Non-linear forced vibration analysis of nanobeams subjected to moving concentrated load resting on a viscoelastic foundation considering thermal and surface effects

Ghadiri, Majid; Rajabpour, Ali; Akbarshahi, Amir

doi:10.1016/j.apm.2017.06.019

Cited by 50 publications

(13 citation statements)

References 49 publications

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“…where the complex functions in are ( = 1, 2, ..., 5), and that are presented at appendix. To form the ODE for , substituting Eqs.…”

Section: Time History and Phase Plane By Numerical Simulationmentioning

confidence: 99%

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The effectiveness of nonlinear integral positive position feedback control on a duffing oscillator system based on primary and super harmonic resonances

Amer¹,

EL-Sayed²,

Abdelwahab³

et al. 2019

J. vibroeng.

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In this paper, we applied three different control methods; Positive Position Feedback (PPF), Integral Resonance Control (IRC) and Nonlinear Integrated Positive Position Feedback (NIPPF) added to a Duffing oscillator system subjected to harmonic force. An analytic solution is introduced using the multiple scales perturbation technique (MSPT) to solve the nonlinear differential equations, which simulate the system with NIPPF controller. Before and after control at the primary and superharmonic resonances, the nonlinear systems' steady-state amplitude and stability are studied and examined. The influences of various parameters of the system after being connected to NIPPF are illustrated. Optimum working conditions for the NIPPF controller are obtained at internal resonance ratio 1:1. A Comparison is also made to validate the closeness between the numerical solution and the analytical perturbative one at time-history and frequency response curves (FRC). Finally, a comparison with the available results in the literature is presented. From this comparison, we find that the best control to the system is via the NIPPF controller.

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“…where the complex functions in are ( = 1, 2, ..., 5), and that are presented at appendix. To form the ODE for , substituting Eqs.…”

Section: Time History and Phase Plane By Numerical Simulationmentioning

confidence: 99%

“…In [5], Ghadiri et al have examined some considerable effects imposed by thermal environments to the nonlinear vibrations of a just supported Euler-Bernoulli nanobeam, which depends on a viscoelastic fundamental with surface elasticity. In addition, the Galerkin and the multiple scales technique were applied to disband the problem.…”

Section: Introductionmentioning

confidence: 99%

The effectiveness of nonlinear integral positive position feedback control on a duffing oscillator system based on primary and super harmonic resonances

Amer¹,

EL-Sayed²,

Abdelwahab³

et al. 2019

J. vibroeng.

View full text Add to dashboard Cite

show abstract

“…Exclusion the secular terms from equations (19), (20), the general solutions of these equations are obtained as follows:…”

Section: Mathematical Analysismentioning

confidence: 99%

“…The FRE are perturbed to research the stability of the steady-state solutions. Nonlinear vibration of Nanobeam based on thermal and surface effects were investigated in [19]. The Galerkin and the Multiple Scales techniques are applied to disband the problem.…”

Section: Introductionmentioning

confidence: 99%

Positive Position Feedback Controller for Nonlinear Beam Subject to Harmonically Excitation

Amer

EL-Sayed

Abdelwahab

et al. 2019

ARJOM

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In this paper, the vibration reduction of the harmonically excited nonlinear beam is introduced using positive position feedback controller (PPF). The multiple-scale perturbation techniques (MSPT) up is applied to second-order to obtain the analytic results. Numerical simulations are used to compare between time-history and the analytical solution. The frequency response equation (FRE) is studied to illustrate the steady state solutions near the simultaneous resonances. The influences of the different parameters and the system behavior at resonance case are studied to show the optimum conditions of decreasing the vibration. A comparison between the numerical and analytical solutions is presented to appear the validity of the results.

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“…Nazemnezhad and Hosseini-Hashemi (2014) studied non-linear free vibration of FG beams under different boundary conditions with the aid of the multiplescale perturbation method. Ghadiri et al (2017) used Euler-Bernoulli beam model to analyze forced vibration of beams subjected to moving concentrated load. To obtain analytical solution from non-linear differential equations, they used the perturbation technique.…”

Section: Introductionmentioning

confidence: 99%

Free vibration analysis of nano-tubes consisted of functionally graded bi-semi-tubes by a two-steps perturbation method

Gao

Xiao

Zhu

2019

Lat. Am. j. solids struct.

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Free vibration of a bimaterial circular nano-tube is investigated. The tube is formed by bonding together a Si3N4/SUS304 functionally graded upper semi tube and a ZrO2/Ti-6Al-4V functionally graded lower semi tube. The material properties of the tube are assumed to vary along the radius according to power law with the power index of upper semi tube differing from that of lower semi tube. Based on non-local elasticity theory and Hamilton's principle, a refined beam model considering the effect of transverse shear deformation is used to derive the governing equations, then analytical solution is obtained by using a two-steps perturbation method. Our results were compared with the existing ones. The effects on tube's linear and non-linear frequency are analyzed of the factors, including small scale parameter, temperature, the double volume fraction indexes, slenderness ratio and different types of beam model. A new approach is suggested in this article to change the natural frequency of the tubes by adjusting constituent materials. In contrast to conventional approach, the new one can result in more accurate frequency control in the same dimensionless size of tubes.

show abstract

Non-linear forced vibration analysis of nanobeams subjected to moving concentrated load resting on a viscoelastic foundation considering thermal and surface effects

Cited by 50 publications

References 49 publications

The effectiveness of nonlinear integral positive position feedback control on a duffing oscillator system based on primary and super harmonic resonances

The effectiveness of nonlinear integral positive position feedback control on a duffing oscillator system based on primary and super harmonic resonances

Positive Position Feedback Controller for Nonlinear Beam Subject to Harmonically Excitation

Free vibration analysis of nano-tubes consisted of functionally graded bi-semi-tubes by a two-steps perturbation method

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