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1. Introduction
A number of systems in the fields of navigation and mechanical engineering can be modeled as rotating hub-beam system with a tip mass. For example, flexible manipulators, spacecraft structures, and cranes carrying moving loads can be studied in this way. In these systems, the beams carrying a tip mass are rotating in a horizontal plane with the whole systems mounted on a rotating hub. In order to study their dynamic characteristics, the rotating beam systems are simplified as a rotating hub-beam system with a tip mass model. In recent years much attention has been placed on linear and nonlinear dynamic characteristics of rotating beam with a tip mass, and earlier work has been done with the linear analysis. For instance, Conrad and Morgül [1] used linearized feedback law to study the stabilization of a flexible beam with a tip mass. Rao [2] derived the time-dependent equations of motion that governs the vibration of an Euler-Bernoulli beam; it was used to obtain the linear dynamic response of the beam under moving load mass. Demetriou [3] presented a method for construction of observer for linear second-order lumped and distributed parameter systems using parameter-dependent Lyapunov functions. Furta [4] proved that the attached point mass on a thin elastic beam plays a destabilizing role for any values of the problem parameters and studied the dynamical stability of the rectilinear shape of the beam by means of the direct Lyapunov method. In [5], the extended Hamilton principle was employed to derive the equations of motion of a rotating beam with a tip mass undergoing coupled torsional-bending vibrations and analyzing the exact frequencies leading to a better control of the system.
Recently, the nonlinear vibration of a rotating beam with a tip mass has been studied by numerous researchers. Yang et al. [6] presented a finite element model for a flexible hub-beam system with a tip mass where viscous damping of the hub and the air drag force were considered. They showed that the traditional linear model cannot account for the dynamic stiffening and it may lead to erroneous...