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Journal articles on the topic 'Time domain spectral element'

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Author: Grafiati

Published: 6 September 2023

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1

Mukherjee, Shuvajit, S. Gopalakrishnan, and Ranjan Ganguli. "Stochastic time domain spectral element analysis of beam structures." Acta Mechanica 230, no. 5 (November 12, 2018): 1487–512. http://dx.doi.org/10.1007/s00707-018-2272-6.

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2

Liu, Yaxing, Joon-Ho Lee, Tian Xiao, and Qing H. Liu. "A spectral-element time-domain solution of Maxwell's equations." Microwave and Optical Technology Letters 48, no. 4 (2006): 673–80. http://dx.doi.org/10.1002/mop.21440.

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3

Mukherjee, Shuvajit, S. Gopalakrishnan, and Ranjan Ganguli. "Time domain spectral element-based wave finite element method for periodic structures." Acta Mechanica 232, no. 6 (March 15, 2021): 2269–96. http://dx.doi.org/10.1007/s00707-020-02917-y.

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4

Fiborek, Piotr, Paweł H. Malinowski, Paweł Kudela, Tomasz Wandowski, and Wiesław M. Ostachowicz. "Time-domain spectral element method for modelling of the electromechanical impedance of disbonded composites." Journal of Intelligent Material Systems and Structures 29, no. 16 (February 27, 2018): 3214–21. http://dx.doi.org/10.1177/1045389x18758193.

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The research focuses on the electromechanical impedance method. The electromechanical impedance method can be treated as non-destructive testing or structural health monitoring approach. It is important to have a reliable tool that allows verifying the integrity of the investigated objects. The electromechanical impedance method was applied here to assess the carbon fibre–reinforced polymer samples. The single and adhesively bonded samples were investigated. In the reported research, the electromechanical impedance spectra up to 5 MHz were considered. The investigation comprised of modelling using spectral element method and experimental measurements. Numerical and experimental spectra were analysed. Differences in spectra caused by differences in considered samples were observed.

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5

Pind, Finnur, Allan P. Engsig-Karup, Cheol-Ho Jeong, Jan S. Hesthaven, Mikael S. Mejling, and Jakob Strømann-Andersen. "Time domain room acoustic simulations using the spectral element method." Journal of the Acoustical Society of America 145, no. 6 (June 2019): 3299–310. http://dx.doi.org/10.1121/1.5109396.

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6

Pranowo, Pranowo, and Djoko Budiyanto Setyohadi. "Numerical simulation of electromagnetic radiation using high-order discontinuous galerkin time domain method." International Journal of Electrical and Computer Engineering (IJECE) 9, no. 2 (April 1, 2019): 1267. http://dx.doi.org/10.11591/ijece.v9i2.pp1267-1274.

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<span>In this paper, we propose the simulation of 2-dimensional electromagnetic wave radiation using high-order discontinuous Galerkin time domain method to solve Maxwell's equations. The domains are discretized into unstructured straight-sided triangle elements that allow enhanced flexibility when dealing with complex geometries. The electric and magnetic fields are expanded into a high-order polynomial spectral approximation over each triangle element. The field conservation between the elements is enforced using central difference flux calculation at element interfaces. Perfectly matched layer (PML) boundary condition is used to absorb the waves that leave the domain. The comparison of numerical calculations is performed by the graphical displays and numerical data of radiation phenomenon and presented particularly with the results of the FDTD method. Finally, our simulations show that the proposed method can handle simulation of electromagnetic radiation with complex geometries easily.</span>

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7

Lee, Joon-Ho, and Qing Huo Liu. "A 3-D Spectral-Element Time-Domain Method for Electromagnetic Simulation." IEEE Transactions on Microwave Theory and Techniques 55, no. 5 (May 2007): 983–91. http://dx.doi.org/10.1109/tmtt.2007.895398.

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8

Sheng, YiJun, XiaoDong Ye, Gui Wang, and TianYu Lu. "Stability-Improved Spectral-Element Time-Domain Method Based on Newmark-$\beta$." IEEE Microwave and Wireless Components Letters 29, no. 4 (April 2019): 243–45. http://dx.doi.org/10.1109/lmwc.2019.2900842.

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9

Yin, Changchun, Zonghui Gao, Yang Su, Yunhe Liu, Xin Huang, Xiuyan Ren, and Bin Xiong. "3D Airborne EM Forward Modeling Based on Time-Domain Spectral Element Method." Remote Sensing 13, no. 4 (February 8, 2021): 601. http://dx.doi.org/10.3390/rs13040601.

