This paper analyses vibration of uniform flexible simply supported rectangular isotropic beam under large deformation with uniformly distributed mass elements. The method of equivalent pseudolinear systems was employed. The deformation of the beam was assumed to be large and the beam was also assumed to be inextensible. The expressions for elastic and nonlinear bending moments were determined. The numerical values of horizontal displacements of the movable support, and the equivalent lengths at various depth-to-breadth (aspect) ratios were determined. The corresponding equivalent pseudolinear systems for various nonlinear bending moment diagrams at various aspect ratios were determined. Consequently the concentrated loads yielding the equivalent pseudolinear systems were converted to point masses using the gravitational acceleration; and subsequently a unit load system was applied successively and independently at each mass point. The Vereshchagin’s method was applied to determine the displacements for canonical equations of motion. Non-trivial solution of the canonical equations at each aspect ratio was sought for the desired eigenvalues. The first mode frequencies at aspect ratios, β = 1.00 and β = 1.25 are complex eigenvalues. Also the natural frequencies exhibit hard-spring type with aspect ratios; and the fundamental frequencies for all the aspect ratios are at seventh mode. Conclusively, the dynamic stability of the flexible rectangular beam of 0.25m-breadth and 15m-undeformed length is not guaranteed when the aspect ratio is less than or equal to 1.25. It is also concluded that deepness of the flexible rectangular beam loaded with uniformly distributed mass elements influences the vibratory characteristics.
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