold. Numerical analysis based on the frequency domain finite element method was carried out to supplement the experimental results. Our results demonstrate that diatom valves of different shapes can enhance the SERS signal, offering a toolbox for SERS-based sensors, where the magnitude of the enhancement depends on valve geometry and ultrastructure.

Finite-element modelling of seismoelectric and electroseismic waves in frequency domain: 2-D SHTE mode

SUMMARYWe propose a frequency-domain finite-element (FDFE) method to simulate the 2-D SHTE mode seismoelectric and electroseismic waves. By neglecting the secondary weak wavefield feedbacks, the SH and TE waves are solved, separately. In a finite plane region, propagations of both SH and TE waves can be described as the Helmholtz equation with boundary conditions, which is proved to be equivalent to the extremum of functional by conducting calculus of variation. The computation region is partitioned into structured rectangular elements with the bilinear interpolation. The proposed FDFE algorithm solves the wavefield in frequency domain and avoids adopting the quasi-static approximation. One advantage of the proposed algorithm is its ability to accurately simulate the seismoelectric and electroseismic responses generated from the free surface. We verify the proposed algorithm based on a layered model beneath a free surface by comparing the waveforms calculated using the FDFE algorithm with those calculated using analytically-based method. The proposed algorithm is applied in feasibility studies of interface seismoelectric and electroseismic responses in exploring the hydrocarbon reservoir and monitoring the time-lapse pollutant within a sand channel.

Electrothermal analysis of a TEC-less IR microbolometer detector including self-heating and thermal drift

ABSTRACT The article presents the results of modelling and experiments of the self-heating and thermal drift effects of microbolometric sensors of infrared radiation. The developed electrothermal model of the readout electronic circuit generates the power dissipated in the active microbolometer during row-by-row scanning implemented in the focal plane array (FPA) detector. Two approaches to thermal modelling are presented. Both 1D frequency domain and 2D time domain finite element method models allow estimation of the thermal behaviour of an FPA microbolometer. The modelling and presented experiment results lead to the estimation of the deterioration in FPA performance and allow definition of the basic limits of resistive bolometers in operation.

Parameter Analysis on Seismic Response of Long Lined Tunnel by 2.5D Substructure Method

When the numerical analysis of a long lined tunnel is carried out, the calculation amount of the finite element model becomes restricted large-scale parameter analysis. In this paper, an efficient and high-precision 2.5-dimensional (2.5D) frequency-domain finite element method is used to simulate the three-dimensional response of tunnels under the action of oblique incident plane seismic waves. This method can save calculations and avoid the boundary effect caused by the longitudinal truncation of the tunnel. The 2.5D zigzag-paraxial boundary is developed. The artificial boundary is attached to the structure’s surface. The substructure method for oblique plane seismic waves is established. Comparing the substructure method with the analytical solution, the correctness of the site response is verified first. The accuracy of the 2.5D finite element substructure method is further verified. The parameter analysis of different incident angles and conversion angles shows that the underground tunnel does not reach the maximum of structural seismic response when the seismic wave is vertically incident. The location of the soil–rock interface on the tunnel is further discussed. The results show that when the underground tunnel crosses the location of the soil–rock interface, the seismic response of the tunnel will be amplified.

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.

An Artificial Immune System Model Tightly Coupled to the Inverse Design of Photonic Crystals

We propose a model based on an Artificial Immune System (AIS) to be used in conjunction with any electromagnetic solver in order to solve inverse design problems of integrated photonics. The proposed AIS was inspired by the Opt-aiNET algorithm coupled to a homemade electromagnetic solver based on the frequency domain Finite Element Method (FEM), which was used for calculating the fitness function. To validate the proposed model, we evaluate the photonic bandgap (PBG) of photonic crystals by the inverse design approach by assuming triangular lattices comprised of Si and air, and compared the results with other metaheuristics. The proposed AIS model is tightly coupled to such type of problem when the photonic structure is discretized in the binary-valued domain. Interestingly, different from many bio-immune-inspired metaheuristics, this proposed model has one of its metaheuristics parameters highly related to the characteristics of the application, which allows the algorithm itself to get a better “learning” of the problem and, additionally, reveals the designer some features intrinsic to the application. We have obtained midgap ratios of the first PBGs in triangular lattices of 47.55% and 49.11% for transversal magnetic (TM) and transversal electric (TE) polarizations, respectively. Additionally, the proposed model was applied to achieve large PBGs assuming the TM polarization in PhCs based on silicon carbide, and a new structure presented a PBG equals to 33.94%.

