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Journal articles on the topic 'Laplace and Fourier transforms'

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Published: 4 June 2021
Last updated: 30 January 2023

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1

Corinthios, Michael J. "New Laplace, z and Fourier-related transforms." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 463, no. 2081 (February 6, 2007): 1179–98. http://dx.doi.org/10.1098/rspa.2007.1814.

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In this paper, the author uses his recently proposed complex variable generalized distribution theory to expand the domains of existence of bilateral Laplace and z transforms, as well as a whole new class of related transforms. A vast expansion of the domains of existence of bilateral Laplace and z transforms and continuous-time and discrete-time Hilbert, Hartley and Mellin transforms, as well as transforms of multidimensional functions and sequences are obtained. It is noted that the Fourier transform and its applications have advanced by leaps and bounds during the last century, thanks to the introduction of the theory of distributions and, in particular, the concept of the Dirac-delta impulse. Meanwhile, however, the truly two-sided ‘bilateral’ Laplace and z transforms, which are more general than Fourier, remained at a standstill incapable of transforming the most basic of functions. In fact, they were reduced by half to one-sided transforms and received no more than a passing reference in the literature. It is shown that the newly proposed generalized distributions expand the domains of existence and application of Laplace and z transforms similar to and even more extensively than the expansion of the domain of Fourier transform that resulted from the introduction, nearly a century ago, of the theory of distributions and the Dirac-delta impulse. It is also shown that the new generalized distributions put an end to an anomaly that still exists today, which meant that for a large class of basic functions, the Fourier transform exists while the more general Laplace and z transforms do not. The anomaly further manifests itself in the fact that even for the one-sided causal functions, such as the Heaviside unit step function u ( t ) and the sinusoid sin βtu ( t ), the Laplace transform does not exist on the j ω -axis, and the Fourier transform which does exist cannot be deduced thereof by the substitution s =j ω in the Laplace transform, which by definition it should. The extended generalized transforms are well defined for a large class of functions ranging from the most basic to highly complex fast-rising exponential ones that have so far had no transform. Among basic applications, the solution of partial differential equations using the extended generalized transforms is provided. This paper clearly presents and articulates the significant impact of extending the domains of Laplace and z transforms on a large family of related transforms, after nearly a century during which bilateral Laplace and z transforms of even the most basic of functions were undefined, and the domains of definition of related transforms such as Hilbert, Hartley and Mellin transforms were confined to a fraction of the space they can now occupy.
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2

Saberi-Nadjafi, Jafar. "A Computational Method for n-Dimensional Laplace Transforms Involved with Fourier Cosine Transform." ISRN Applied Mathematics 2013 (August 28, 2013): 1–4. http://dx.doi.org/10.1155/2013/748417.

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In 2007, the author published some results on n-dimensional Laplace transform involved with the Fourier sine transform. In this paper, we propose some new result in n-dimensional Laplace transforms involved with Fourier cosine transform; these results provide few algorithms for evaluating some n-dimensional Laplace transform pairs. In addition, some examples are also presented, which explain the useful applications of the obtained results. Therefore, one can produce some two- and three- as well as n-dimensional Laplace transforms pairs.
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3

Salamat, Kaushef, and Nousheen Ilyas. "DUALITIES BETWEEN FOURIER SINE AND SOME USEFUL INTEGRAL TRANSFORMATIONS." Journal of Mathematical Sciences & Computational Mathematics 2, no. 4 (July 5, 2021): 542–63. http://dx.doi.org/10.15864/jmscm.2408.

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The most useful technique of the mathematics which are used to finding the solutions of a lot of problems just like bending of beam, electrical network, heat related problems, which occurs in many disciplines of engineering and sciences are the techniques of integral transforms. In our research I discussed the duality between Fourier Sine transforms and some others effective integral transforms (namely Laplace transform, Mahgoub transform, Aboodh transform and Mohand transform). To justify the scope of dualities relation between Fourier Sine transform and other integral transforms (that are mentioned above, I presented the tabular representation of integral transform (namely Laplace transform, Aboodh transform, Mohand transform and Mahgoub transform) of various used functions by using Fourier Sine and other integral transforms dualities relation to signify fruitfulness of such connections. Results showed that these integral transform are strongly related with Fourier Sine transform.
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4

Fitzsimmons, Patrick, and Tucker McElroy. "On Joint Fourier–Laplace Transforms." Communications in Statistics - Theory and Methods 39, no. 10 (May 12, 2010): 1883–85. http://dx.doi.org/10.1080/03610920902923502.

