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Metin Gürgöze,Serkan Zeren 국제구조공학회 2015 Structural Engineering and Mechanics, An Int'l Jou Vol.53 No.6
Many vibrating mechanical systems from the real life are modeled as combined dynamicalsystems consisting of beams to which spring-mass secondary systems are attached. In most of thepublications on this topic, masses of the helical springs are neglected. In a paper (Cha et al. 2008) publishedrecently, the eigencharacteristics of an arbitrary supported Bernoulli-Euler beam with multiple in-spanhelical spring-mass systems were determined via the solution of the established eigenvalue problem, wherethe springs were modeled as axially vibrating rods. In the present article, the authors used the assumedmodes method in the usual sense and obtained the equations of motion from Lagrange Equations and arrivedat a generalized eigenvalue problem after applying a Galerkin procedure. The aim of the present paper issimply to show that one can arrive at the corresponding generalized eigenvalue problem by following a quitedifferent way, namely, by using the so-called “characteristic force” method. Further, parametricinvestigations are carried out for two representative types of supporting conditions of the bending beam.
On the dynamics of rotating, tapered, visco-elastic beams with a heavy tip mass
Serkan Zeren,Metin Gürgöze 국제구조공학회 2013 Structural Engineering and Mechanics, An Int'l Jou Vol.45 No.1
The present study deals with the dynamics of the flapwise (out-of-plane) vibrations of a rotating, internally damped (Kelvin-Voigt model) tapered Bernoulli-Euler beam carrying a heavy tip mass. The centroid of the tip mass is offset from the free end of the beam and is located along its extended axis. The equation of motion and the corresponding boundary conditions are derived via the Hamilton’s Principle, leading to a differential eigenvalue problem. Afterwards, this eigenvalue problem is solved by using Frobenius Method of solution in power series. The resulting characteristic equation is then solved numerically. The numerical results are tabulated for a variety of nondimensional rotational speed, tip mass, tip mass offset, mass moment of inertia, internal damping parameter, hub radius and taper ratio. These are compared with the results of a conventional finite element modeling as well, and excellent agreement is obtained.