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Airborne electromagnetic (AEM) method uses aircraft as a carrier to tow EM instruments for geophysical survey. Because of its huge amount of data, the traditional AEM data inversions take one-dimensional (1D) models. However, the underground earth is very complicated, the inversions based on 1D models can frequently deliver wrong results, so that the modeling and inversion for three-dimensional (3D) models are more practical. In order to obtain precise underground electrical structures, it is important to have a highly effective and efficient 3D forward modeling algorithm as it is the basis for EM inversions. In this paper, we use time-domain spectral element (SETD) method based on Gauss-Lobatto-Chebyshev (GLC) polynomials to develop a 3D forward algorithm for modeling the time-domain AEM responses. The spectral element method combines the flexibility of finite-element method in model discretization and the high accuracy of spectral method. Starting from the Maxwell's equations in time-domain, we derive the vector Helmholtz equation for the secondary electric field. We use the high-order GLC vector interpolation functions to perform spectral expansion of the EM field and use the Galerkin weighted residual method and the backward Euler scheme to do the space- and time-discretization to the controlling equations. After integrating the equations for all elements into a large linear equations system, we solve it by the multifrontal massively parallel solver (MUMPS) direct solver and calculate the magnetic field responses by the Faraday's law. By comparing with 1D semi-analytical solutions for a layered earth model, we validate our SETD method and analyze the influence of the mesh size and the order of interpolation functions on the accuracy of our 3D forward modeling. The numerical experiments for typical models show that applying SETD method to 3D time-domain AEM forward modeling we can achieve high accuracy by either refining the mesh or increasing the order of interpolation functions.

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10

Waszkowiak, Wiktor, Marek Krawczuk, and Magdalena Palacz. "Finite Element Approaches to Model Electromechanical, Periodic Beams." Applied Sciences 10, no. 6 (March 14, 2020): 1992. http://dx.doi.org/10.3390/app10061992.

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Periodic structures have some interesting properties, of which the most evident is the presence of band gaps in their frequency spectra. Nowadays, modern technology allows to design dedicated structures of specific features. From the literature arises that it is possible to construct active periodic structures of desired dynamic properties. It can be considered that this may extend the scope of application of such structures. Therefore, numerical research on a beam element built of periodically arranged elementary cells, with active piezoelectric elements, has been performed. The control of parameters of this structure enables one for active damping of vibrations in a specific band in the beam spectrum. For this analysis the authors propose numerical models based on the finite element method (FEM) and the spectral finite element methods defined in the frequency domain (FDSFEM) and the time domain (TDSFEM).

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11

Bao, H. G., D. Z. Ding, and R. S. Chen. "A Hybrid Spectral-Element Finite-Difference Time-Domain Method for Electromagnetic Simulation." IEEE Antennas and Wireless Propagation Letters 16 (2017): 2244–48. http://dx.doi.org/10.1109/lawp.2017.2711001.

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12

Joon-Ho Lee, Jiefu Chen, and Qing Huo Liu. "A 3-D Discontinuous Spectral Element Time-Domain Method for Maxwell's Equations." IEEE Transactions on Antennas and Propagation 57, no. 9 (September 2009): 2666–74. http://dx.doi.org/10.1109/tap.2009.2027731.

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13

Jin, Jian-Ming, Mohammad Zunoubi, Kalyan C. Donepudi, and Weng C. Chew. "Frequency-domain and time-domain finite-element solution of Maxwell's equations using spectral Lanczos decomposition method." Computer Methods in Applied Mechanics and Engineering 169, no. 3-4 (February 1999): 279–96. http://dx.doi.org/10.1016/s0045-7825(98)00158-3.

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14

Zunoubi, M., Jian-Ming Jin, and Weng Cho Chew. "Spectral Lanczos decomposition method for time domain and frequency domain finite-element solution of Maxwell's equations." Electronics Letters 34, no. 4 (1998): 346. http://dx.doi.org/10.1049/el:19980333.

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15

Liu, Xuan, Kevin Kolpatzeck, Lars Häring, Jan C. Balzer, and Andreas Czylwik. "Wideband Beam Steering Concept for Terahertz Time-Domain Spectroscopy: Theoretical Considerations." Sensors 20, no. 19 (September 28, 2020): 5568. http://dx.doi.org/10.3390/s20195568.