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5

Kaneta, H. "Fourier-Laplace transforms decaying exponentially." Mathematical Proceedings of the Cambridge Philosophical Society 103, no. 2 (March 1988): 321–22. http://dx.doi.org/10.1017/s0305004100064896.

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Let ƒ(x) be a C-valued function which is integrable with respect to a positive measure m on the Borel σ-field of R = (– ∞, ∞). We shall give necessary and sufficient conditions under which the following Fourier-Laplace transform f(λ) of ƒ(x) decays exponentially as λ → ∞:where θ is a constant with –π/2 ≤ θ ≤ π/2.
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6

Bhandari, Piyush Kumar, and Sushil Kumar Bissu. "Inequalities for some classical integral transforms." Tamkang Journal of Mathematics 47, no. 3 (September 30, 2016): 351–56. http://dx.doi.org/10.5556/j.tkjm.47.2016.1981.

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By using a form of the Cauchy-Bunyakovsky-Schwarz inequality, we establish new inequalities for some classical integral transforms such as Laplace transform,Fourier transform, Fourier cosine transform, Fourier sine transform, Mellin transform and Hankel transform.
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7

Lima, Fátima D. P., Jorge M. A. Garcia, and Alfredo D. Egídio Dos Reis. "Fourier/Laplace Transforms and Ruin Probabilities." ASTIN Bulletin 32, no. 1 (May 2002): 91–105. http://dx.doi.org/10.2143/ast.32.1.1017.

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AbstractIn this paper we use Fourier/Laplace transforms to evaluate numerically relevant probabilities in ruin theory as an application to insurance. The transform of a function is split in two: the real and the imaginary parts. We use an inversion formula based on the real part only, to get the original function.By using an appropriate algorithm to compute integrals and making use of the properties of these transforms we are able to compute numerically important quantities either in classical or non-classical ruin theory. As far as the classical model is concerned the problems considered have been widely studied. In what concerns the non-classical model, in particular models based on more general renewal risk processes, there is still a long way to go. In either case the approach presented is an easy method giving good approximations for reasonable values of the initial surplus.To show this we compute numerically ruin probabilities in the classical model and in a renewal risk process in which claim inter-arrival times have an Erlang(2) distribution and compare to exact figures where available. We also consider the computation of the probability and severity of ruin in the classical model.
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8

Xuan Thao, Nguyen, Vu Kim Tuan, Le Xuan Huy, and Nguyen Thanh Hong. "On the Fourier–Laplace convolution transforms." Integral Transforms and Special Functions 26, no. 4 (January 28, 2015): 303–13. http://dx.doi.org/10.1080/10652469.2014.1002781.

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9

Lee, S. L. "Fourier–Laplace transforms and orthogonal polynomials." Journal of Approximation Theory 256 (August 2020): 105436. http://dx.doi.org/10.1016/j.jat.2020.105436.

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10

Dimitrov, Dimitar K., and Yuan Xu. "Wronskians of Fourier and Laplace transforms." Transactions of the American Mathematical Society 372, no. 6 (June 3, 2019): 4107–25. http://dx.doi.org/10.1090/tran/7809.

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11

Grubb, Daniel J. "Ranges of joint Laplace-Fourier transforms." Proceedings of the American Mathematical Society 97, no. 2 (February 1, 1986): 372. http://dx.doi.org/10.1090/s0002-9939-1986-0835901-6.

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12

Khudair, Ayad R. "Random Fractional Laplace Transform for Solving Random Time-Fractional Heat Equation in an Infinite Medium." BASRA JOURNAL OF SCIENCE 38, no. 2 (April 1, 2020): 223–47. http://dx.doi.org/10.29072/basjs.202025.

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The random Laplace and Fourier transforms are very important tools to solve random heat problems. Unfortunately, it is difficult to use these random integral transforms for solving the fractional random heat problems, where the mean square conformable fractional derivative is used to express for the time fractional derivative. Therefore, this work adopts the extension of the random Laplace transform into random fractional Laplace transform in order to solve this kind of heat problems. The stochastic process solution of the fractional random heat in an infinite medium is investigated by using random fractional Laplace transform together with random Fourier transform. The mean and the standard diffusion of the stochastic process solution is computed for different value of fractional order. When α = 1, the results show agree with the available results in the references context.
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13

Povstenko, Yuriy, and Joanna Klekot. "Time-Fractional Heat Conduction in Two Joint Half-Planes." Symmetry 11, no. 6 (June 16, 2019): 800. http://dx.doi.org/10.3390/sym11060800.

