Solution of differential equation for the Euler-Bernoulli beam

• Autorzy: Zamorska I.
• Języki publikacji: EN

Abstrakty

EN

The paper presents the solution of a fourth order differential equation with various coefficients occurring in the vibration problem of the Euler-Bernoulli beam. The concerning equation is written as a first order matrix differential equation. To solve the equation, the power series method is proposed.

Słowa kluczowe

EN

Euler-Bernoulli beam; power series method; mathematical modeling

PL

belka Bernoulliego-Eulera; modelowanie matematyczne

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2014
• Tom: Vol. 13, nr 4
• Strony: 157--162
• Opis fizyczny: Bibliogr. 10 poz., rys.

Twórcy

autor

Zamorska I.

• Institute of Mathematics, Czestochowa University of Technology Częstochowa, Poland

Bibliografia

• [1] Elishakoff I., Becquet R., Closed-form solutions for natural frequency for inhomogeneous beams with one sliding support and the other pinned, Journal of Sound and Vibration 2000, 238(3), 529-539.
• [2] Chen D.-W., Wu J.-S., The exact solutions for the natural frequencies and mode shapes of nonuniform beams with multiple spring - mass systems, Journal of Sound and Vibration 2002, 255(2), 299-322.
• [3] Hassan H.N., El-Tawil M.A., A new technique of using homotopy analysis method for second order nonlinear differential equations, Applied Mathematics and Computation 2012, 219, 708-728.
• [4] Kukla S., Zamojska I., Application of the Green’s function method in free vibration analysis of non-uniform beams, Scientific Research of the Institute of Mathematics and Computer Science 2005, 1(4), 87-94.
• [5] Yeh Y-L., Jang M-J., Wang C-C., Analyzing the free vibrations of a plate using finite difference and differential transformation method, Applied Mathematics and Computation 2006, 178, 493-501.
• [6] Qaisi M.I., A power series solution for the non-linear vibration of beams, Journal of Sound and Vibration 1997, 199(4), 587-594.
• [7] Ozgumus O.O., Kaya M.O., Flapwise bending vibration analysis of double tapered rotating Euler-Bernoulli beam by using the differential transform method, Meccanica 2006, 41, 661-670.
• [8] Mei C., Application of differential transformation technique to free vibration analysis of a centrifugally stiffened beam, Computers and Structures 2008, 86, 1280-1284.
• [9] Cekus D., Free vibration of a cantilever tapered Timoshenko beam, Scientific Research of the Institute of Mathematics and Computer Science 2012, 4(11), 11-17.
• [10] Kukla S., Zamorska I., Power series solution of first order matrix differential equations, Journal of Applied Mathematics and Computational Mechanics 2014, 13(3), 123-128.