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Photonic true time delay beam steering on the transmitter side of terahertz time-domain spectroscopy (THz TDS) systems requires many wideband variable optical delay elements and an array of coherently driven emitters operating over a huge bandwidth. We propose driving the THz TDS system with a monolithic mode-locked laser diode (MLLD). This allows us to use integrated optical ring resonators (ORRs) whose periodic group delay spectra are aligned with the spectrum of the MLLD as variable optical delay elements. We show by simulation that a tuning range equal to one round-trip time of the MLLD is sufficient for beam steering to any elevation angle and that the loss introduced by the ORR is less than 0.1 dB. We find that the free spectral ranges (FSRs) of the ORR and the MLLD need to be matched to 0.01% so that the pulse is not significantly broadened by third-order dispersion. Furthermore, the MLLD needs to be frequency-stabilized to about 100 MHz to prevent significant phase errors in the terahertz signal. We compare different element distributions for the array and show that a distribution according to a Golomb ruler offers both reasonable directivity and no grating lobes from 50 GHz to 1 THz.

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16

Raja Sekhar, B., S. Gopalakrishnan, and MVVS Murthy. "Wave transmission characteristics for higher-order sandwich panel with flexible core using time-domain spectral element method." Journal of Sandwich Structures & Materials 19, no. 3 (December 5, 2016): 364–93. http://dx.doi.org/10.1177/1099636216664536.

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A new time-domain spectral element with nine degrees of freedom per node is formulated based on higher-order sandwich panel theory, incorporating the flexible behaviour of the core with composite face sheets. Static, free vibrations and wave propagation analysis are carried out using the formulated element. Results obtained using this element are compared with those available in the literature and with commercial finite element codes. The fast convergence of the spectral element method is demonstrated by solving the high-frequency wave propagation problem. A method of computing the wave characteristics, namely wavenumbers and group velocities, in a higher-order sandwich panel is developed using the formulated element. The effect of core damping is studied in detail with different core types, which can be used effectively in sandwich beam design.

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17

Kronowetter, Felix, Lennart Moheit, Martin Eser, Kian K. Sepahvand, and Steffen Marburg. "Spectral Stochastic Infinite Element Method in Vibroacoustics." Journal of Theoretical and Computational Acoustics 28, no. 02 (June 2020): 2050009. http://dx.doi.org/10.1142/s2591728520500097.

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A novel method to solve exterior Helmholtz problems in the case of multipole excitation and random input data is developed. The infinite element method is applied to compute the sound pressure field in the exterior fluid domain. The consideration of random input data leads to a stochastic infinite element formulation. The generalized polynomial chaos expansion of the random data results in the spectral stochastic infinite element method. As a solution technique, the non-intrusive collocation method is chosen. The performance of the spectral stochastic infinite element method is demonstrated for a time-harmonic problem and an eigenfrequency study.

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18

Xu, Kan, Rushan Chen, Yijun Sheng, Ping Fu, Chuan Chen, Qingshang Yan, and YanYan Yu. "Transient analysis of microwave Gunn oscillator using extended spectral element time domain method." Radio Science 46, no. 5 (September 15, 2011): n/a. http://dx.doi.org/10.1029/2011rs004706.

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19

Liu, Youshan, Jiwen Teng, Haiqiang Lan, Xiang Si, and Xueying Ma. "A comparative study of finite element and spectral element methods in seismic wavefield modeling." GEOPHYSICS 79, no. 2 (March 1, 2014): T91—T104. http://dx.doi.org/10.1190/geo2013-0018.1.

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The computational accuracy and efficiency of finite element method and spectral element method (SEM) are investigated thoroughly in time-domain elastic wavefield modeling. The diagonal mass matrices of the FEM and SEM free from matrix inversion are compared comprehensively by making full use of the mass-lumped technique and quadrature rules. We investigate the FEM and SEM based, respectively, on quadrilateral with the polynomials of degrees one and two, and on triangular grids with the polynomials of degrees one and three. Generally, the numerical solutions based on quadrilateral grids have a higher precision than those computed on triangular grids when the same order of polynomials is used. The FEM has a comparable accuracy to the SEM with the same number of interpolant points. In view of the triangular and quadrilateral SEMs, the former suffers from larger computational costs and relatively lower accuracy compared with the latter. Furthermore, the convergence study proves that the triangular SEM produces consistently larger errors than the quadrilateral SEM for any order and element sizes. However, the triangular SEM can adapt to arbitrary complex geometries effectively. In terms of efficiency, the FEM has an efficiency comparable with the SEM on condition that the order of interpolation polynomials is identical. In addition, a perfectly matched layer (PML) boundary condition in variational form is deduced. By introducing four intermediate variables in frequency domain, the PML avoids convolution calculation and obtains an exact solution through inverse Fourier transform in time domain. The numerical examples verify the validity and effectiveness of the PML.

