Large-deflection and large-amplitude free vibrations of laminated composite-material plates

Reddy, J. N.; Chao, Wu

doi:10.1016/0045-7949(81)90142-5

Cited by 81 publications

(5 citation statements)

References 29 publications

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“…Analytical investigations of multimode nonlinear vibrations of rectangular angle-ply and cross-ply plates were investigated by Chia and Prabhakara [8]. Reddy and Chao [30,31] and Reddy [29] used a finite-element method to study the nonlinear vibrations of laminated plates with all clamped and all simply supported edges. Nonlinear vibrations of an imperfect laminated plate were investigated by Kapania and Yang [17] using the finite-element method.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear combination resonances in cantilever composite plates

Nayfeh

1996

Nonlinear Dyn

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We experimentally investigated nonlinear combination resonances in two graphite-epoxy cantilever plates having the configurations (90/30/-30/-30/30/90L and (-75/75/75/-75/75/-75)~. As a first step, we compared the natural frequencies and modes shapes obtained from the finite-element and experimental-modal analyses. The largest difference in the obtained frequencies for both plates was 6%. Then, we transversely excited the plates and obtained force-response and frequency-response curves, which were used to characterize the plate dynamics. We acquired time-domain data for specific input conditions using an A/D card and used them to generate time traces, power spectra, pseudo-state portraits, and Poincarg maps. The data were obtained with an accelerometer monitoring the excitation and a laser vibrometer monitoring the plate response. We observed the external combination resonance f~ ~ a)2 -t-037 in the quasi-isotropic plate and the external combination resonance f~ ~ (1/2) (a~2 + cJs) and the internal combination resonance f~ ~ w8 ~ (1/2)(co2 + w13) in the +75 plate, where the wi are the natural frequencies of the plate and fZ is the excitation frequency. The results show that a low-amplitude high-frequency excitation can produce a high-amplitude low-frequency motion.

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Section: Introductionmentioning

confidence: 99%

Nonlinear combination resonances in cantilever composite plates

Nayfeh

1996

Nonlinear Dyn

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“…By the use of relation (12) and the same shape functions for the displacements u and v, the following strain-displacement relations are defined: …”

Section: Appendix: Strain-displacement Relationsmentioning

confidence: 99%

“…For example, in Ref. 12, the large deflection bending and large-amplitude free vibrations of laminated composite and isotropic plates are analyzed by the finite element method, following the first-order shear deformation theory. Chen and Liu studied the static deflections and linear natural frequencies of isotropic and laminated composite Mindlin plates using a Levy-type solution (see Ref.…”

Section: Introductionmentioning

confidence: 99%

First-Order Shear Deformation, p-Version, Finite Element for Laminated Plate Nonlinear Vibrations

Ribeiro

2005

AIAA Journal

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A p-version, hierarchical finite element for moderately thick composite laminated plates is presented, where the effects of the rotary inertia, transverse shear, and geometrical nonlinearity are taken into account. The timedomain free-vibration equations of motion are obtained by applying the principle of virtual work. Those equations are mapped into the frequency domain by the harmonic balance method and solved by a predictor-corrector procedure. The linear natural frequencies of vibration of several plates are determined, and the convergence properties of the element are investigated. It is shown that the element is not prone to shear locking and that a moderate number of degrees of freedom is sufficient for accuracy. The influences of the plate's thickness, of the width to length ratio, and of the fiber orientation on nonlinear free vibrations are investigated.

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“…This theory incorporates geometrical nonlinearity in the form of von Karman strains (see Refs. [14][15][16].…”

Section: Introductionmentioning

confidence: 98%

Free vibration behavior of spinning shear-deformable plates composedof composite materials

1990

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A first-order shear-deformation plate theory is used to predict the free vibration frequencies and mode shapes in spinning laminated composite plates. The theory accounts for geometric nonlinearity in the form of the von Karman strains and the effects of rotatory inertia. The plate is permitted to have an arbitrary orientation offset from the axis of rotation. A finite element model is developed to obtain numerical solutions to this class of problems. The model is validated by comparing the results for isotropic plates with those available in literature. The natural frequencies and mode shapes of isotropic and laminated composite plates as functions of angular velocity, pitch angle, and sweep angle are presented. Though the expected increase in frequency with angular velocity is observed for most modes, it is seen that there is a decrease in the free vibration frequency with angular velocity for torsional modes of swept and pitched plates.

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Large-deflection and large-amplitude free vibrations of laminated composite-material plates

Cited by 81 publications

References 29 publications

Nonlinear combination resonances in cantilever composite plates

Nonlinear combination resonances in cantilever composite plates

First-Order Shear Deformation, p-Version, Finite Element for Laminated Plate Nonlinear Vibrations

Free vibration behavior of spinning shear-deformable plates composedof composite materials

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