Variational formulation for Timoshenko beam element by separation of deformation mode

Lee, Seok-Soon; Koo, Jeong-Seo; Choi, Jin-Min

doi:10.1002/cnm.1640100804

Cited by 17 publications

(9 citation statements)

References 12 publications

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“…This is done by using one Gauss point in the integration instead of 3. The Timoshenko beam element yields the exact solution for the deflection of a thick beam ͑even with one element͒, 17 while the other elements deviate significantly ͑particularly the Euler element͒ unless a large number of elements are used. The different elements will be compared in Sec.…”

Section: Study Of a Gearboxmentioning

confidence: 99%

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Mobility analysis of structure-borne noise power flow through bearings in gearbox-like structures

Rook¹,

Singh²

1996

Noise Control Eng. J.

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A narrow-band vibratory power flow calculation procedure based on the mobility method is described which recognizes rolling element bearings as a multi-dimensional compliant and dissipative connection. A gearbox with rigid casing, compliant mounts, one spur gear pair, and four bearings is analyzed and concepts for reduced noise and vibration are identified. Some pertinent modeling issues that are related to the truncated modal bases of components being synthesized are discussed. An experimental system which conceptually simulates the structure-borne noise phenomena of a gearbox is also studied. The proposed theory has been found to agree well with limited measurements. © 1996 Institute of Noise Control Engineering.

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Section: Study Of a Gearboxmentioning

confidence: 99%

“…The shape functions for these different beam elements are given elsewhere. 14,17 The Mindlin beam is the easiest to formulate, while the Timoshenko is the most dif-ficult. However the Mindlin beam is prone to shear locking unless reduced integration is used.…”

Section: Study Of a Gearboxmentioning

confidence: 99%

Mobility analysis of structure-borne noise power flow through bearings in gearbox-like structures

Rook¹,

Singh²

1996

Noise Control Eng. J.

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“…Vibrations of shear deformable beams have been of interest to the researchers for many years since they are found in wide application of various problems in mechanical, aeronautical and structural engineering. The majority of the available publications are based on the analytical and numerical solution of shear deformable beams [2][3][4][5][6][7][8][9][10][11][12]. In the past 10 years, the methods of differential quadrature (DQ), discrete singular convolution (DSC) and meshless methods have become increasingly popular in the numerical solution of initial and boundary value problems [13][14][15][16][17][18][19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Free vibration analysis of Timoshenko beams by DSC method

Cívalek

Kiracioglu

2009

Numer Methods Biomed Eng

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SUMMARYFree vibration analysis of Timoshenko beams has been presented. Discrete singular convolution method is used for numerical solution of equation of motion of Timoshenko beam. Clamped, pinned and sliding boundary conditions and their combinations are taken into account. Typical results are presented for different parameters and boundary conditions. Numerical results are presented and compared with that available in the literature. It is shown that very good results are obtained. This method is very effective for the study of vibration problems of Timoshenko beam.

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“…Theoretical proofs have been made for both problem with single variable [1] and that with multiple variables [2]. Elements that can be used to produce exact solutions for linear static analysis have also been developed based on different formulations; see, for example, [2][3][4][5]. For dynamic analysis, on the other hand, performance of these elements is not as good as desired.…”

Section: Introductionmentioning

confidence: 99%

Exact solution of vibration problems of frame structures

2008

Numer Methods Biomed Eng

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SUMMARYAlthough exact solutions for linear static analysis of most frame structures can be obtained by the finite element method, it is very difficult to get exact solutions for free vibration and harmonic analyses for nontrivial cases. This paper extends an earlier study on exact solutions of axial vibration problems of elastic bars to dynamic analyses of elastic frame structures. New shape functions for the transverse displacement field are constructed by using the homogeneous governing equations and then a novel beam element is formulated. Combining the new (bending) beam element and the one developed earlier for elastic bars yields a new element for general frame structures. The new frame element can be used to get exact solutions for both natural frequency and undamped harmonic analyses of frame structures. Illustrative examples are presented to demonstrate the effectiveness of the new element and the algorithm.

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Variational formulation for Timoshenko beam element by separation of deformation mode

Cited by 17 publications

References 12 publications

Mobility analysis of structure-borne noise power flow through bearings in gearbox-like structures

Mobility analysis of structure-borne noise power flow through bearings in gearbox-like structures

Free vibration analysis of Timoshenko beams by DSC method

Exact solution of vibration problems of frame structures

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