Abstract
Dynamic characteristics of a flexible hub-beam system with a tip mass under gravity loads are investigated. The slope angle of the centroid line of the beam is utilized to describe its motion. Hamilton’s principle is used to derive the equations of motion and their boundary conditions. By using Lagrange’s equations, spatially discretized equations based on assumed mode method are derived, and the equations of motion are expressed in nondimensional matrix form. The incremental harmonic balance (IHB) method is used to solve for periodic responses of a high-dimensional model of the rotating hub-beam system with a tip mass for which convergence is reached. A frequency equation is derived giving the relationship between the nondimensional natural frequencies and three nondimensional parameters, that is, the rotating angular velocity, the tip mass, and the hub radius ratio. A comparative study is performed for nonlinear frequency responses of the system with a tip mass under different values of tip masses and damping ratios.
Highlights
A number of systems in the fields of navigation and mechanical engineering can be modeled as rotating hub-beam system with a tip mass
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
To investigate the bending vibration natural frequencies of the rotating beam at various rotational velocities mtg under different values of tip masses and hub radius ratios, natural frequencies of the rotating beam can be approximated by neglecting the nonlinear terms, the damping terms, and gravity loads in (27)
Summary
A number of systems in the fields of navigation and mechanical engineering can be modeled as rotating hub-beam system with a tip mass. 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. 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. 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
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