Analyzing Free-Free Beams by Green's Functions and Fredholm Alternative Theorem. (10th July 2017)

• Record Type: Journal Article
• Authors: Rezaiee-Pajand, M.; Aftabi Sani, A.; Hozhabrossadati, S. M.
• Is Part Of: Journal of mechanics. Volume 35:Number 1(2019)
• Page Start: 27
• Page End: 39
• Publication Date: 2017-07-10
• Subjects: Modified Green's functions -- Fredholm Alternative Theorem -- Deflection functions -- Solvability conditions; Mechanics, Analytic -- Periodicals; Mechanics -- Periodicals; 620.1005
• DOI: 10.1017/jmech.2017.57
• Languages: English
• ISSNs: 1727-7191

Abstract

Abstract : This article deals with the analysis of free-free beams by an analytical method. The well-known Green's function method is employed, and exact solution for the problem is obtained. As a second problem, the simply supported-free beam with rotational rigid body motion is analyzed. It is initially shown that ordinary Green's functions cannot be constructed due to a mathematical contradiction. To remedy this limitation, the Fredholm Alternative Theorem is utilized. This theorem eliminates the contradiction and enables analysts to obtain modified Green's functions. The fundamental existence conditions are derived and thoroughly investigated from the structural point of view. Finally, the deflection functions of these beams are found using modified Green's functions.