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20

Zunoubi, M. R., K. C. Donepudi, Jian-Ming Jin, and Weng Cho Chew. "Efficient time-domain and frequency-domain finite-element solution of Maxwell's equations using spectral Lanczos decomposition method." IEEE Transactions on Microwave Theory and Techniques 46, no. 8 (1998): 1141–49. http://dx.doi.org/10.1109/22.704957.

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21

Huang, Xin, Changchun Yin, Colin G. Farquharson, Xiaoyue Cao, Bo Zhang, Wei Huang, and Jing Cai. "Spectral-element method with arbitrary hexahedron meshes for time-domain 3D airborne electromagnetic forward modeling." GEOPHYSICS 84, no. 1 (January 1, 2019): E37—E46. http://dx.doi.org/10.1190/geo2018-0231.1.

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Mainstream numerical methods for 3D time-domain airborne electromagnetic (AEM) modeling, such as the finite-difference (FDTD) or finite-element (FETD) methods, are quite mature. However, these methods have limitations in terms of their ability to handle complex geologic structures and their dependence on quality meshing of the earth model. We have developed a time-domain spectral-element (SETD) method based on the mixed-order spectral-element (SE) approach for space discretization and the backward Euler (BE) approach for time discretization. The mixed-order SE approach can contribute an accurate result by increasing the order of polynomials and suppress spurious solutions. The BE method is an unconditionally stable technique without limitations on time steps. To deal with the rapid variation of the fields close to the AEM transmitting loop, we separate a secondary field from the primary field and simulate the secondary field only, for which the primary field is calculated in advance. To obtain a block diagonal mass matrix and hence minimize the number of nonzero elements in the system of equations to be solved, we apply Gauss-Lobatto-Legendre integral techniques of reduced order. A direct solver is then adopted for the system of equations, which allows for efficient treatment of the multiple AEM sources. To check the accuracy of our SETD algorithm, we compare our results with the semianalytical solution for a layered earth model. Then, we analyze the modeling accuracy and efficiency for different 3D models using deformed physical meshes and compare them against results from 3D FETD codes, to further show the flexibility of SETD for AEM forward modeling.

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22

Kudela, P., and W. Ostachowicz. "3D time-domain spectral elements for stress waves modelling." Journal of Physics: Conference Series 181 (August 1, 2009): 012091. http://dx.doi.org/10.1088/1742-6596/181/1/012091.

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23

Hesthaven, J. S., P. G. Dinesen, and J. P. Lynov. "Spectral Collocation Time-Domain Modeling of Diffractive Optical Elements." Journal of Computational Physics 155, no. 2 (November 1999): 287–306. http://dx.doi.org/10.1006/jcph.1999.6333.

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24

Schulte, Rolf T., Ke Jia Xing, and Claus Peter Fritzen. "Spectral Element Modelling of Wave Propagation and Impedance Based SHM Systems." Key Engineering Materials 413-414 (June 2009): 683–90. http://dx.doi.org/10.4028/www.scientific.net/kem.413-414.683.

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In recent years many SHM approaches based on elastic waves that are generated and sensed by surface-bonded piezoelectric patches have been developed. Some of those utilize wave propagation phenomena; others use changes in the electromechanical impedance to detect structural damage. The capability of most approaches strongly depends on adequate choice of SHM system parameters like excitation signals and actuator/sensor types and positions. For this reason there is a growing interest in efficient and accurate simulation tools to shorten time and cost of the necessary tedious pretests. To detect small damage generally high frequency excitation signals have to be used. Because of this a very dense finite element mesh is required for an accurate simulation. As a consequence a conventional finite element simulation becomes computationally inefficient. A new approach that seems to be more promising is the time domain spectral element method. This contribution presents the theoretical background and some results of numerical calculations of the propagation of waves. The simulation is performed using the spectral element method (SEM), which leads to a diagonal mass matrix. Besides a significant saving of memory this leads to a crucial reduction of complexity of the time integration algorithm for the wave propagation calculation. A new approach to simulate the E/M impedance using time domain spectral elements is shown. An example demonstrates a good correlation of simulation and measurement data, so that the proposed simulation methodology seems to be a promising tool to make impedance based SHM systems more efficient, especially regarding the necessary parameter studies.

