# Integral Transforms in Applied Mathematics: Frontmatter

01 Jan 1971-

About: The article was published on 1971-01-01. It has received 24 citations till now. The article focuses on the topics: Integral transform.

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TL;DR: In this article , a finite cosine integral transform (FCT) was used for the analysis of the vibration response of a beam-stiffened Mindlin plate having a completely free boundary condition.

Abstract: This paper presents a new analytical solution for the vibration response of a beam‐stiffened Mindlin plate having a completely free boundary condition by utilizing a finite cosine integral transform. In the solution, the unknown coupling force and moments at the beam/plate interface and the unknown modal constants from the integral transform are determined by the continuity and compatibility conditions at the interface as well as the boundary conditions. It provides an easily implemented tool for exploring complex edge value problems for a class of higher‐order partial differential equations represented by fully free‐stiffened Mindlin thick plates. The validity of the model is evaluated by comparing the calculated free and forced vibration responses of the beam‐stiffened plate with those calculated using a beam‐stiffened thin plate and those from finite element analysis.

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01 Mar 1991TL;DR: In this article, the heat transfer phenomena for single and double layer inclined absorbers which absorb synchrotron radiation has been studied using analytical and numerical methods, and the effects of the spectral variation of the absorption coefficients and variable thermal conductivities have been examined.

Abstract: The heat transfer phenomena for single and double layer inclined absorbers which absorb synchrotron radiation has been studied using analytical and numerical methods. Photon penetration through the metal layers has been included and the effects of the spectral variation of the absorption coefficients and variable thermal conductivities have been examined. Different thickness ratios and inclination angles have been studied for double layer absorbers and it has been shown that double layer inclined absorbers significantly reduce the peak temperatures.

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TL;DR: An analytical solution utilizing a double finite sine integral transform method is presented in this paper for the sound radiation prediction of a ribbed rectangular plate structure under various combinations of clamped and simply supported boundary conditions.

Abstract: An analytical solution utilizing a double finite sine integral transform method is presented in this study for the sound radiation prediction of a ribbed rectangular plate structure under various combinations of clamped and simply supported boundary conditions. An advantage of the modeling method is that the plate-beam structural coupling and the structure-fluid coupling are automatically defined in the integral transformation without the need to manually select the mode shape function. The model is then utilized to investigate the effect of ribs on the radiated sound power and directivity of the plate structure under resonant and non-resonant conditions, respectively. The result shows that the ribbing effect on the omnidirectional radiated sound field of the rectangular plate is consistent with the change of the radiated sound power. However, the radiated sound pressure may increase at certain directions even if the radiated sound power of the rectangular plate is suppressed by the inclusion of ribs. The effect of periodic ribs on the sound radiation of the rectangular plate is also explored. The insights gained from this study can inspire the noise design for structures such as marine platforms and high-speed rail carriages.

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01 Jan 2022

TL;DR: In this paper , a large number of examples are given with detailed solutions obtained both manually and using symbolic computations in the Wolfram Mathematica, and examples of solutions for systems of integral equations with difference kernels using the integral Laplace transform are also given.

Abstract: This chapter is devoted to integral equations with difference kernels. The solution of integral equations with difference kernels using integral Laplace and Fourier transforms is discussed in detail. A large number of examples are given with detailed solutions obtained both manually and using symbolic computations in the Wolfram Mathematica. Examples of solutions for systems of integral equations with difference kernels using the integral Laplace transform are also given. In addition, the considered method is applied to solve various examples of integro-differential equations.