Geometrically Non-Linear Analysis of a Thick Annular Plate With Elastically Constrained Edge Using Galerkin's Method

Dumir, P.C.; Dube, G.

doi:10.1006/jsvi.2001.3598

Cited by 3 publications

(1 citation statement)

References 9 publications

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“…An investigation of geometrically non-linear thin plates has been reported recently, with introduction of an approximate approach [9]. An investigation of a geometrically non-linear thick annular plate with elastic constrained edges has also been conducted in recent research [10]. The forced response of a nearly square plate, non-linear dynamics of a shallow arch, and the chaotic motion of a circular plate and cylindrical shells are other examples of recent studies on non-linear aspects of mechanical and structural systems [11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Chaotic response of a Galerkin shell to constant load and periodic excitation

Dai

Han

Dong

2005

Proceedings of the Institution of Mechanical Engineers, Part K:

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This study intends to investigate the dynamic behaviour of a non-linear elastic shallow shell of large deflection subjected to constant boundary loading and harmonic lateral excitation. The general governing equation for the shell is established using the Galerkin Principle. Three types of dynamic equation of the shell are developed, corresponding to certain geometry and loading conditions. Melnikov functions are considered for each type. Non-linear responses of the shell to the loads are analysed theoretically. Centre points, saddle points, and homoclinic orbits are determined and analysed on the basis of the governing equations established. The critical conditions for chaos to occur are provided for the vibrations of the shell. Numerical analysis is also performed for the non-linear elastic shell. Chaotic and regular vibrations of the shell are analysed with presentations of time history plots, phase diagrams, and Poincaré maps.

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Section: Introductionmentioning

confidence: 99%

Chaotic response of a Galerkin shell to constant load and periodic excitation

Dai

Han

Dong

2005

Proceedings of the Institution of Mechanical Engineers, Part K:

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Bifurcation and Chaotic Motion of an Elastic Plate of Large Deflection Under Parametric Excitation

Han

Dai

Dong

2005

Int. J. Bifurcation Chaos

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The dynamic behavior of a nonlinear elastic rectangular plate of large deflection subjected to harmonic excitation is investigated. Using the Galerkin principle, a double mode model is established for the plate. The stability and bifurcation behavior of the plate is studied in detail for various loading conditions and system parameters. A set of autonomous equations is derived with the method of averaging. The bifurcation behavior is examined on the basis of the autonomous equations, and the results of theoretical bifurcation analysis are numerically verified. The chaotic response of the plate to the external excitation is also investigated. The governing equations of single as well as double modes are established and the comparison between the single and double mode models is carried out. The applicable conditions of the single mode method are provided. The results obtained show that the single mode approach usually used may lead to incorrect conclusions under certain conditions.

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Assessment of Rpim Shape Parameters for Solution Accuracy of 2d Geometrically Nonlinear Problems

Bozkurt

Kanber

Aşık

2013

Int. J. Comput. Methods

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This study discussed the effects of shape parameters on the radial point interpolation method (RPIM) accuracy in 2D geometrically nonlinear problems. Four finite deformation problems with compressible Neo-Hookean material are numerically solved with the RPIM algorithm using the multi-quadric (MQ) radial basis function. Both regular and irregular node distributions are used. Their displacements and Cauchy stresses are compared for different values of shape parameters and monomial basis. It is found that the shape parameters proposed for linearly elastic problems (q = 1.03, αc = 4) can still be applicable to 2D geometrically nonlinear problems but careful selections should be made for the calculation of stress. For example, when q is used as 1.75 with irregular node distributions, stresses can be calculated more precisely.

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Geometrically Non-Linear Analysis of a Thick Annular Plate With Elastically Constrained Edge Using Galerkin's Method

Cited by 3 publications

References 9 publications

Chaotic response of a Galerkin shell to constant load and periodic excitation

Chaotic response of a Galerkin shell to constant load and periodic excitation

Bifurcation and Chaotic Motion of an Elastic Plate of Large Deflection Under Parametric Excitation

Assessment of Rpim Shape Parameters for Solution Accuracy of 2d Geometrically Nonlinear Problems

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