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The heat conduction equations with Caputo fractional derivative are considered in two joint half-planes under the conditions of perfect thermal contact. The fundamental solution to the Cauchy problem as well as the fundamental solution to the source problem are examined. The Fourier and Laplace transforms are employed. The Fourier transforms are inverted analytically, whereas the Laplace transform is inverted numerically using the Gaver–Stehfest method. We give a graphical representation of the numerical results.
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14

Singh, Gavendra, Varun Gupta, Shekhar Pundir, and Shobhit Sharma. "An Interesting Difference between Fourier Transform & Laplace Transform." Advanced Materials Research 403-408 (November 2011): 114–19. http://dx.doi.org/10.4028/www.scientific.net/amr.403-408.114.

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Many authors have been found the difference between Fourier Transform & Laplace Transform. In this paper we are highlighting the major or you can say interesting difference between Fourier Transform & Laplace Transform . If we look on the step signal , we will found that there will be interesting difference among these two transforms. In this paper we are giving the interesting reason behind this.
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15

Aghili, Arman. "New trends in Laplace type integral transforms with applications." Boletim da Sociedade Paranaense de Matemática 35, no. 1 (October 26, 2017): 173. http://dx.doi.org/10.5269/bspm.v35i1.28645.

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AbstractIn this paper, the authors provided a discussion on one and two dimensional Laplace transforms and generalized Stieltjes transform and their applications in evaluating special series and integrals. Finally, we implemented the joint Laplace – Fourier transforms to construct exact solution for a variant of the Kd.V equation. Illustrative examples are also provided.
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16

Ciulla, Carlo. "Theory and Applications of Fourier, Laplace, and Z Transformations." Journal of CIEES 2, no. 1 (July 26, 2022): 32–43. http://dx.doi.org/10.48149/jciees.2022.2.1.6.

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This study presents the mathematics for the implementation of direct and inverse Fourier, Laplace, and Z transformations. This research is at the intersection between signal processing, applied mathematics, and software engineering, and it provides a study guide to implementers. Mathematical concepts and details necessary to transform the math into code are provided as theoretical background. Validation is conducted for the cases when the transforms do intersect, when the transforms do not intersect, and when, in Fourier and Z-transformations, the frequency domain encodes a phase shift which is reconstructed as an image space shift. Coherence between the software implementation of the three transformations is confirmed when: 1. The real component of the complex variable s = σ + i ω is σ = 0, which is the case when Fourier and Laplace transforms are the same. 2. When the magnitude of the complex variable z = r e jω is r = 1, which is the case when Fourier and Z transforms are the same. Congruency between software implementation of transformations is confirmed comparing departing image and inverse reconstructed image. The novelty of this research is the presentation style of the theory of direct and inverse Fourier, Laplace, and Z transforms. Details provided in this research make this paper a study guide that is not found elsewhere.
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17

Pavlov, A. V. "The Fourier transform and an inversion formula for Laplace transforms." Mathematical Notes 90, no. 5-6 (December 2011): 775–79. http://dx.doi.org/10.1134/s0001434611110174.

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18

Sharma, M. D., and S. Nain. "Numerical evaluation of inverse integral transforms: Dynamic response of elastic materials." International Journal of Engineering, Science and Technology 12, no. 2 (June 1, 2020): 29–34. http://dx.doi.org/10.4314/ijest.v12i2.4.

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This study discusses the use of numerical integration in evaluating the improper integrals appearing as inverse integral transforms of non-analytic functions. These transforms appear while studying the response of various sources in an elastic medium through integral transform method. In these studies, the inverse Fourier transforms are solved numerically without bothering about the singularities and branch points in the corresponding integrands. References on numerical integration cited in relevant papers do not support such an evaluation but suggest contrary. Approximation of inverse Laplace transform integral into a series is used without following the essential restrictions and assumptions. Volume of the published papers using these dubious procedures has reached to an alarming level. The discussion presented aims to draw the attention of researchers as well as journals so as to stop this menace at the earliest possible.Keywords: Inverse Fourier transforms, inverse Laplace transforms, Romberg integration, improper integral, elastic waves
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19

Saitoh, Saburou. "Fourier-Laplace transforms and the Bergman spaces." Proceedings of the American Mathematical Society 102, no. 4 (April 1, 1988): 985. http://dx.doi.org/10.1090/s0002-9939-1988-0934879-6.

