Large amplitude free vibration analysis of Timoshenko beams using a relatively simple finite element formulation

Gunda, Jagadish Babu; Gupta, Rekha; Janardhan, G. Ranga; Rao, G. Venkateswara

doi:10.1016/j.ijmecsci.2010.07.009

Cited by 26 publications

(17 citation statements)

References 22 publications

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“…Similar problems for carbon nanotubes were solved by Yang et al in [15]. A solution to the nonlinear vibration problem by means of the nonlinear finite element method was presented by Gunda et al in [16]. The problem of the nonlinear vibration of the Timoshenko beam-column partially supported on the tensionless Winkler foundation was described by Sapountzakis and Kampitsis in [17].…”

Section: Introductionmentioning

confidence: 90%

Nonlinear analysis of nonprismatic Timoshenko beam for different geometric nonlinearity models

Ruta

Szybiński

2015

International Journal of Mechanical Sciences

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Section: Introductionmentioning

confidence: 90%

Nonlinear analysis of nonprismatic Timoshenko beam for different geometric nonlinearity models

Ruta

Szybiński

2015

International Journal of Mechanical Sciences

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“…NL H / presented in Table 6 are obtained on the basis of SHM assumption and these expressions can be corrected by using the harmonic balance method (HBM) discussed in Refs. [16,17]. The non-linear frequency parameters .…”

Section: Z âZmentioning

confidence: 99%

“…Large amplitude free vibration behavior of plates [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] have received considerable attention by various researchers due to its relative importance to the field of structural engineering. Leung and Mao [7] applied an Hamilton's formulation and symplectic integration methods to investigate the non-linear vibration behavior of beams and plates.…”

Section: Introductionmentioning

confidence: 99%

Large Amplitude Free Vibration Analysis of Thin Rectangular Plates: Simple Closed-form Solutions

Gunda¹

2013

Nonlinear Engineering

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Large amplitude free vibration behavior of thin, isotropic rectangular plate configurations are expressed in the form of simple closed-form solutions by using an application of the Ritz method based on coupled displacement fields. Influence of plate aspect ratio a b and Poisson ratio . / on the behavior of back-bone curves is briefly discussed for various boundary configurations of the rectangular plate. Proposed closed-form solutions are corrected for the simple harmonic motion (SHM) assumption using the well established harmonic balance method which is applicable for the homogeneous form of cubic non-linear Duffing equation.Keywords. Large amplitude free vibration, Thin rectangular plates, Ritz method, Closed-form solutions, Coupled displacement fields, von-Kármán type of geometric nonlinearity, Non-linear frequency. Nomenclature a = length of the rectangular plate b = width of the rectangular plate C = axial rigidity of the plate E h .1 2 / Á D = flexural rigidity of the plate E h 3 12.1 2 / Á E = Young's modulus h= thickness of the plate N x , N y and N xy = in-plane stress resultants M x , M y and M xy = moment resultants u = displacement in x-direction v = displacement in y-direction U = strain energy of the plate w = transverse displacement T = kinetic energy of the plate x, y = in-plane co-ordinates z 1 = maximum reference amplitude of the rectangular plate z 1 h = maximum reference amplitude to thickness ratio x , y and xy = in-plane strain terms L = linear frequency parameter h! L 2 a 4 4 D Á NL H = non-linear frequency parameter obtained on the basis of SHM assumption Â h! NL H 2 a 4 4 D Ã NL = non-linear frequency parameter h! NL 2 a 4 4 D Á = Poisson ratiox , y and xy = curvature terms Subscripts L = linear NL = non-linear NL H = non-linear based on harmonic motion assumption x = partial derivative with respect to x xx = second partial derivative with respect to x y = partial derivative with respect to y yy = second partial derivative with respect to y xy = partial derivative with respect to x and y 1 Introduction

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“…The beams are also used to model rotating blades dynamics, for example blades of a helicopter rotor [4,5] or blades of turbines. Many authors use the classical FEM [6,7] and semi-analytical methods [8,9] to study this problem.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear dynamics of a reduced multimodal Timoshenko beam subjected to thermal and mechanical loadings

2014

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Large amplitude vibrations of a Timoshenko beam under an influence of temperature are analysed in this paper. In the considered model the temperature increases instantly and the heat is uniformly distributed along the beams length and crosssection. The mathematical model, represented by partial differential equations takes into account thermal and mechanical loadings. Next, the problem is reduced by means of the Galerkin method, considering the first three natural vibration modes of a simply supported beam in the both ends. The influence of the temperature on amplitudes and localisation of the resonance zones and stability of the solutions is studied numerically and analytically by the multiple time scale method. The bifurcation points, existence of unstable lobes and transition from regular to chaotic oscillations are shown.

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Large amplitude free vibration analysis of Timoshenko beams using a relatively simple finite element formulation

Cited by 26 publications

References 22 publications

Nonlinear analysis of nonprismatic Timoshenko beam for different geometric nonlinearity models

Nonlinear analysis of nonprismatic Timoshenko beam for different geometric nonlinearity models

Large Amplitude Free Vibration Analysis of Thin Rectangular Plates: Simple Closed-form Solutions

Nonlinear dynamics of a reduced multimodal Timoshenko beam subjected to thermal and mechanical loadings

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