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25

Galanopoulos, Anastasios, Finnur Pind, Hermes Sampedro Llopis, and Cheol-Ho Jeong. "Binaural reproduction of time-domain spectral element method simulations using spherical harmonic spatial encoding." Journal of the Acoustical Society of America 149, no. 4 (April 2021): A20—A21. http://dx.doi.org/10.1121/10.0004403.

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26

Yu, Zexing, Seyed Hossein Mahdavi, and Chao Xu. "Time-domain Spectral Element Method for Impact Identification of Frame Structures using Enhanced GAs." KSCE Journal of Civil Engineering 23, no. 2 (December 17, 2018): 678–90. http://dx.doi.org/10.1007/s12205-018-0478-8.

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27

Kudela, Paweł, Arkadiusz Żak, Marek Krawczuk, and Wiesław Ostachowicz. "Modelling of wave propagation in composite plates using the time domain spectral element method." Journal of Sound and Vibration 302, no. 4-5 (May 2007): 728–45. http://dx.doi.org/10.1016/j.jsv.2006.12.016.

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28

Sun, Qingtao, Runren Zhang, Qiwei Zhan, and Qing Huo Liu. "3-D Implicit–Explicit Hybrid Finite Difference/Spectral Element/Finite Element Time Domain Method Without a Buffer Zone." IEEE Transactions on Antennas and Propagation 67, no. 8 (August 2019): 5469–76. http://dx.doi.org/10.1109/tap.2019.2913740.

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29

Kim, Taehyun, and Usik Lee. "Vibration Analysis of Thin Plate Structures Subjected to a Moving Force Using Frequency-Domain Spectral Element Method." Shock and Vibration 2018 (September 24, 2018): 1–27. http://dx.doi.org/10.1155/2018/1908508.

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A frequency-domain spectral element method (SEM) is proposed for the vibration analysis of thin plate structures subjected to a moving point force. The thin plate structures may consist of multiple rectangular thin plates with arbitrary boundary conditions that form multispan thin plate structures, such as bridges. The time-domain point force moving on a thin rectangular plate with arbitrary trajectory is transformed into a series of stationary point forces in the frequency domain. The vibration responses induced by the moving point force are then obtained by superposing all vibration responses excited by each stationary point force. For the vibration response of a specific stationary point force, the plate subjected to the specific stationary point force is represented by four spectral finite plate elements, which were developed in the authors’ previous work. The SEM-based vibration analysis technique is first presented for single-span thin plate structures and then extended to the multispan thin plate structures. The high accuracy and computational efficiency of the proposed SEM-based vibration analysis technique are verified by comparison with other well-known solution methods, such as the exact theory, integral transform method, finite element method, and the commercial finite element analysis package ANSYS.

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30

Kang, Hyun-Gyu, and Hyeong-Bin Cheong. "Effect of a High-Order Filter on a Cubed-Sphere Spectral Element Dynamical Core." Monthly Weather Review 146, no. 7 (June 29, 2018): 2047–64. http://dx.doi.org/10.1175/mwr-d-17-0226.1.

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Abstract A high-order filter for a cubed-sphere spectral element model was implemented in a three-dimensional spectral element dry hydrostatic dynamical core. The dynamical core incorporated hybrid sigma–pressure vertical coordinates and a third-order Runge–Kutta time-differencing method. The global high-order filter and the local-domain high-order filter, requiring numerical operation with a huge sparse global matrix and a locally assembled matrix, respectively, were applied to the prognostic variables, except for surface pressure, at every time step. Performance of the high-order filter was evaluated using the baroclinic instability test and quiescent atmosphere with underlying topography test presented by the Dynamical Core Model Intercomparison Project. It was revealed that both the global and local-domain high-order filters could better control the numerical noise in the noisy circumstances than the explicit diffusion, which is widely used for the spectral element dynamical core. Furthermore, by adopting the high-order filter, the effective resolution of the dynamical core could be increased, without weakening the stability of the dynamical core. Computational efficiency of the high-order filter was demonstrated in terms of both the time step size and the wall-clock time. Because of the nature of an implicit diffusion, the dynamical core employing this filter can take a larger time step size, compared to that using the explicit diffusion. The local-domain high-order filter was computationally more efficient than the global high-order filter, but less efficient than the explicit diffusion.