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20

Onural, L., M. F. Erden, and H. M. Ozaktas. "Extensions to common Laplace and Fourier transforms." IEEE Signal Processing Letters 4, no. 11 (November 1997): 310–12. http://dx.doi.org/10.1109/97.641396.

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21

Gzyl, Henryk. "Maxentropic reconstruction of Fourier and Laplace transforms." Applied Mathematics and Computation 73, no. 2-3 (December 1995): 181–89. http://dx.doi.org/10.1016/0096-3003(94)00248-7.

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22

HO, KWOK-PUN. "FOURIER-TYPE TRANSFORMS ON REARRANGEMENT-INVARIANT QUASI-BANACH FUNCTION SPACES." Glasgow Mathematical Journal 61, no. 1 (June 20, 2018): 231–48. http://dx.doi.org/10.1017/s0017089518000186.

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AbstractWe establish the mapping properties of Fourier-type transforms on rearrangement-invariant quasi-Banach function spaces. In particular, we have the mapping properties of the Laplace transform, the Hankel transforms, the Kontorovich-Lebedev transform and some oscillatory integral operators. We achieve these mapping properties by using an interpolation functor that can explicitly generate a given rearrangement-invariant quasi-Banach function space via Lebesgue spaces.
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23

Youssef, Hamdy M., Mowffaq Oreijah, and Hunaydi S. Alsharif. "Three-dimensional generalized thermoelasticity with variable thermal conductivity." International Journal of Computational Materials Science and Engineering 09, no. 01 (March 2020): 2050002. http://dx.doi.org/10.1142/s2047684120500025.

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In this paper, a three-dimensional model of the generalized thermoelasticity with one relaxation time and variable thermal conductivity is constructed. The resulting nondimensional governing equations, together with the Laplace and double Fourier transform techniques have been applied to a three-dimensional half-space subjected to thermal loading with rectangular pulse and traction free surface. The inverses of double Fourier transforms and Laplace transforms have been obtained numerically. Numerical results for the temperature increment, the invariant stress, the invariant strain, and the displacement are represented graphically. The variability of thermal conductivity has significant effects on all the studied fields.
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24

Huang, F. "Analytical Solution for the Time-Fractional Telegraph Equation." Journal of Applied Mathematics 2009 (2009): 1–9. http://dx.doi.org/10.1155/2009/890158.

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We discuss and derive the analytical solution for three basic problems of the so-called time-fractional telegraph equation. The Cauchy and Signaling problems are solved by means of juxtaposition of transforms of the Laplace and Fourier transforms in variabletandx,respectively. the appropriate structures and negative prosperities for their Green functions are provided. The boundary problem in a bounded space domain is also solved by the spatial Sine transform and temporal Laplace transform, whose solution is given in the form of a series.
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25

Ezzat, Magdy A., and Hamdy M. Youssef. "Stokes’ first problem for an electro-conducting micropolar fluid with thermoelectric properties." Canadian Journal of Physics 88, no. 1 (January 2010): 35–48. http://dx.doi.org/10.1139/p09-100.

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This work is related to the flow of an electro-conducting micropolar fluid presenting thermoelectric properties effect in the presence of a magnetic field. The electro-conducting thermofluid equation of heat transfer with one relaxation time is derived. The flow of an electro-conducting micropolar fluid over a plate that is moved suddenly is considered. The governing coupled equations in the frame of the boundary-layer model are applied to Stokes' first problem with heat sources. Laplace-transform and Fourier-transform techniques are used to obtain the solution. The inverses of the Fourier transforms are obtained analytically. The Laplace transforms are obtained using the complex inversion formula of the transform together with Fourier-expansion techniques. Numerical results for the temperature distribution, the velocity, and the microrotation components are represented graphically. Thermoelectric figure-of-merit, Seebeck and Peltier effects on a micropolar fluid are studied.
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26

Abbas, Ibrahim A., and Aatef D. Hobiny. "Eigenvalue Approach in a Generalized Thermal Shock Problem for a Transversely Isotropic Half-Space." Journal of Molecular and Engineering Materials 05, no. 01 (March 2017): 1750002. http://dx.doi.org/10.1142/s2251237317500022.

