• Journal of KSNVE
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• v.6 no.2
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• pp.179-185
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• 1996

This paper presents a modeling method for the vibration analysis of a rotating beam the slenderness ratio of which is relatively small. The smaller the slenderness ratio becomes, the larger the shear and rotary inertia effects become. Such effects become critical for the accurate estimation of the natural frequencies and modeshapes, especially higher frequencies and modes, as the angular speed increases. It is also shown that the effects are important for the accurate estimation of the critical angular speed of the beam.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2014.10a
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• pp.389-391
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• 2014

The Vibration Analysis of Rotating Inward Beams Considering The Tip-Mass is presented based on Euler-Bernoulli beam theory. The frequency equations, which are coupled through gyroscopic coupling terms, are calculated using hybrid deformation variable modeling along with the Rayleigh-Ritz assumed mode methods. In this study, resulting system of ordinary differential equations shows the effects of angular speed, and Young's modulus ratio. It is believed that the results will be a reference with which other researchers and commercial FE analysis program, ANSYS can compare their results.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.8
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• pp.2516-2523
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• 1996

The equations of motion for rotating contilever beams with a concentrated mass loated in an arbitrary position are derived. For the modeling of the concentrated mass the Dirac delta function is used for the mass density function. Parametric studies are performed with five dimensionless variables ; natural frequencies, angular velocity, hub radius, concentrated mass, and the mass location. The concentrated mass, whereverit may locate, lowers the natural frequencies of a stationaly beam. However, when the beam rotates, the natural frequencies(if they increase or decrease) are dictated by the location of the concentrated mass.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.18 no.1
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• pp.101-109
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• 2008

The stability of a rotating cantilever pipe conveying fluid with a crack and tip mass is investigated by the numerical method. That is, the effects of the rotating angular velocity, mass ratio, crack severity and tip mass on the critical flow velocity for flutter instability of system are studied. The equations of motion of rotating pipe are derived by using the Euler-Bernoulli beam theory and the extended Hamilton's principle. The crack section of pipe is represented by a local flexibility matrix connecting two undamaged pipe segments. Also, the crack is assumed to be in the first mode of fracture and always opened during the vibrations. When the tip mass and crack are constant, the critical flow velocity for flutter is proportional to the rotating angular velocity of pipe. In addition, the stability maps of the rotating pipe system as a rotating angular velocity and mass ratio ${\beta}$ are presented.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2000.11a
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• pp.527-533
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• 2000

It is investigated that the characteristics of rotating cantilevered composite beam with a breathing crack. In the present study, the crack is modeled as a breathing crack which opens and closes with the motion of the unidirectional graphite-fiber reinforced polyimide beam. For the finite element analysis, the cracked element is modelled by the local flexibility matrix calculated on the basis of fracture mechanics using Castiligano theorem. Rotating beam is considered only transverse bending motion so that the element includes two degrees of freedom per node such as the transverse deflection and slope. The time history and frequency response function of the beam with a breathing crack are studied by Newmark direct time integration method and FFT(Fast Fourier Transform)simulation. Effects of various parameters such as the crack depths, crack locations, ply angles, volume fraction ratios, and rotating speeds of the beam are also studied. Numerical results indicate that it is more reliable to be modelled as a breathing crack than an open crack.

• Journal of Mechanical Science and Technology
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• v.18 no.2
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• pp.240-245
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• 2004

A modeling method for the modal analysis of a rotating composite cantilever beam is presented in this paper. Linear differential equations of motion are derived using the assumed mode method. For the modeling, hybrid deformation variables are employed and approximated to derive the equations of motion. Symmetrical laminated composite beams are considered to obtain the numerical results. The effects of the dimensionless angular velocity, the hub radius and the fiber orientation angle on the variations of modal characteristics are investigated.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2009.04a
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• pp.573-578
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• 2009

Starting from the rotating beam finite element in which the interpolating shape functions satisfies the governing static homogeneous differential equation of Euler-Bernoulli rotating beams, we derived new shape functions that satisfies the governing differential equation which contains the terms of hub radius and setting angle. The shape functions are rational functions which depend on hub radius, setting angle, rotational speed and element position. Numerical results for uniform and tapered cantilever beams with and without hub radius and setting angle are compared with the available results. It is shown that the present element offers an accurate method for solving the free vibration problems of rotating beam.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2001.05a
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• pp.115-120
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• 2001

A gyroscope is a rotating body possessing one axis of symmetry and whose rotation about the symmetry axis is relatively large compared with the rotation about any other axis. Tuning fork is this type of structure that various modem gyro-sensors are based on. In this paper, dynamic behavior of a cantilevered beam subjected ta a base rotation with respect to the eccentric axis that is parallel to the beam axis is analyzed. The final equations of motion in terms of generalized coordinates can be solved with numerical scheme with various values of angular velocities and angular accelerations of the rotating axis. In contrast to the case of rotating cantilever beam like helicopter blade, the rotational motion with respect to the beam axis has effect to decrease the stiffness of the beam and has unstable region depending on the magnitude of the rotational angular velocity and angular acceleration.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.21 no.10
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• pp.1580-1588
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• 1997

A modeling method for the flapwise bending vibration of a rotating cantilever beam which has small slenderness ratio is presented in this paper. It is shown that as the slenderness ratio decreases the shear and rotary inertia effects increase. Such effects become critical for the accurate estimation of the natural frequencies and modeshapes, especially higher frequencies and modes, as the angular speed increases. It is also shown that the flapwise bending natural frequencies are higher than the chordwise bending natural frequencies. The discrepancy between first natural frequencies are especially significant when the hub radius ratio is small.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.7 s.178
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• pp.1826-1832
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• 2000

A modelling method for the bending vibration analysis of rotating cantilever beams employing finite element method is presented in this paper. Different from the conventional modelling method in wh ich only Cartesian deformation variables are used, a non-Cartesian deformation variable is introduced and approximated to derive the equations of motion. Numerical results obtained by using the presented modelling method are compared to those obtained by using other methods in the related literature, and the accuracy of the presented method is verified through the comparison study. The presented modelling method is superior to other previous methods in a sense that several advantages of the previous methods are incorporated into the presented method.