Resonant Green's function for Euler-Bernoulli beams by means of the Fredholm Alternative Theorem

• Autorzy: Hozhabrossadati S. M. , Sani A. A. , Mofid M.
• Języki publikacji: EN

Abstrakty

EN

This paper presents the Green's function for a uniform thin beam which is assumed to obey the Euler-Bernoulli theory at resonant condition. The beam under study has a simple support at one end and a sliding support at the other. First, the differential equation governing the free vibration of the beam is obtained in the frequency domain using the Fourier transform. Then, we try to find the corresponding Green's function of the problem. But a contradiction occurs due to the special properties of resonance. In order to overcome this hurdle, the Fredholm Alternative Theorem is utilized. Remarkably, it is shown that this theorem, by adding a particular term to the Green's function, can remedy this problem and the modified Green's function is consequently established. Moreover, the deformation function of the beam is found in an integral equation form. Some diagrams and tables conclude this study.

Słowa kluczowe

EN

Fredholm Alternative Theorem; modified Green’s function; resonance; Euler-Bernoulli beam

PL

rezonans

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2013
• Tom: Vol. 12, nr 3
• Strony: 55--67
• Opis fizyczny: Bibliogr. 10 poz., rys., tab.

Twórcy

autor

Hozhabrossadati S. M.

• Department of Civil Engineering, Mashhad Branch, Islamic Azad University, Mashhad, Iran

autor

Sani A. A.

• Department of Civil Engineering, Mashhad Branch, Islamic Azad University, Mashhad, Iran

autor

Mofid M.

• Department of Civil Engineering, Sharif University of Technology, Tehran, Iran

Bibliografia

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