Stress Online Monitoring Method Based on Multifrequency SH0 Guided Wave Information Fusion

This article proposes a stress monitoring technique based on multifrequency SH0 guided wave information fusion. Its nondispersive acoustoelastic characteristic facilitates joint analysis in the whole frequency band. Moreover, the typical representation of broadband multifrequency signal is equivalent to realizing multiple measurements simultaneously, effectively improving the measurement efficiency and reliability. First, a generalized multifrequency comprehensive measurement model is established, which combines with specific data analysis and postprocessing criteria to construct a new stress characterization method. Then, the acoustoelastic effect of SH0 guided wave is investigated. Next, the wideband shear piezoelectric transducer based on the out-of-plane d15 mode is designed. The frequency-domain finite-element method (FDFEM) is applied to optimize the SH0 guided wave excitation and reception interval. Finally, the laboratory experiments of 6061-T6 aluminum plates with a thickness of 1 mm are conducted to verify the proposed strategy. The fitting result of multifrequency component fusion is better than that of any single-frequency algorithm. The actual measurements from the same batch are carried out through the calibration results. The maximum error does not exceed 2.5 MPa and the maximum relative standard deviation (RSD) is 7% in the range of 15–85 MPa, demonstrating good measurement accuracy and consistency.

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.

Control of Quasibound Waves in Spiral Metasurfaces

Resonant light scattering by a subwavelength dielectric resonator array can show narrow, highly tunable resonant lineshapes from the interaction among multiple resonances. Several approaches have been introduced to control the spectral response of resonant light scattering, including optimization of the aspect ratio of cylindrical resonators, breaking in-plane inverse symmetry of coupled resonators, and operating periodic structures at the Γ point in reciprocal space. In this paper, we report the experimental demonstration of the control of resonant light scattering by subwavelength spiral resonator arrays. The fabricated metasurfaces support two types of resonances: the first one characterized by a Lorentzian peak with a long lifetime and the second type with a short lifetime supported by the lattice. By controlling the coupling strength between these two resonances through tailored broken symmetries, the resonant line shape of the spiral metasurface can be precisely tuned. The measured spectra show an ultrawide frequency tuning (over 16 THz) of the resonant mode by changing the spiral parameter at a fixed lattice constant. A temporal couple-mode theory combined with frequency-domain finite element method simulations was used to describe the measured transmission spectra of the fabricated metasurfaces.

Convex-optimization-based post-processing for computing room impulse response by frequency-domain FEM

Numerical simulation of impulse responses is an important task for room acoustic design and prediction. Since an impulse response is a concept in the time domain, time-domain simulation methods are popular for this task. At the same time, frequency-domain simulation methods are also used for simulating a room impulse response by computing frequency responses and applying the inverse discrete Fourier transform (IDFT). In this case, well-established frequency-domain solvers, including finite element method (FEM) and boundary element method (BEM), can be used. However, IDFT generates some artifacts that are undesirable for room acoustic evaluation. If such artifacts can be attenuated, then the frequency-domain methods become more attractive for simulating room impulse responses. In this paper, we propose a post-processing method to attenuate the artifacts from the impulse responses computed by the combination of frequency-domain simulation and IDFT. It is formulated as a convex optimization problem, and the alternating direction method of multipliers (ADMM) is applied to obtain the solution. Numerical experiments confirmed that the proposed method can effectively reduce the undesirable artifacts from the reconstructed impulse responses. An example implementation of the proposed method in MATLAB is provided at https://doi.org/g9h5.

A Detailed FEM Study on the Vibro-acoustic Behaviour of Crash and Splash Musical Cymbals

Advanced numerical simulations, that include modal and frequency response function finite element analysis, frequency domain and time domain finite element method – boundary element method analysis, are performed to study the vibro-acoustic behaviour of crash and splash musical cymbals. The results of the modal analysis agree well with experimental measurements found in literature. The frequency domain and time domain coupled finite – boundary element method simulations, despite their high computational resources and time demands, are used for the crucial comparison of the velocity spectrograms on the cymbal to the radiated sound pressure spectrograms in the air. The computational analysis results show that the splash cymbal is characterized by a faster decay and a higher frequency content compared to the crash cymbal. The advanced multiphysics vibro-acoustic simulations that correlate the displacements and velocities of the vibrated structure with the radiated sound pressure results demonstrate the future capability to synthesize the sounds of cymbal music instruments.

