Large amplitude vibration analysis of composite beams: Simple closed-form solutions

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

doi:10.1016/j.compstruct.2010.07.006

Cited by 54 publications

(30 citation statements)

References 27 publications

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“…For the sake of brevity, the HBM method is not discussed here and readers can refer to these Refs. [16][17][18] for more details on HBM.…”

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%

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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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“…For the sake of brevity, the HBM method is not discussed here and readers can refer to these Refs. [16][17][18] for more details on HBM.…”

Section: Z âZmentioning

confidence: 99%

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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“…For instance, Filipich, Rosales et al used the Fourier series and Timoshenko beam theory to calculate the exact values of natural frequencies [3]. Gunda, Gupta et al studied a large amplitude free vibration of uniform isotropic Timoshenko beams with geometric nonlinearity and all possible boundary conditions using the finite element method (FEM) and harmonic balance method [4]. An alternative approach was proposed by Liao and Zhong in [10]: nonlinear flexural vibration of tapered Timoshenko beams were calculated with the aid of the differential quadrature method.…”

Section: Related Papersmentioning

confidence: 99%

Vibrations of Functionally Graded Timoshenko Beams

Lepik

Hein

2014

Mathematical Engineering

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“…They used first order shear deformation theory (FSDT) and Ritz method to obtain the natural frequencies. Gunda et al [2011] investigated large amplitude vibration of laminated composite beams with symmetric and asymmetric layup orientations and axially immovable ends. They used CBT and solved the equations by Rayleigh-Ritz method.…”

Section: Introductionmentioning

confidence: 99%

Analytical Solution for Free Vibration of Laminated Curved Beam with Magnetostrictive Layers

Bayat

Jafari

Rahmani

2015

Int. J. Appl. Mechanics

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An analytical model to study the free vibration suppression of laminated curved beam with embedded actuating layers is presented in this study. The magnetostrictive layers are used to control and enhance the vibration suppression. The governing differential equations of the model are derived using the Hamilton principle. Analytical solution of the equations governing laminated curved beam with embedded magnetostrictive layers are obtained for simply-supported boundary conditions. Velocity feedback with constant gain distributed controller, by using Terfenol-D as smart material, is chosen to achieve vibration suppression. The effects of material properties, radius of curvature, lamination scheme, and placement of magnetostrictive layers with respect to laminate midplane on vibration suppression are studied in details.

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Large amplitude vibration analysis of composite beams: Simple closed-form solutions

Cited by 54 publications

References 27 publications

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

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

Vibrations of Functionally Graded Timoshenko Beams

Analytical Solution for Free Vibration of Laminated Curved Beam with Magnetostrictive Layers

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