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31

Chen, Lizhen, and Chuanju Xu. "A Time Splitting Space Spectral Element Method for the Cahn-Hilliard Equation." East Asian Journal on Applied Mathematics 3, no. 4 (November 2013): 333–51. http://dx.doi.org/10.4208/eajam.150713.181113a.

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AbstractWe propose and analyse a class of fully discrete schemes for the Cahn-Hilliard equation with Neumann boundary conditions. The schemes combine large-time step splitting methods in time and spectral element methods in space. We are particularly interested in analysing a class of methods that split the original Cahn-Hilliard equation into lower order equations. These lower order equations are simpler and less computationally expensive to treat. For the first-order splitting scheme, the stability and convergence properties are investigated based on an energy method. It is proven that both semi-discrete and fully discrete solutions satisfy the energy dissipation and mass conservation properties hidden in the associated continuous problem. A rigorous error estimate, together with numerical confirmation, is provided. Although not yet rigorously proven, higher-order schemes are also constructed and tested by a series of numerical examples. Finally, the proposed schemes are applied to the phase field simulation in a complex domain, and some interesting simulation results are obtained.

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32

Bi, Guo, Jin Chen, Jun He, Fuchang Zhou, and Gui Cai Zhang. "Application of Degree of Cyclostationarity in Rolling Element Bearing Diagnosis." Key Engineering Materials 293-294 (September 2005): 347–54. http://dx.doi.org/10.4028/www.scientific.net/kem.293-294.347.

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Minor and random slip between rolling elements and races in rolling element bearings makes vibration signals have periodically time-varying ensemble statistics, which is known as cyclostationarity. Two second-order cyclostationary methods, the spectral correlation density (SCD) and the degree of cyclostationarity (DCS), are talked about in this paper based on a statistical model of rolling element bearings. The SCD provides redundant information in bi-frequency plane and cyclic frequency domain embodies the majority of it, which is a series of non-zero discrete cyclic frequencies completely reflecting the fault characters of rolling element bearings. The DCS has virtues of less computation and clearer representation, at the same time keeps the same characters with SCD in cyclic frequency domain. And the DCS is also proved to be resistant to the additive and multiplicative stationary noise. Simulation and experiential results from three rolling element bearing faults: outer race defect, inner race defect and rolling element defect, indicate practicability of the DCS analysis in rolling element bearing condition monitoring and fault diagnosis.

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33

Dirlik, Turan, and Denis Benasciutti. "Dirlik and Tovo-Benasciutti Spectral Methods in Vibration Fatigue: A Review with a Historical Perspective." Metals 11, no. 9 (August 24, 2021): 1333. http://dx.doi.org/10.3390/met11091333.

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The frequency domain techniques (also known as “spectral methods”) prove significantly more efficient than the time domain fatigue life calculations, especially when they are used in conjunction with finite element analysis. Frequency domain methods are now well established, and suitable commercial software is commonly available. Among the existing techniques, the methods by Dirlik and by Tovo–Benasciutti (TB) have become the most used. This study presents the historical background and the motivation behind the development of these two spectral methods, by also emphasizing their application and possible limitations. It further presents a brief review of the other spectral methods available for cycle counting directly from the power spectral density of the random loading. Finally, some ideas for future work are suggested.

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34

Jiefu Chen, Joon-Ho Lee, and Qing Huo Liu. "A High-Precision Integration Scheme for the Spectral-Element Time-Domain Method in Electromagnetic Simulation." IEEE Transactions on Antennas and Propagation 57, no. 10 (October 2009): 3223–31. http://dx.doi.org/10.1109/tap.2009.2028633.

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35

Kim, Yujun, Sungwon Ha, and Fu-Kuo Chang. "Time-Domain Spectral Element Method for Built-In Piezoelectric-Actuator-Induced Lamb Wave Propagation Analysis." AIAA Journal 46, no. 3 (March 2008): 591–600. http://dx.doi.org/10.2514/1.27046.

