Three-dimensional nonlinear vibrations of composite beams — I. Equations of motion

Pai, P. Frank; Nayfeh, Ali H.

doi:10.1007/bf01856950

Cited by 61 publications

(27 citation statements)

References 21 publications

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“…Stearman et al [75] studied resonances in aeroelastic systems, and showed that both combination-type and parametric resonances can occur. These resonances occurred if…”

Section: Nonlinear Internal Resonance Behaviormentioning

confidence: 98%

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Dowell

2015

A Modern Course in Aeroelasticity

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“…Stearman et al [75] studied resonances in aeroelastic systems, and showed that both combination-type and parametric resonances can occur. These resonances occurred if…”

Section: Nonlinear Internal Resonance Behaviormentioning

confidence: 98%

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Dowell

2015

A Modern Course in Aeroelasticity

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“…Da Silva in [102,103] presented the nonlinear flexural-torsional-extensional vibrations of Euler-Bernoulli doubly symmetric thin-walled closed cross section beams, primarily focusing on flexural vibrations and neglecting the effect of torsional warping. Pai and Nayfeh in [104][105][106] studied also the nonlinear flexuraltorsional-extensional vibrations of metallic and composite slewing or rotating closed cross section beams, primarily focusing on flexural vibrations and neglecting again the effect of torsional warping. Di Egidio et al in [107,108] presented also a FEM solution to the nonlinear flexuraltorsional vibrations of shear undeformable thin-walled open beams taking into account in-plane and out-of-plane warpings and neglecting warping inertia.…”

Section: Nonlinear Elastic Torsional Vibrations Of Barsmentioning

confidence: 99%

Bars under Torsional Loading: A Generalized Beam Theory Approach

Sapountzakis

2013

ISRN Civil Engineering

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In this paper both the static and dynamic analyses of the geometrically linear or nonlinear, elastic or elastoplastic nonuniform torsion problems of bars of constant or variable arbitrary cross section are presented together with the corresponding research efforts and the conclusions drawn from examined cases with great practical interest. In the presented analyses, the bar is subjected to arbitrarily distributed or concentrated twisting and warping moments along its length, while its edges are supported by the most general torsional boundary conditions. For the dynamic problems, a distributed mass model system is employed taking into account the warping inertia. The analysis of the aforementioned problems is complete by presenting the evaluation of the torsion and warping constants of the bar, its displacement field, its stress resultants together with the torsional shear stresses and the warping normal and shear stresses at any internal point of the bar. Moreover, the construction of the stiffness matrix and the corresponding nodal load vector of a bar of arbitrary cross section taking into account warping effects are presented for the development of a beam element for static and dynamic analyses. Having in mind the disadvantages of the 3D FEM solutions, the importance of the presented beamlike analyses becomes more evident.

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“…The excitation is along the direction of the width of the cross section, which is called the chordwise direction. The equations of motion [8,9] nondimensionalized using the length L of the beam and the characteristic time L2~33 are …”

Section: Equations Of Motion and Perturbation Solutionsmentioning

confidence: 99%

Three-dimensional nonlinear vibrations of composite beams ? III. Chordwise excitations

Pai

Nayfeh

1991

Nonlinear Dyn

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Three nonlinear integro-differential equations of motion derived in Part I are used to investigate the forced nonlinear vibration of a symmetrically laminated graphite-epoxy composite beam. The analysis focuses on the case of primary resonance of the first in-plane flexural (chordwise) mode when its frequency is approximately twice the frequency of the first out-of-plane flexural-torsional (flapwise-torsional) mode. A combination of the fundamental-matrix method and the method of multiple scales is used to derive four first-order ordinary-differential equations describing the modulation of the amplitudes and phases of the interacting modes with damping, nonlinearity, and resonances. The eigenvalues of the Jacobian matrix of the modulation equations are used to determine the stability of their constant solutions, and Floquet theory is used to determine the stability and bifurcations of their limit-cycle solutions. Hopf bifurcations, symmetrybreaking bifurcations, period-multiplying sequences, and chaotic motions of the modulation equations are studied. The results show that the motion can be nonplanar although the input force is planar. Nonplanar responses may be periodic, periodically modulated, or chaotically modulated motions.

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Three-dimensional nonlinear vibrations of composite beams — I. Equations of motion

Abstract: I>olx'lec/*#lir ' ht,vlilt~tt' and Slaw Unirer.~itv. Bl+.'k~l~ur Show more

Cited by 61 publications

References 21 publications

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Bars under Torsional Loading: A Generalized Beam Theory Approach

Three-dimensional nonlinear vibrations of composite beams ? III. Chordwise excitations

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