Results 11 to 20 of about 72,497 (130)

Buckling Behavior of Nanobeams Placed in Electromagnetic Field Using Shifted Chebyshev Polynomials-Based Rayleigh-Ritz Method [PDF]

Nanomaterials, 2019
In the present investigation, the buckling behavior of Euler−Bernoulli nanobeam, which is placed in an electro-magnetic field, is investigated in the framework of Eringen’s nonlocal theory.
Subrat Kumar Jena, Snehashish Chakraverty, Francesco Tornabene   +2 more
doaj   +5 more sources

An improvement of the Euler–Chebyshev iterative method

Journal of Mathematical Analysis and Applications, 2006
The computation of a simple root of a sufficiently smooth scalar function \(f\) is discussed. The Newton method and the Euler-Chebyshev method are briefly presented. A method based on the Euler-Chebyshev method using a linear combination of function values of \(f\) with a convergence order of 5 is constructed.
Grau, Miquel, Díaz-Barrero, José Luis
semanticscholar   +6 more sources

Explicit Chebyshev Petrov–Galerkin scheme for time-fractional fourth-order uniform Euler–Bernoulli pinned–pinned beam equation

Nonlinear Engineering, 2023
In this research, a compact combination of Chebyshev polynomials is created and used as a spatial basis for the time fractional fourth-order Euler–Bernoulli pinned–pinned beam.
Moustafa Mohamed, Youssri Youssri Hassan, Atta Ahmed Gamal   +2 more
doaj   +4 more sources

An Efficient Petrov–Galerkin Scheme for the Euler–Bernoulli Beam Equation via Second-Kind Chebyshev Polynomials

Fractal and Fractional
The current article introduces a Petrov–Galerkin method (PGM) to address the fourth-order uniform Euler–Bernoulli pinned–pinned beam equation. Utilizing a suitable combination of second-kind Chebyshev polynomials as a basis in spatial variables, the ...
Youssri Hassan Youssri, Waleed Mohamed Abd-Elhameed, Amr Ahmed Elmasry, Ahmed Gamal Atta   +3 more
doaj   +4 more sources

Initial approximations in Euler-Chebyshev's method

Journal of Computational and Applied Mathematics, 1995
The author considers a polynomial \(f(x)\) of degree \(n\) and the Euler-Chebyshev iterative method for approximating its zeros. He proves that for any monic polynomial \(f(x)\) of degree \(n\), there exists a set \(\Gamma_f\subset \mathbb{C}^n\) such that the Euler-Chebyshev method starting from \(x^0= x\in \Gamma_f\) does not converge to the zeros of
N. Kjurkchiev
semanticscholar   +5 more sources

On a generalization of the Euler-Chebyshev method for simultaneous extraction of only a part of all roots of polynomials [PDF]

Japan Journal of Industrial and Applied Mathematics, 2006
The authors generalize the Euler-Chebyshev method for the case when only a part of the roots of a polynomial is sought for. Local cubic convergence is proved for the case of sufficiently separated roots. Numerical experiments are given.
Iliev, Anton, Kyurkchiev, Nikolay, Fang, Qing   +2 more
openaire   +3 more sources

A Chebyshev Spectral Method with Null Space Approach for Boundary-Value Problems of Euler-Bernoulli Beam

Shock and Vibration, 2018
We proposed a Chebyshev spectral method with a null space approach for investigating the boundary-value problem of a nonprismatic Euler-Bernoulli beam with generalized boundary or interface conditions.
C. P. Hsu, C. F. Hung, J. Y. Liao
doaj   +2 more sources

A Unified Numerical Approach to the Dynamics of Beams with Longitudinally Varying Cross-Sections, Materials, Foundations, and Loads Using Chebyshev Spectral Approximation

Aerospace, 2023
Structures with inhomogeneous materials, non-uniform cross-sections, non-uniform supports, and subject to non-uniform loads are increasingly common in aerospace applications. This paper presents a simple and unified numerical dynamics model for all beams
Haizhou Liu, Yixin Huang, Yang Zhao
doaj   +2 more sources

Natural vibrations of double bi-directional functionally graded Euler–Bernoulli beams connected by a variable Winkler elastic layer

Journal of Low Frequency Noise, Vibration and Active Control, 2022
The free transverse vibrations of two-dimensional functionally graded double Euler–Bernoulli beam system connected through a variable Winkler elastic layer are presented.
Ma’en S Sari
doaj   +2 more sources

Nondeterministic dynamic stability assessment of Euler–Bernoulli beams using Chebyshev surrogate model

Applied Mathematical Modelling, 2019
A novel nondeterministic dynamic stability assessment of Euler–Bernoulli beams using Chebyshev surrogate model is proposed to investigate the upper and lower bounds of the dynamic buckling responses in this paper.
K. Gao, Wei Gao, Binhua Wu, Chongmin Song   +3 more
semanticscholar   +3 more sources