Abstract
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.
Highlights
Many engineering problems can be idealized as a beam on foundation
The main objective is to introduce a practical numerical solution based on quintic B-spline collocation method for elastically restrained tapered damped EB rested on variable Winkler foundation
C- 2,...,cN + 2 are unknown coefficients that can be determined using the collocation form of the governing differential equation of the tapered damped EB rested on variable Winkler foundation and boundary conditions at each end of the beam
Summary
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. It is assumed the beam rested on variable Winkler foundation The simplicity of this approximation method makes it an ideal candidate for computer implementation. 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. KEYWORDS Collocation method; Tapered Euler-Bernoulli beam; Winkler foundation; boundary conditions; B-spline function
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