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36

Ostachowicz, W., and P. Kudela. "Wave propagation numerical models in damage detection based on the time domain spectral element method." IOP Conference Series: Materials Science and Engineering 10 (June 1, 2010): 012068. http://dx.doi.org/10.1088/1757-899x/10/1/012068.

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37

Bottero, Alexis, Paul Cristini, Dimitri Komatitsch, and Mark Asch. "An axisymmetric time-domain spectral-element method for full-wave simulations: Application to ocean acoustics." Journal of the Acoustical Society of America 140, no. 5 (November 2016): 3520–30. http://dx.doi.org/10.1121/1.4965964.

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38

Sheng, Yijun, Kan Xu, Daoxiang Wang, and Rushan Chen. "Performance analysis of FET microwave devices by use of extended spectral-element time-domain method." International Journal of Electronics 100, no. 5 (May 2013): 699–717. http://dx.doi.org/10.1080/00207217.2012.720947.

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39

Yu, Zexing, Chao Xu, Fei Du, Shancheng Cao, and Liangxian Gu. "Time-domain Spectral Finite Element Method for Wave Propagation Analysis in Structures with Breathing Cracks." Acta Mechanica Solida Sinica 33, no. 6 (June 3, 2020): 812–22. http://dx.doi.org/10.1007/s10338-020-00170-3.

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40

Rizzi, S. A., and J. F. Doyle. "A Spectral Element Approach to Wave Motion in Layered Solids." Journal of Vibration and Acoustics 114, no. 4 (October 1, 1992): 569–77. http://dx.doi.org/10.1115/1.2930300.

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A matrix methodology similar to that of the finite element method is developed for the analysis of stress waves in layered solids. Because the mass distribution is modeled exactly, the approach gives the exact frequency response of each layer. The fast Fourier transform and Fourier series are used for inversion to the time/space domain. The impact of a structured medium with multiple layers is used to demonstrate the method. Comparison with existing propagator and direct global matrix methods show the present approach to be computationally more efficient.

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Luo, Zhengbo, Huaihai Chen, Xudong He, and Ronghui Zheng. "Two time domain models for fatigue life prediction under multiaxial random vibrations." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 233, no. 13 (February 7, 2019): 4707–18. http://dx.doi.org/10.1177/0954406219827038.

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Two time domain models for fatigue life prediction under multiaxial random vibrations are developed on the basis of the critical plane approach. Firstly, the stress power spectral density matrix of each node at the notch root of the test specimen is obtained by the random vibration analysis with finite element method, and the stress time-histories are generated from the stress power spectral density matrix by the time domain randomization approach. Then, the fatigue life of each node is predicted based on the damage on the critical plane, where the cumulative damage value is the greatest. The minimum fatigue life of all nodes at the notch root is considered as the fatigue life of the test specimen. Finally, the proposed models are validated by the multiaxial random vibration fatigue test with the 6061-T4 aluminum alloy. The results show that the predicted fatigue lives and predicted crack orientation angles are in good agreement with the experimental fatigue lives and experimentally observed crack orientation angles, respectively.

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Smallwood, David O., and Thomas L. Paez. "A Frequency Domain Method for the Generation of Partially Coherent Normal Stationary Time Domain Signals." Shock and Vibration 1, no. 1 (1993): 45–53. http://dx.doi.org/10.1155/1993/537658.

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A procedure for generating vectors of time domain signals that are partially coherent in a prescribed manner is described. The procedure starts with the spectral density matrix,[Gxx(f)], that relates pairs of elements of the vector random process{X(t)},−∞<t<∞. The spectral density matrix is decomposed into the form[Gxx(f)]=[U(f)][S(f)][U(f)]'where[U(f)]is a matrix of complex frequency response functions, and[S(f)]is a diagonal matrix of real functions that can vary with frequency. The factors of the spectral density matrix,[U(f)]and[S(f)], are then used to generate a frame of random data in the frequency domain. The data is transformed into the time domain using an inverse FFT to generate a frame of data in the time domain. Successive frames of data are then windowed, overlapped, and added to form a vector of normal stationary sampled time histories,{X(t)}, of arbitrary length.

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Rekatsinas, Christoforos S., and Dimitris A. Saravanos. "A time domain spectral layerwise finite element for wave structural health monitoring in composite strips with physically modeled active piezoelectric actuators and sensors." Journal of Intelligent Material Systems and Structures 28, no. 4 (July 28, 2016): 488–506. http://dx.doi.org/10.1177/1045389x16649700.