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In the present work, the investigating of the disturbances in a homogeneous, transversely isotropic elastic medium with generalized thermoelastic theory has been concerned. The formulation is applied to generalized thermoelasticity based on three different theories. Laplace and Fourier transforms are used to solve the problem analytically. The essential equations have been written as a vector-matrix differential equation in the Laplace transform domain, then solved by an eigenvalue approach. The inverses of Fourier transforms are obtained analytically. The result is used to solve a specific two-dimensional problem. The technique is illustrated by means of several numerical experiments performed. The results were verified numerically and are plotted.
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27

Grubb, Daniel J. "Shorter Notes: Ranges of Joint Laplace-Fourier Transforms." Proceedings of the American Mathematical Society 97, no. 2 (June 1986): 372. http://dx.doi.org/10.2307/2046534.

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28

Fusai, Gianluca. "Pricing Asian options via Fourier and Laplace transforms." Journal of Computational Finance 7, no. 3 (2004): 87–106. http://dx.doi.org/10.21314/jcf.2004.122.

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29

Lederman, Roy R., and Stefan Steinerberger. "Lower Bounds for Truncated Fourier and Laplace Transforms." Integral Equations and Operator Theory 87, no. 4 (March 27, 2017): 529–43. http://dx.doi.org/10.1007/s00020-017-2364-z.

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30

Sakurai, T. "Numerical inversion for Laplace transforms of functions with discontinuities." Advances in Applied Probability 36, no. 2 (June 2004): 616–42. http://dx.doi.org/10.1239/aap/1086957588.

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We analyse the role of Euler summation in a numerical inversion algorithm for Laplace transforms due to Abate and Whitt called the EULER algorithm. Euler summation is shown to accelerate convergence of a slowly converging truncated Fourier series; an explicit bound for the approximation error is derived that generalizes a result given by O'Cinneide. An enhanced inversion algorithm called EULER-GPS is developed using a new variant of Euler summation. The algorithm EULER-GPS makes it possible to accurately invert transforms of functions with discontinuities at arbitrary locations. The effectiveness of the algorithm is verified through numerical experiments. Besides numerical transform inversion, the enhanced algorithm is applicable to a wide range of other problems where the goal is to recover point values of a piecewise-smooth function from the Fourier series.
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31

Sakurai, T. "Numerical inversion for Laplace transforms of functions with discontinuities." Advances in Applied Probability 36, no. 02 (June 2004): 616–42. http://dx.doi.org/10.1017/s000186780001363x.

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We analyse the role of Euler summation in a numerical inversion algorithm for Laplace transforms due to Abate and Whitt called the EULER algorithm. Euler summation is shown to accelerate convergence of a slowly converging truncated Fourier series; an explicit bound for the approximation error is derived that generalizes a result given by O'Cinneide. An enhanced inversion algorithm called EULER-GPS is developed using a new variant of Euler summation. The algorithm EULER-GPS makes it possible to accurately invert transforms of functions with discontinuities at arbitrary locations. The effectiveness of the algorithm is verified through numerical experiments. Besides numerical transform inversion, the enhanced algorithm is applicable to a wide range of other problems where the goal is to recover point values of a piecewise-smooth function from the Fourier series.
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32

Zhao, Yang, Dumitru Baleanu, Mihaela Cristina Baleanu, De-Fu Cheng, and Xiao-Jun Yang. "Mappings for Special Functions on Cantor Sets and Special Integral Transforms via Local Fractional Operators." Abstract and Applied Analysis 2013 (2013): 1–6. http://dx.doi.org/10.1155/2013/316978.

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The mappings for some special functions on Cantor sets are investigated. Meanwhile, we apply the local fractional Fourier series, Fourier transforms, and Laplace transforms to solve three local fractional differential equations, and the corresponding nondifferentiable solutions were presented.
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33

Singh, Pushpendra, Anubha Gupta, and Shiv Dutt Joshi. "General Parameterized Fourier Transform: A Unified Framework for the Fourier, Laplace, Mellin and $Z$ Transforms." IEEE Transactions on Signal Processing 70 (2022): 1295–309. http://dx.doi.org/10.1109/tsp.2022.3152607.

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34

Chill, Ralph. "Tauberian theorems for vector-valued Fourier and Laplace transforms." Studia Mathematica 128, no. 1 (1998): 55–69. http://dx.doi.org/10.4064/sm-128-1-55-69.

