Nonlinear vibration of buckled beams: some exact solutions

Lestari, Wahyu; Hanagud, S.

doi:10.1016/s0020-7683(00)00300-0

Cited by 95 publications

(42 citation statements)

References 13 publications

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“…It is also noted that the primary resonances of Equations (9) and (10) under certain specific cases were investigated via Nayfeh-Mook multiple scale method in Nayfeh [26]. Exact solutions of the nonlinear vibration of buckled beams in Lestari and Hanagud [17] were studied for certain special cases. With the involvement of S, K , = 0, and r = 0 in Equations (9) and (11), no papers on the chaotic flexural vibrational mechanisms of the spinning nanoresonator under appropriate external excitations can be found.…”

Section: Integral-differential Equations Of the Spinning Nano-resonatormentioning

confidence: 99%

Chaotic flexural oscillations of a spinning nanoresonator

Kuang

Leung

2007

Nonlinear Dyn

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The paper investigates the chaotic flexural oscillations of the spinning nanoresonator. The influence of cubic nonlinearity arising from the van der Waals interactions between two neighboring layers of carbon nanotubes on the structural oscillations of the system is considered. The integraldifferential equations describing the flexural displacements of the nanoresonator are discretized into two coupled Duffing-type equations using the GalerkinRitz procedures. The linear stiffness can be either positive or negative, depending on the amplitudes of the linear trap rigidity arising from both the van der Waals interactions and the axial tensile loads. The chaotic flexural oscillations of the appropriately excited spinning nanoresonator are predicted theoretically. Using the Nayfeh-Mook multiscale perturbation algorithms, the coupled Duffing-type equations with linear positive stiffness may be transformed into autonomous equations of slowly modulated amplitudes whose equilibrium points and chaotic dynamics are investigated numerically. The potential chaotic oscillations of the elastic nanoresonator can be determined by the Melnikov-Holmes-Marsden (MHM) integral associated with the homoclinic/heteroclinic solutions of the disturbed Hamiltonian systems with linear negative stiffness. The findings are validated through the Poincare sections and Lyapunov exponents.

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Section: Integral-differential Equations Of the Spinning Nano-resonatormentioning

confidence: 99%

Chaotic flexural oscillations of a spinning nanoresonator

Kuang

Leung

2007

Nonlinear Dyn

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“…Lestari and Hanagud found closed-form exact solutions to the problem of nonlinear vibrations of buckled beams. 19 They assumed that their model consisted of axial springs in spite of it having general support conditions. Lacarbonara et al developed the open-loop nonlinear control strategy and applied it to a hinged hinged shallow arch.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Transverse Vibrations of a Slightly Curved Beam resting on Multiple Springs

Özkaya¹,

Sarıgül²,

Boyacı³

2016

IJAV

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In this study, nonlinear vibrations of a slightly curved beam of arbitrary rise functions is handled in case it rests on multiple springs. The beam is simply supported on both ends and is restricted in longitudinal directions using the supports. Thus, the equations of motion have nonlinearities due to elongations during vibrations. The method of multiple scales (MMS), a perturbation technique, is used to solve the integro-differential equation analytically. Primary and 3 to 1 internal resonance cases are taken into account during steady-state vibrations. Assuming the rise functions are sinusoidal in numerical analysis, the natural frequencies are calculated exactly for different spring numbers, spring coefficients, and spring locations. Frequency-amplitude graphs and frequency-response graphs are plotted by using amplitude-phase modulation equations.

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“…They used Melnikov theory in their analysis. Lestari and Hanagud [8] used a single--mode approximation to study the nonlinear vibrations of buckled beams with elastic end constraints. They considered the beam to be subjected simultaneously to axial and lateral loads without rst statically buckling the beam.…”

Section: Introductionmentioning

confidence: 99%

An Analytical Study of Nonlinear Vibrations of Buckled Euler--Bernoulli Beams

Pakar¹,

Bayat²

2013

Acta Phys. Pol. A

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The current research deals with a way of using a new kind of periodic solutions called He's max-min approach for the nonlinear vibration of axially loaded EulerBernoulli beams. By applying this technique, the beam's natural frequencies and mode shapes can be easily obtained and a rapidly convergent sequence is obtained during the solution. The eect of vibration amplitude on the non-linear frequency and buckling load is discussed. To verify the results some comparisons are presented between max-min approach results and the exact ones to show the accuracy of this new approach. It has been discovered that the max-min approach does not necessitate small perturbation and is also suitably precise to both linear and nonlinear problems in physics and engineering.

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Nonlinear vibration of buckled beams: some exact solutions

Cited by 95 publications

References 13 publications

Chaotic flexural oscillations of a spinning nanoresonator

Chaotic flexural oscillations of a spinning nanoresonator

Nonlinear Transverse Vibrations of a Slightly Curved Beam resting on Multiple Springs

An Analytical Study of Nonlinear Vibrations of Buckled Euler--Bernoulli Beams

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