• Structural Engineering and Mechanics
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• v.34 no.2
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• pp.231-245
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• 2010

Vibration analysis of rotating beams is a topic of constant interest in mechanical engineering. The differential quadrature method (DQM) is used to obtain the natural frequencies of free transverse vibration of rotating beams. As it is known the DQM offers an accurate and useful method for solution of differential equations. And it is an effective technique for solving this kind of problems as it is shown comparing the obtained results with those available in the open literature and with those obtained by an independent solution using the finite element method. The beam model is based on the Timoshenko beam theory.

• Journal of KSNVE
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• v.8 no.2
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• pp.353-360
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• 1998

In this paper, a modeling method for the bending vibration analysis of rotating Timoshenko beams with concentrated mass and mass moment of inertia is presented. The shear and rotary inertia effects become critical for the accurate estimation of the natural frequencies and mode shapes as the slenderness ratio decreases. The natural frequencies obtained by using the Timoshenko beam theory are lower than those by using the Euler beam theory. The critical angular speed, which does not exist only with the concentrated mass, exists with the concentrated mass moment of inertia.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2000.06a
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• pp.689-694
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• 2000

This paper presents a modeling method for the vibration analysis of cantilever beams with an elastically restrained root. Mass and stiffness matrices are derived explicitly by considering the elastically restrained root coupling effect between stretching and bending motion. Numerical results show that the two effects influence the vibration characteristics of rotating beams significantly. The results also present the magnitude of the elastic stiffness of the root to avoid the dynamic buckling. The method presented in this paper can be used to provide accurate predictions of the variations of natural frequencies of rotating beams with an elastically restrained root.

• Journal of the Chungcheong Mathematical Society
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• v.5 no.1
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• pp.111-121
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• 1992

A new method(EVF method) is applied to get lower bounds to frequencies of rotating uniform beams which are clamped or simply supported at one end and free at the other. For the upper bounds, the Rayleigh-Ritz method is employed. Numerical results are presented.

• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.5
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• pp.891-898
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• 1992

When catilever beams rotate about axes perpendicular to the underformed beam's longitudinal axis, 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 lateral motion of rotating cantilever beams. These equations can be used to provide accurate predictions of the 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 lateral motion 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. This technique is simpler and more consistent than other conventional techniques which are commonly used in the literature.

• Structural Engineering and Mechanics
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• v.72 no.2
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• pp.229-244
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• 2019

Weak form integral equations are developed to investigate the flapwise bending vibration of the rotating beams. Rayleigh and Eringen nonlocal elasticity theories are used to investigate the rotatory inertia and Size-dependency effects on the flapwise bending vibration of the rotating cantilever beams, respectively. Through repetitive integrations, the governing partial differential equations are converted into weak form integral equations. The novelty of the presented approach is the approximation of the mode shape function by a power series which converts the equations into solvable one. Substitution of the power series into weak form integral equations results in a system of linear algebraic equations. The natural frequencies are determined by calculation of the non-trivial solution for resulting system of equations. Accuracy of the proposed method is verified through several numerical examples, in which the influence of the geometry properties, rotatory inertia, rotational speed, taper ratio and size-dependency are investigated on the natural frequencies of the rotating beam. Application of the weak form integral equations has made the solution simpler and shorter in the mathematical process. Presented relations can be used to obtain a close-form solution for quick calculation of the first five natural frequencies of the beams with flapwise vibration and non-local effects. The analysis results are compared with those obtained from other available published references.

• Structural Engineering and Mechanics
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• v.27 no.2
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• pp.243-257
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• 2007

A numerically efficient superelement is proposed as a low degree of freedom model for dynamic analysis of rotating tapered beams. The element uses a combination of polynomials and trigonometric functions as shape functions in what is also called the Fourier-p approach. Only a single element is needed to obtain good modal frequency prediction with the analysis and assembly time being considerably less than for conventional elements. The superelement also allows an easy incorporation of polynomial variations of mass and stiffness properties typically used to model helicopter and wind turbine blades. Comparable results are obtained using one superelement with only 14 degrees of freedom compared to 50 conventional finite elements with cubic shape functions with a total of 100 degrees of freedom for a rotating cantilever beam. Excellent agreement is also shown with results from the published literature for uniform and tapered beams with cantilever and hinged boundary conditions. The element developed in this work can be used to model rotating beam substructures as a part of complete finite element model of helicopters and wind turbines.

• Proceedings of the KSME Conference
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• 2000.04a
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• pp.613-618
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• 2000

It is well known that the rotating motion of a blade-like structure induces centrifugal inertia force that causes the variation of the natural frequencies of the structure. Even though most of blade-like structures can be successfully Idealized as beams, some behave like plates rather than beams. This paper presents a modeling method for the flapwise bending vibration analysis of rotating cantilever plates. The dependence of natural frequencies and free vibration modes on the angular speed as well as the aspect ratio of a rotating plate is investigated. Particularly. the natural frequency loci crossing is observed and discussed In the present study.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.11a
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• pp.670-676
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• 2004

In this paper, a modeling method for the vibration analysis of rotating structures composed of beams and shells employing multi-reference frames is presented. The rotary inertia effect and the geometric stiffening effect that results from centrifugal inertia force we considered for beams and shells with lumped mass model. In most previous studies, single reference frame has been employed for the vibration analysis. In the present study, a modeling method employing multi-reference frames is presented and the effects of employing multi-reference frames on the analysis accuracy are investigated through solving numerical examples.

• Structural Engineering and Mechanics
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• v.63 no.4
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• pp.471-480
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• 2017

This paper investigates free vibration characteristics of a rotating functionally graded (FG) beam in hygro environments. In the present study, material properties of the FG beam vary continuously through thickness direction according to the power-law which approximates material properties of FG beam. The governing differential equations of motion are derived based on Euler-Bernoulli beam theory and using the Hamilton's principle which solved utilizing a semi-analytical technique called the Differential Transform Method (DTM). In order to verify the competency and accuracy of the current analysis, a comparative study with previous researches are performed and good agreement is observed. Influences of Several important parameters such as power-law exponent, hygro environment, rotational speed and slenderness ratio on natural frequencies are investigated and discussed in detail. It is concluded that these effects play significant role on dynamic behavior of rotating FG beam in the hygro environments. Numerical results are tabulated in several tables and figures that can be serving as benchmarks for future analyses of rotating FG beams in the hygro environments.