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35

Colzani, Leonardo, Luigi Fontana, and Enrico Laeng. "Asymptotic decay of Fourier, Laplace and other integral transforms." Journal of Mathematical Analysis and Applications 483, no. 1 (March 2020): 123560. http://dx.doi.org/10.1016/j.jmaa.2019.123560.

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36

FEDOTENKOV, Grigory V., Andrey V. GRITSKOV GRITSKOV, Dmitry Y. LEVITSKIY, Yana A. VAHTEROVA, and Ying SUN. "Timoshenko beam and plate non-stationary vibrations." INCAS BULLETIN 13, S (August 3, 2021): 41–56. http://dx.doi.org/10.13111/2066-8201.2021.13.s.5.

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The problems of Timoshenko beams and plates lateral vibrations under the influence of unsteady loads are considered. Both beam and plate is supposed to be unlimited. In case of the plate the problem has been simply studied. The approach to the solution was based on dominant function method and principle of superposition. Integral models of solutions with cores as dominant functions were built which could be analytically found with the help of the Fourier and Laplace integral transforms. Two original analytical methods for Fourier and Laplace transforms were offered and realized. The examples of calculations were given.
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37

Suthar, Dayalal, Sunil Dutt Purohit, Haile Habenom, and Jagdev Singh. "Class of integrals and applications of fractional kinetic equation with the generalized multi-index Bessel function." Discrete & Continuous Dynamical Systems - S 14, no. 10 (2021): 3803. http://dx.doi.org/10.3934/dcdss.2021019.

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<p style='text-indent:20px;'>In this article, we have investigated certain definite integrals and various integral transforms of the generalized multi-index Bessel function, such as Euler transform, Laplace transform, Whittaker transform, K-transform and Fourier transforms. Also found the applications of the problem on fractional kinetic equation pertaining to the generalized multi-index Bessel function using the Sumudu transform technique. Mittage-Leffler function is used to express the results of the solutions of fractional kinetic equation as well as its special cases. The results obtained are significance in applied problems of science, engineering and technology.</p>
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38

Gzyl, Henryk. "Maxentropic reconstruction of Fourier and Laplace transforms under nonlinear constraints." Applied Mathematics and Computation 85, no. 2-3 (September 1997): 117–26. http://dx.doi.org/10.1016/s0096-3003(96)00116-6.

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39

Hörmander, Lars, and Ragnar Sigurdsson. "Growth properties of plurisubharmonic functions related to Fourier-Laplace transforms." Journal of Geometric Analysis 8, no. 2 (June 1998): 251–311. http://dx.doi.org/10.1007/bf02921643.

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40

Napalkov, V. V., and R. S. Yulmukhametov. "WEIGHTED FOURIER-LAPLACE TRANSFORMS OF ANALYTIC FUNCTIONALS ON THE DISK." Russian Academy of Sciences. Sbornik Mathematics 77, no. 2 (February 28, 1994): 385–90. http://dx.doi.org/10.1070/sm1994v077n02abeh003447.

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41

Moorthy, M. V. "Numerical inversion of two-dimensional Laplace transforms—Fourier series representation." Applied Numerical Mathematics 17, no. 2 (May 1995): 119–27. http://dx.doi.org/10.1016/0168-9274(95)00015-m.

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42

Li, Xian-Fang. "Dynamic T-Stress for a Mode-I Crack in an Infinite Elastic Plane." Journal of Applied Mechanics 74, no. 2 (February 2, 2006): 378–81. http://dx.doi.org/10.1115/1.2190232.

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An integral equation method is presented to determine dynamic elastic T-stress. Special attention is paid to a single crack in an infinite elastic plane subjected to impact loading. By using the Laplace and Fourier transforms, the associated initial-boundary value problem is transformed to a Fredholm integral equation. The dynamic T-stress in the Laplace transform domain can be expressed in terms of its solution. Moreover, an explicit expression for initial T-stress is derived in closed form. Numerically solving the resulting equation and performing the inverse Laplace transform, the transient response of T-stress is determined in the time space, and the response history of the T-stress is shown graphically. Results indicate that T-stress exhibits apparent transient characteristic.
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43

Moldovan, Dumitrița, and Radu Fechete. "Bimodal 1H Double Quantum Build-Up Curves by Fourier and Laplace-like Transforms on Aged Cross-Linked Natural Rubber." Polymers 13, no. 20 (October 13, 2021): 3523. http://dx.doi.org/10.3390/polym13203523.

