Non-Linear Vibration of Timoshenko Beam Due to a Moving Force and the Weight of Beam

Wang, R.-T.; Chou, Tse-Heng

doi:10.1006/jsvi.1998.1827

Cited by 37 publications

(16 citation statements)

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“…Moreover, the beam deforms within the linear elastic range and therefore Hooke's laws are prevailing. In this study the Mindlin plate theory [11] is employed and the von-Karman's strain-displacement relations are as:…”

Section: Mathematical Modelingmentioning

confidence: 99%

“…n = 1 to 10. The reason for adopting the first ten modes is based on a separate convergence study on u(x,t), w(x,t) and ψ(x,t) which indicated that for n < 10 the obtained results will not be satisfactory [9,11].…”

Section: Verifications and Case Studiesmentioning

confidence: 99%

“…The linear vibration analysis using the Galerkin's technique for a Timoshenko beam traversed by a moving mass was applied in [9] and this work was verified by [10] using the linear finite element method. The effect of weight of the beam on the dynamic behavior of a horizontal simply supported Timoshenko beam subjected to moving forces was studied in [11] using the Galerkin's approach. The linear dynamic analysis of a simply-supported Timoshenko beam under the act of a moving mass has been studied in [12].…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear Dynamic Analysis of an Inclined Timoshenko Beam Subjected to a Moving Mass/Force with Beam’s Weight Included

Mamandi

Kargarnovin

2011

Shock and Vibration

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Abstract. In this study, the nonlinear vibrations analysis of an inclined pinned-pinned self-weight Timoshenko beam made of linear, homogenous and isotropic material with a constant cross section and finite length subjected to a traveling mass/force with constant velocity is investigated. The nonlinear coupled partial differential equations of motion for the rotation of warped cross-section, longitudinal and transverse displacements are derived using the Hamilton's principle. These nonlinear coupled PDEs are solved by applying the Galerkin's method to obtain dynamic responses of the beam. The dynamic magnification factor and normalized time histories of mid-point of the beam are obtained for various load velocity ratios and the outcome results have been compared to the results with those obtained from linear solution. The influence of the large deflections caused by a stretching effect due to the beam's fixed ends is captured. It was seen that existence of quadratic-cubic nonlinear terms in the nonlinear governing coupled PDEs of motion causes stiffening (hardening) behavior of the dynamic responses of the self-weight beam under the act of a traveling mass as well as equivalent concentrated moving force. Furthermore, in a case where the object leaves the beam, its planar motion path is derived and the targeting accuracy is investigated and compared with those from the rigid solution assumption.

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Section: Mathematical Modelingmentioning

confidence: 99%

Section: Verifications and Case Studiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Nonlinear Dynamic Analysis of an Inclined Timoshenko Beam Subjected to a Moving Mass/Force with Beam’s Weight Included

Mamandi

Kargarnovin

2011

Shock and Vibration

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show abstract

“…Among the few methods existing in the literature, we cite the following approaches with some representative works: the finite element method (Kapur, 1966;Hoa, 1979;Kolberg 1987), the Galerkin method (Wang and Chou, 1998;Dadfarnia et al, 2005), the Rayleigh-Ritz method (Oguamanam and Heppler, 1996), the Laplace transform method resulting in an integral form solution (Boley & Chao, 1955;Wang & Guan, 1994;Ortner & Wagner, 1996), and the eigenfunction expansion method, also referred to as the series or modal expansion method (Anderson, 1953;Dolph, 1954;Huang, 1961;Ekwaro-Osire et al, 2001;Loudini et al 2006;Loudini et al 2007a;Loudini et al 2007b). …”

Section: Derivation Of the Governing Equations Of Motionmentioning

confidence: 99%

Timoshenko Beam Theory based Dynamic Modeling of Lightweight Flexible Link Robotic Manipulators

Loudini¹

2010

Advances in Robot Manipulators

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“…(Lin, 1997) suggested the effects of both centrifugal and Coliolis forces should be taken into account to obtain the dynamic deflection. (Wang & Chou, 1998) conducted nonlinear vibration of Timoshenko beam due to a moving force and the weight of beam. Recently, (Wu, 2005) studied dynamic analysis of an inclined beam due to moving loads.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Responses and Active Vibration Control of Beam Structures Under a Travelling Mass

Ryu¹,

Kong²

2012

Advances on Analysis and Control of Vibrations - Theory and Applications

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Non-Linear Vibration of Timoshenko Beam Due to a Moving Force and the Weight of Beam

Cited by 37 publications

References 0 publications

Nonlinear Dynamic Analysis of an Inclined Timoshenko Beam Subjected to a Moving Mass/Force with Beam’s Weight Included

Nonlinear Dynamic Analysis of an Inclined Timoshenko Beam Subjected to a Moving Mass/Force with Beam’s Weight Included

Timoshenko Beam Theory based Dynamic Modeling of Lightweight Flexible Link Robotic Manipulators

Dynamic Responses and Active Vibration Control of Beam Structures Under a Travelling Mass

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