scholarly journals Fourier Sine Transform Method for the Free Vibration of Euler-Bernoulli Beam Resting on Winkler Foundation

2018 ◽  
Vol 7 (1) ◽  
pp. 1 ◽  
Author(s):  
Charles Chinwuba Ike
Keyword(s):  
Free Vibration ◽  
Winkler Foundation ◽  
Bernoulli Beam ◽  
Transform Method ◽  
Sine Transform ◽  
Fourier Sine ◽  
Fourier Sine Transform ◽  
Euler Bernoulli Beam

scholarly journals Quintic B-spline collocation method for numerical solution of free vibration of tapered Euler-Bernoulli beam on variable Winkler foundation

2021 ◽  
Vol 15 (2) ◽  
pp. 8193-8204
Author(s):  
Amin Ghannadiasl
Keyword(s):  
Free Vibration ◽  
Numerical Solution ◽  
Collocation Method ◽  
Winkler Foundation ◽  
Finite Dimensional Space ◽  
Spline Collocation ◽  
Bernoulli Beam ◽  
B Spline ◽  
Spline Collocation Method ◽  
Euler Bernoulli Beam

The collocation method is the method for the numerical solution of integral equations and partial and ordinary differential equations. The main idea of this method is to choose a number of points in the domain and a finite-dimensional space of candidate solutions. So, that solution satisfies the governing equation at the collocation points. The current paper involves developing, and a comprehensive, step-by step procedure for applying the collocation method to the numerical solution of free vibration of tapered Euler-Bernoulli beam. In this stusy, it is assumed the beam rested on variable Winkler foundation. The simplicity of this approximation method makes it an ideal candidate for computer implementation. Finally, the numerical examples are introduced to show efficiency and applicability of quintic B-spline collocation method. Numerical results are demonstrated that quintic B-spline collocation method is very competitive for numerical solution of frequency analysis of tapered beam on variable elastic foundation.

Free Vibration Analysis of Rotating Euler–Bernoulli Beam with Exponentially Varying Cross-Section by Differential Transform Method

2018 ◽  
Vol 18 (02) ◽  
pp. 1850024 ◽  
Author(s):  
Mostafa Nourifar ◽  
Ali Keyhani ◽  
Ahmad Aftabi Sani
Keyword(s):  
Free Vibration ◽  
Recurrence Relation ◽  
Cross Section ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Differential Transform Method ◽  
Bernoulli Beam ◽  
Transform Method ◽  
Differential Transform ◽  
Euler Bernoulli Beam

In this paper, the free vibration analysis of non-uniform rotating Euler–Bernoulli beam is carried out. It is assumed that the beam has exponentially decaying circular cross-section. In order to solve the problem, the differential transform method (DTM) is utilized. Based on our knowledge, we claim that the recurrence relation presented herein is an elaborate recurrence relation which has been obtained for ordinary differential equations. Non-dimensional natural frequencies of the beam are obtained and tabulated for different values of the beam parameters such as taper ratio and rotating speed. Furthermore, the finite element method (FEM) is employed to solve the problem. Comparison of the results obtained by DTM and FEM indicates the accuracy of proposed solutions.

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.

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