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The 1H DQ Fourier and Laplace-like spectra for a series of cross-linked natural rubber (NR) samples naturally aged during six years are presented and characterized. The DQ build-up curves of these samples present two peaks which cannot be described by classical functions. The DQ Fourier spectra can be obtained after a numeric procedure which introduces a correction time which depends less on the chosen approximation, spin-½ and isolated CH2 and CH3 functional groups. The DQ Fourier spectra are well described by the distributions of the residual dipolar coupling correlated with the distribution of the end-to-end vector of the polymer network, and with the second and fourth van Vleck moments. The deconvolution of DQ Fourier spectra with a sum of four Gaussian variates show that the center and the width of Gaussian functions increase linearly with the increase in the cross-link density. The Laplace-like spectra for the natural aged NR DQ build-up curves are presented. The centers of four Gaussian distributions obtained via both methods are consistent. The differences between the Fourier and Laplace-like spectra consist mainly of the spectral resolution in the favor of Laplace-like spectra. The last one was used to discuss the effect of natural aging for cross-linked NR.
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44

Rubio-Gonzalez, C., and J. J. Mason. "Response of Finite Cracks in Orthotropic Materials due to Concentrated Impact Shear Loads." Journal of Applied Mechanics 66, no. 2 (June 1, 1999): 485–91. http://dx.doi.org/10.1115/1.2791073.

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The elastodynamic response of an infinite orthotropic material with a finite crack under concentrated in-plane shear loads is examined. A solution for the stress intensity factor history around the crack tips is found. Laplace and Fourier transforms are employed to solve the equations of motion leading to a Fredholm integral equation on the Laplace transform domain. The dynamic stress intensity factor history can be computed by numerical Laplace transform inversion of the solution of the Fredholm equation. Numerical values of the dynamic stress intensity factor history for several example materials are obtained. The results differ from mode I in that there is heavy dependence upon the material constants. This solution can be used as a Green's function to solve dynamic problems involving finite cracks and in-plane shear loading.
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45

Povstenko, Y. Z. "Fundamental Solutions to Time-Fractional Advection Diffusion Equation in a Case of Two Space Variables." Mathematical Problems in Engineering 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/705364.

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The fundamental solutions to time-fractional advection diffusion equation in a plane and a half-plane are obtained using the Laplace integral transform with respect to timetand the Fourier transforms with respect to the space coordinatesxandy. The Cauchy, source, and Dirichlet problems are investigated. The solutions are expressed in terms of integrals of Bessel functions combined with Mittag-Leffler functions. Numerical results are illustrated graphically.
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46

Shindo, Yasuhide, Hiroaki Higaki, and Hideaki Nozaki. "Impact Response of a Single Edge Crack in an Orthotropic Strip." Journal of Applied Mechanics 59, no. 2S (June 1, 1992): S152—S157. http://dx.doi.org/10.1115/1.2899480.

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The elastodynamic response of a single edge crack in an orthotropic strip under normal impact is considered in this study. The edge crack is oriented in a direction normal to the edge of the strip. Laplace and Fourier transforms are used to reduce the transient problem to the solution of a pair of dual integral equations in the Laplace transform plane. The solution to the dual integral equations is then expressed in terms of a Fredholm integral equation of the second kind. A numerical Laplace inversion routine is used to recover the time dependence of the solution. Numerical values on the dynamic stress intensity factor for several fiber-reinforced composite materials are obtained, and the results are graphed to display the influence of the material orthotropy.
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47

Aouadi, Moncef. "Discontinuities in an axisymmetric generalized thermoelastic problem." International Journal of Mathematics and Mathematical Sciences 2005, no. 7 (2005): 1015–29. http://dx.doi.org/10.1155/ijmms.2005.1015.

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This paper deals with discontinuities analysis in the temperature, displacement, and stress fields of a thick plate whose lower and upper surfaces are traction-free and subjected to a given axisymmetric temperature distribution. The analysis is carried out under three thermoelastic theories. Potential functions together with Laplace and Hankel transform techniques are used to derive the solution in the transformed domain. Exact expressions for the magnitude of discontinuities are computed by using an exact method developed by Boley (1962). It is found that there exist two coupled waves, one of which is elastic and the other is thermal, both propagating with finite speeds with exponential attenuation, and a third which is called shear wave, propagating with constant speed but with no exponential attenuation. The Hankel transforms are inverted analytically. The inversion of the Laplace transforms is carried out using the inversion formula of the transform together with Fourier expansion techniques. Numerical results are presented graphically along with a comparison of the three theories of thermoelasticity.
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48

Arifin, Arifin, Muhammad Wakhid Musthofa, and Sugiyanto Sugiyanto. "Aplikasi Transformasi Laplace Pada Rangkaian Listrik." Jurnal Fourier 2, no. 1 (April 1, 2013): 45. http://dx.doi.org/10.14421/fourier.2013.21.45-61.

