• Journal of Mechanical Science and Technology
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• v.18 no.2
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• pp.246-252
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• 2004

The modal characteristics of rotating structures vary with the rotating speed. The material and the geometric properties of the structures as well as the rotating speed influence the variations of their modal characteristics. Very often, the modal characteristics of rotating structures need to be specified at some rotating speeds to meet their design requirements. In this paper, rotating cantilever beam is chosen as a design target structure. Optimization problems are formulated and solved to find the optimal shapes of rotating beams with rectangular cross section.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.19 no.6
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• pp.591-598
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• 2009

Starting from the rotating beam finite element in which the interpolating shape functions satisfy the governing static homogeneous differential equation of Euler-Bernoulli rotating beams, we derived new shape functions that satisfy 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 beams.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.14 no.1
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• pp.73-79
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• 2004

When structures undergo rotating motion, their modal characteristics often vary significantly. The variations of modal characteristics are determined from their geometric shapes and their rotating angular speed. Since the modal characteristics vary during the operation of the structures, they should be carefully scrutinized. In this paper, rotating cantilever beams are chosen as design targets which need to meet some specific design requirements. The thickness and the width of the rotating beams are assumed as multi-stage spline functions and the stage values for the thickness and the width are used as design variables for the optimization problems.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.11a
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• pp.684-689
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• 2003

When structures undergo rotating motion, their modal characteristics often vary significantly. The variations of modal characteristics are determined from their geometric shapes and their rotating angular speed. Since the modal characteristics vary during the operation of the structures, they should be carefully scrutinized. In this paper, rotating cantilever beams are chosen as design targets which need to meet some specific design requirements. The thickness and the width of the rotating beams are assumed as multi-stage spline functions and the stage values for the thickness and the width are used as design variables for the optimization problems.

• Proceedings of the KSME Conference
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• 2007.05a
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• pp.1045-1050
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• 2007

Equations of motion of rotating cantilever curved beams are derived based on a dynamic modeling method developed in this paper. The Kane's method is employed to derive the equations of motion. Different from the classical linear modeling method which employs two cylindrical deformation variables, the present modeling method employs a non-cylindrical variable along with a cylindrical variable to describe the elastic deformation. The derived equations (governing the stretching and the bending motions) are coupled but linear. So they can be directly used for the vibration analysis. The coupling effect between the stretching and the bending motions which could not be considered in the conventional modeling method is considered in this modeling method. The natural frequencies of the rotating curved beams versus the rotating speed are calculated for various radii of curvature and hub radius ratios.

• 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.

• Structural Engineering and Mechanics
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• v.54 no.3
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• pp.419-432
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• 2015

The free vibration of rotating Euler-Bernoulli beams with the thickness and/or width of the cross-section vary linearly along the length is investigated by using the Adomian modified decomposition method (AMDM). Based on the AMDM, the governing differential equation for the rotating tapered beam becomes a recursive algebraic equation. By using the boundary condition equations, the dimensionless natural frequencies and the closed form series solution of the corresponding mode shapes can be easily obtained simultaneously. The computed results for different taper ratios as well as different offset length and rotational speeds are presented in several tables and figures. The accuracy is assured from the convergence and comparison with the previous published results. It is shown that the AMDM provides an accurate and straightforward method of free vibration analysis of rotating tapered beams.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.2
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• pp.348-353
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• 1995

When cantilever beams rotate, their bending stiffnesses change due to the stretching caused by centrifugal inertia forces. Such phenomena result in variations of natural frequencies and mode shapes associated with constant speed rotational motions of the beams. These variations are important in many practical applications such as helicopter blades, turbomachines, and space structures. This paper presents the formulation of a set of linear equations governing the flapwise bending vibration of rotating cantilever beams. These equations can be used to provide accurate predictions of the variations of natural frequencies and mode shapes due to rotation.

• 제어로봇시스템학회:학술대회논문집
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• 1990.10a
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• pp.382-387
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• 1990

In this paper, the dynamic modeling and tip position of rotating Timoshenko beam analyzed by means of FEM (finite element method) and Hyperstability MRAC(model referenced adaptive control) technique of each other. The governing equations of the rotating beams are drived from Hamilton's principle. The dynamic model of this multi-link is drived by Lagrange approach. The shear deformation and rotary inertia are incorporated into a finite element model for determining the bending frequencies of the rotating beam. Simulation results for uniform cantilever beams by using the MRAC are compared with the available results. It will be shown that the proposed method offers an accurate and effective one to solve the free vibration problems of rotating beams' stability.

• Journal of KSNVE
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• v.10 no.6
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• pp.1022-1028
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• 2000

This paper presents a modeling method for the vibration analysis of rotating cantilever beams considering the elastic foundation effect. Mass and stiffness matrices are derided explicitly by considering coupling effect between stretching and bonding motion. Numerical results show that the bending direction elastic foundation stiffness influences the vibration characteristics significantly in practical range of beam configuration. The ranges of elastic foundation stiffness to avoid the dynamic buckling are also presented. The method presented in this paper can be used to predict the variations of natural frequencies of rotating cantilever beams with elastically restrained root.