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A new explicit, two-dimensional plane strain, time domain spectral finite element is developed to enhance the simulation of guided waves generated by active piezoelectric sensors in laminated composite strips. A new multi-field layerwise theory is formulated for composite laminates with piezoelectric actuators and sensors which captures straight-crested symmetric and anti-symmetric Lamb waves. Third-order Hermite polynomial splines are employed for the approximation of displacements and electric potential through the thickness, and the piezoelectric actuators and sensors are physically modeled through coupled electromechanical governing equations. A multi-node finite element formulation is presented entailing displacement and electric degrees of freedom at nodes collocated with Gauss–Lobatto–Legendre integration points. Stiffness, diagonal mass, piezoelectric, and electric permittivity matrices are described, and the coupled transient electromechanical response is predicted by a properly formulated explicit time integration scheme. The numerical results of a nine-node time domain spectral finite element are correlated with the reported numerical results and with measured Lamb wave data generated by piezoceramic active sensor pairs in carbon/epoxy plate strips. Important effects introduced by the stiffness and mass of the active actuator/sensor system on Lamb wave propagation are captured by the developed finite element and quantified.

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Kulkarni, Raghavendra B., S. Gopalakrishnan, and Manish Trikha. "Impact force identification in structures using time-domain spectral finite elements." Acta Mechanica 231, no. 11 (August 12, 2020): 4513–28. http://dx.doi.org/10.1007/s00707-020-02775-8.

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Chen, Shitao, Dazhi Ding, and Rushan Chen. "A Hybrid Volume–Surface Integral Spectral-Element Time-Domain Method for Nonlinear Analysis of Microwave Circuit." IEEE Antennas and Wireless Propagation Letters 16 (2017): 3034–37. http://dx.doi.org/10.1109/lawp.2017.2759147.

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Sharma, Himanshu, Shuvajit Mukherjee, and Ranjan Ganguli. "Uncertainty analysis of higher-order sandwich beam using a hybrid stochastic time-domain spectral element method." International Journal for Computational Methods in Engineering Science and Mechanics 21, no. 5 (August 19, 2020): 215–30. http://dx.doi.org/10.1080/15502287.2020.1808912.

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Qian, Cheng, Dazhi Ding, Zhenhong Fan, and Rushan Chen. "A fluid model simulation of a simplified plasma limiter based on spectral-element time-domain method." Physics of Plasmas 22, no. 3 (March 2015): 032111. http://dx.doi.org/10.1063/1.4916055.

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Zakian, P., and N. Khaji. "A novel stochastic-spectral finite element method for analysis of elastodynamic problems in the time domain." Meccanica 51, no. 4 (July 24, 2015): 893–920. http://dx.doi.org/10.1007/s11012-015-0242-9.

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Mokhtari, Ali, Hamid Reza Mirdamadi, Mostafa Ghayour, and Vahid Sarvestan. "Time/wave domain analysis for axially moving pre-stressed nanobeam by wavelet-based spectral element method." International Journal of Mechanical Sciences 105 (January 2016): 58–69. http://dx.doi.org/10.1016/j.ijmecsci.2015.11.006.

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Borrel-Jensen, Nikolas, Allan Peter Engsig-Karup, Maarten Hornikx, and Cheol-Ho Jeong. "Accelerated sound propagation using an error-free Fourier method coupled with the spectral-element method." INTER-NOISE and NOISE-CON Congress and Conference Proceedings 265, no. 5 (February 1, 2023): 2731–42. http://dx.doi.org/10.3397/in_2022_0383.

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Simulating acoustics using numerical methods efficiently and accurately has been an active research area for the last decades and has applications in computer games, VR/AR, and architectural design. However, their extensive computation time makes these methods challenging for large scenes and broad frequency ranges. This work attempts to accelerate the simulations using rectangular decomposition, enabling error-free propagation in the bulk of the domain consisting of air. We exploit the analytical solution to the wave equation calculated using the Fast Fourier Transform with near-optimal spatial and temporal discretizations satisfying the Nyquist criterium. Coupling with the spectral-element method near the boundaries results in a method capable of handling complex geometries with realistic boundaries, though with the caveat that additional errors and computational overhead may result from the interface. This talk will investigate the accuracy and efficiency of the proposed domain decomposition method compared to a spectral-element method running in the entire domain.

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