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Menyelesaikan persamaan diferensial sering terkendala oleh masalah syarat awal atau syarat batas. Masalah syarat batas ini sering dijumpai pada penerapan persamaan diferensial, salah satunya adalah rangkaian listrik. Metode yang dapat digunakan untuk menyelesaikan masalah syarat batas pada persamaan diferensial salah satu diantaranya adalah metode transformasi Laplace. Transformasi Laplace yang didefinisikan dengan L{f(t)}= dapat digunakan untuk mencari solusi dari suatu sistem persamaan diferensial koefisien konstan. Metode penyelesaian suatu rangkaian Listrik dengan menggunakan transformasi Laplace adalah dengan mengubah persamaan diferensial dari domain waktu (t) ke dalam domain frekuensi (s), memetakan masalah nilai awal ke dalam persamaan pembantu, menyelesaikan dengan perhitungan aljabar, dan menggunakan invers transformasi Laplace untuk mendapatkan solusi khusus secara langsung dari sistem persamaan diferensial rangkaian listrik tersebut.
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49

Singh, Biswajit, Smita Pal (Sarkar), and Krishnendu Barman. "Memory-dependent derivative under generalized three-phase-lag thermoelasticity model with a heat source." Multidiscipline Modeling in Materials and Structures 16, no. 6 (May 20, 2020): 1337–56. http://dx.doi.org/10.1108/mmms-10-2019-0182.

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PurposeThis study aims to attempt to construct a new mathematical model of the generalized thermoelasiticity theory based on the memory-dependent derivative (MDD) considering three-phase-lag effects. The governing equations of the problem associated with kernel function and time delay are illustrated in the form of vector matrix differential equations. Implementing Laplace and Fourier transform tools, the problem is sorted out analytically by an eigenvalue approach method. The inversion of Laplace and Fourier transforms are executed, incorporating series expansion procedures. Displacement component, temperature and stress distributions are obtained numerically and illustrated graphically and compared with the existing literature.Design/methodology/approachThis study is to analyze the influence of MDD of three-phase-lag heat conduction interaction in an isotropic semi-infinite medium. The current model has been connected to generalize two-dimensional (2D) thermoelasticity problem. The governing equations are shown in vector matrix form of differential equation concerning Laplace-transformed domain and solved by using the eigenvalue technique. The combined Laplace Fourier transform is applied to find the analytical interpretations of temperature, stresses, displacement for silicon material in a non-dimensional form. Inverse Laplace transform has been found by applying Fourier series expansion techniques introduced by Honig and Hirdes (1984) after performing the inverse Fourier transform.FindingsThe main conclusion of this current study is to demonstrate an innovative generalized concept for heat conducting Fourier’s law associated with moderation of time parameter, time delay variable and kernel function by applying the MDDs. However, an important role is played by the time delay parameter to characterize the behavioral patterns of the physical field variables. Further, a new categorization for materials may be created rendering to this new idea along MDD for the time delay variables to develop a new measure of its potential to regulate heat in the medium.Originality/valueGeneralized thermoelasticity is hastily undergoing modification day-by-day from basic thermoelasticity. It has been progressed to get over from the limitations of fundamental thermoelasticity, for instance, infinite velocity components of thermoelasticity interference, in the adequate thermoelastic response of a solid to short laser pulses and deprived illustrations of thermoelastic performance at low temperature. In the past few decades, the fractional calculus is used to change numerous existing models of physical procedure, and its applications are used in various fields of physics, continuum mechanics, fluid mechanics, biology, viscoelasticity, biophysics, signal and image processing, control theory, engineering fields, etc.
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Fiorito, Giovanni. "On Laplace and Fourier transforms of periodically monotone functions and distributions." Publicationes Mathematicae Debrecen 57, no. 1-2 (July 1, 2000): 105–14. http://dx.doi.org/10.5486/pmd.2000.2221.

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