Determination of methanol concentration in ethanol in liquid phase by a phononic crystal Mach-Zehnder interferometer

A practical and portable ultrasonic interferometric sensor to detect methanol concentration in ethanol in the liquid phase is numerically investigated. For high-sensitivity operation, the sensor is designed as a Mach–Zehnder interferometer based on a linear-defect waveguide in a two-dimensional phononic crystal, which consists of square array of cylindrical steel rods in water. The waveguide core comprises polyethylene tubing, impedance-matched with water, filled with either pure ethanol or ethanol-methanol binary mixture, allowing fast replacement of the analyte. Band structure analyses through the finite-element method are carried out to obtain guiding modes at frequencies around 200 kHz. With 50 × 21 cells with 4.2 mm periodicity, the total sensor area is 210-by-88.2 millimeters, which can be significantly reduced by increasing the operating frequency to megahertz range. The interferometer is constructed via T junctions of the waveguide, which facilitates low-loss equal splitting and recollection of ultrasonic waves. Sample and reference wave paths are constructed by filling polyethylene tubing on the upper and lower halves of the interferometer with the ethanol-methanol mixture and pure ethanol, respectively. Frequency-domain finite-element method simulations reveal that the sensor output is characterized by several transmission peaks, one of which is centered at 203.35 kHz with a full-width at half-maximum of 20 Hz, resulting in a quality factor of 10167. The peak frequency of this peak redshifts at a rate of 7.24 Hz per percent volume fraction change in methanol. The peak shift is linear when the methanol volume fraction is below 10%. Besides, the interferometric sensor has a figure of merit around 0.35. The proposed ultrasonic sensor offers rapid detection of methanol content in ethanol with high sensitivity.

Quantitative super-resolution solid immersion microscopy via refractive index profile reconstruction

Solid Immersion (SI) microscopy is a modern imaging modality that overcomes the Abbe diffraction limit and offers novel applications in various branches of visible, infrared, terahertz, and millimeter-wave optics. Despite the widespread use, SI microscopy usually results in qualitative imaging. Indeed, it presents only the raw distributions (in the image plane) of the backscattered field intensity, while unlocking the information about the physical properties of an imaged object, such as its complex refractive index (RI) distribution, requires resolving the inverse problem and remains a daunting task. In this paper, a method for resolving the SI microscopy inverse problem is developed, capable of reconstructing the RI distribution at the object imaging plane with subwavelength spatial resolution, while performing only intensity measurements. The sample RI is retrieved via minimization of the error function that characterizes discrepancy between the experimental data and the predictions of analytical model. This model incorporates all the key features of the electromagnetic-wave interaction with the SI lens and an imaged object, including contributions of the evanescent and ordinary-reflected waves, as well as effects of light polarization and wide beam aperture. The model is verified numerically, using the finite-element frequency-domain method, and experimentally, using the in-house reflection-mode continuous-wave terahertz SI microscope. Spatial distributions of the terahertz RIs of different low-absorbing optical materials and highly absorbing biological objects were studied and compared to a priori known data to demonstrate the potential of the novel SI microscopy modality. Given the linear nature of the Maxwell’s equations, the developed method can be applied for subwavelength-resolution SI microscopy at other spectral ranges.

Rayleigh-Bloch mode based monolayer bend waveguide

A monolayer bend waveguide is designed based on the features of Rayleigh-Bloch (RB) mode wave in one-dimensional diffraction grating. The feasibility that the RB mode wave can transmit along the bend waveguide is demonstrated by the time-domain and frequency-domain finite element method, respectively. The results show that two different modes of transmission wave exist because of employing the circled unit cells. They possess different acoustical energy localization positions. In mode-1, the energy is localized between unit cells. In mode-2, the energy is localized in the center of unit cell, therefore, acoustic wave transmits with nearly no loss. Modulated sinusoidal wave and Gaussian pulse wave are used in the time-domain investigation. Because only RB mode waves can transmit and different modes have different energy distributions, the bend waveguide acts as an acoustic filter for the broadband waves. This study is conducive to the acoustic wave directional transmission, acoustic signal detection and identification.