scholarly journals Fourier Sine Transform Method for Solving the Cerrutti Problem of the Elastic Half Plane in Plane Strain

2018 ◽  
Vol 14 (1) ◽  
pp. 1-11
Author(s):  
Charles Chinwuba Ike
Keyword(s):  
Boundary Conditions ◽  
Half Plane ◽  
Point Load ◽  
Displacement Fields ◽  
Transform Method ◽  
Sine Transform ◽  
Fourier Sine ◽  
Fourier Sine Transform ◽  
Stress Functions ◽  
The Fourier Transform

Abstract The Fourier sine transform method was implemented in this study to obtain general solutions for stress and displacement fields in homogeneous, isotropic, linear elastic soil of semi-infinite extent subject to a point load applied tangentially at a point considered the origin of the half plane. The study adopted a stress based formulation of the elasticity problem. Fourier transformation of the biharmonic stress compatibility equation was done to obtain bounded stress functions for the elastic half plane problem. Stresses and boundary conditions expressed in terms of the Boussinesq-Papkovich potential functions were transformed using Fourier sine transforms. Boundary conditions were used to obtain the unknown constants of the stress functions for the Cerrutti problem considered; and the complete determination of the stress fields in the Fourier transform space. Inversion of the Fourier sine transforms for the stresses yielded the general expressions for the stresses in the physical domain space variables. The strain fields were obtained from the kinematic relations. The displacement fields were obtained by integration of the strain-displacement relations. The solutions obtained were identical with solutions in literature obtained using Cerrutti stress functions.

FOURIER SINE AND COSINE TRANSFORMS ON BOEHMIAN SPACES

2013 ◽  
Vol 06 (01) ◽  
pp. 1350005 ◽  
Author(s):  
R. Roopkumar ◽  
E. R. Negrin ◽  
C. Ganesan
Keyword(s):  
Fourier Transform ◽  
Cosine Transform ◽  
Fourier Cosine ◽  
Sine Transform ◽  
Fourier Sine ◽  
Fourier Sine Transform ◽  
Fourier Cosine Transform ◽  
One To One ◽  
The Fourier Transform

We construct suitable Boehmian spaces which are properly larger than [Formula: see text] and we extend the Fourier sine transform and the Fourier cosine transform more than one way. We prove that the extended Fourier sine and cosine transforms have expected properties like linear, continuous, one-to-one and onto from one Boehmian space onto another Boehmian space. We also establish that the well known connection among the Fourier transform, Fourier sine transform and Fourier cosine transform in the context of Boehmians. Finally, we compare the relations among the different Boehmian spaces discussed in this paper.

Modeling electro-osmotic flow and thermal transport of Caputo fractional Burgers fluid through a micro-channel

2021 ◽  
pp. 095440892110259
Author(s):  
Mohammed Abdulhameed ◽  
Garba Tahiru Adamu ◽  
Gulibur Yakubu Dauda
Keyword(s):  
Electric Field ◽  
Laplace Transform ◽  
Inverse Laplace Transform ◽  
Micro Channel ◽  
Osmotic Flow ◽  
Sine Transform ◽  
Fourier Sine ◽  
Fourier Sine Transform ◽  
Burgers Fluid ◽  
Electro Osmotic Flow

In this paper, we construct transient electro-osmotic flow of Burgers’ fluid with Caputo fractional derivative in a micro-channel, where the Poisson–Boltzmann equation described the potential electric field applied along the length of the microchannel. The analytical solution for the component of the velocity profile was obtained, first by applying the Laplace transform combined with the classical method of partial differential equations and, second by applying Laplace transform combined with the finite Fourier sine transform. The exact solution for the component of the temperature was obtained by applying Laplace transform and finite Fourier sine transform. Further, due to the complexity of the derived models of the governing equations for both velocity and temperature, the inverse Laplace transform was obtained with the aid of numerical inversion formula based on Stehfest's algorithms with the help of MATHCAD software. The graphical representations showing the effects of the time, retardation time, electro-kinetic width, and fractional parameters on the velocity of the fluid flow and the effects of time and fractional parameters on the temperature distribution in the micro-channel were presented and analyzed. The results show that the applied electric field, electro-osmotic force, electro-kinetic width, and relaxation time play a vital role on the velocity distribution in the micro-channel. The fractional parameters can be used to regulate both the velocity and temperature in the micro-channel. The study could be used in the design of various biomedical lab-on-chip devices, which could be useful for biomedical diagnosis and analysis.

scholarly journals Fourier Analysis with Generalized Integration

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1199
Author(s):  
Juan H. Arredondo ◽  
Manuel Bernal ◽  
María Guadalupe Morales
Keyword(s):  
Fourier Transform ◽  
Fourier Analysis ◽  
Integral Theory ◽  
Dense Subspace ◽  
Fourier Cosine ◽  
Sine Transform ◽  
Integrable Functions ◽  
Fourier Sine Transform ◽  
Fourier Cosine Transform ◽  
The Fourier Transform

We generalize the classic Fourier transform operator F p by using the Henstock–Kurzweil integral theory. It is shown that the operator equals the H K -Fourier transform on a dense subspace of L p , 1 < p ≤ 2 . In particular, a theoretical scope of this representation is raised to approximate the Fourier transform of functions on the mentioned subspace numerically. Besides, we show the differentiability of the Fourier transform function F p ( f ) under more general conditions than in Lebesgue’s theory. Additionally, continuity of the Fourier Sine transform operator into the space of Henstock-Kurzweil integrable functions is proved, which is similar in spirit to the already known result for the Fourier Cosine transform operator. Because our results establish a representation of the Fourier transform with more properties than in Lebesgue’s theory, these results might contribute to development of better algorithms of numerical integration, which are very important in applications.

Sign in / Sign up

Export Citation Format

Share Document