Coupled bending-bending vibrations of pretwisted tapered cantilever beams treated by the Reissner method

Subrahmanyam, K.B.; Rao, J. S.

doi:10.1016/0022-460x(82)90408-4

Cited by 36 publications

(8 citation statements)

References 19 publications

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“…Gupta and Rao [21] and Abbas [22] used the "nite element method to determine the natural frequencies of uniformly pretwisted tapered cantilever blading. Subrahmanyam et al [23] and Subrahmanyam and Rao [24] used the "nite element method and the Reissner method to determine the natural frequencies of uniformly pretwisted tapered cantilever blading respectively. Celep and Turhan [25] used the Galerkin method to investigate the in#uence of non-uniform pretwisting on the natural frequencies of uniform cross-sectional cantilever or simply supported beams.…”

Section: Introductionmentioning

confidence: 99%

The Forced Vibration and Boundary Control of Pretwisted Timoshenko Beams With General Time Dependent Elastic Boundary Conditions

Lin¹,

Lee

2002

Journal of Sound and Vibration

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Section: Introductionmentioning

confidence: 99%

The Forced Vibration and Boundary Control of Pretwisted Timoshenko Beams With General Time Dependent Elastic Boundary Conditions

Lin¹,

Lee

2002

Journal of Sound and Vibration

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“…Swaminathan and Rao [15] described the vibrations of a rotating pretwisted and tapered blade. Subrahmanyam et al [16,17] derived the natural frequencies and mode shapes of a uniform pretwisted cantilever blade using the Reissner approach. Chen and Keer [18] examined the transverse vibrations of a rotating pretwisted Timoshenko beam under axial loading.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Analysis of Wind Turbine Blades Using Radial Basis Functions

Hsu

2011

Advances in Acoustics and Vibration

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Wind turbine blades play important roles in wind energy generation. The dynamic problems associated with wind turbine blades are formulated using radial basis functions. The radial basis function procedure is used to transform partial differential equations, which represent the dynamic behavior of wind turbine blades, into a discrete eigenvalue problem. Numerical results demonstrate that rotational speed significantly impacts the first frequency of a wind turbine blade. Moreover, the pitch angle does not markedly affect wind turbine blade frequencies. This work examines the radial basis functions for dynamic problems of wind turbine blade.

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“…Sato [20] used the Ritz method to study the transverse vibration of a linearly tapered beam with ends constrained elastically against rotation and subjected to an axial force. Subrahmanyama and Rao [21] determined the natural frequencies and mode shapes of a pretwisted tapered blading using the Reissner method. Lau [22] studied the free vibrations of a tapered beam with an end mass using the exact method.…”

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confidence: 99%

Free flapewise vibration analysis of rotating double-tapered Timoshenko beams

Zhu

2011

Arch Appl Mech

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Free vibration analysis of a rotating double-tapered Timoshenko beam undergoing flapwise transverse vibration is presented. Using an assumed mode method, the governing equations of motion are derived from the kinetic and potential energy expressions which are derived from a set of hybrid deformation variables. These equations of motion are then transformed into dimensionless forms using a set of dimensionless parameters, such as the hub radius ratio, the dimensionless angular speed ratio, the slenderness ratio, and the height and width taper ratios, etc. The natural frequencies and mode shapes are then determined from these dimensionless equations of motion. The effects of the dimensionless parameters on the natural frequencies and modal characteristics of a rotating double-tapered Timoshenko beam are numerically studied through numerical examples. The tuned angular speed of the rotating double-tapered Timoshenko beam is then investigated. IntroductionThe modal characteristics, i.e., the natural frequencies and the corresponding mode shapes, of rotating beams, especially tapered ones, are critical to the design and analysis of rotating structures, such as the rotating machinery, helicopter blades, wind turbine blades, etc., since most rotating beams in engineering applications are tapered. The modal characteristics of rotating beams often vary significantly from those of non-rotating beams due to the influence of centrifugal inertia force. Due to this significant variation of modal characteristics resulted from rotation, the modal characteristic of rotating beams has been widely investigated.Study of the modal characteristics of rotating beams originated from the pioneering work of Southwell and Gough [1]. Based on the Rayleigh energy theorem, an equation, known as the Southwell equation, that relates the natural frequency to the rotating frequency of a uniform beam was developed. This study was further extended by Liebers [2], Theodorsen [3] and Schilhansl [4], to obtain more accurate natural frequencies of rotating beams. However, due to the large amount of calculation and lack of computational devices, the mode shapes were not available in these investigations. Later, using digital computers, investigations in mode shapes and more accurate natural frequencies were published for uniform rotating and non-rotating beams [5][6][7][8][9][10][11][12][13].The modal characteristics of rotating and non-rotating tapered beams have also been widely investigated. Hodges and Dowell [14] derived the non-linear equations of motion of twisted non-uniform rotor blades based on the Hamilton's Principle and the Newtonian method. Klein [15] analyzed the vibration of a non-rotating tapered beam with a method which combined the advantages of a finite element approach and of a RayleighRitz analysis. Downs [16] applied a dynamic discretization technique to calculate the natural frequencies of a

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Coupled bending-bending vibrations of pretwisted tapered cantilever beams treated by the Reissner method

Cited by 36 publications

References 19 publications

The Forced Vibration and Boundary Control of Pretwisted Timoshenko Beams With General Time Dependent Elastic Boundary Conditions

The Forced Vibration and Boundary Control of Pretwisted Timoshenko Beams With General Time Dependent Elastic Boundary Conditions

Dynamic Analysis of Wind Turbine Blades Using Radial Basis Functions

Free flapewise vibration analysis of rotating double-tapered Timoshenko beams

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