Mathematical modeling of a fractionally damped nonlinear nanobeam via nonlocal continuum approach

Jha, Abhishek Kumar; Dasgupta, Sovan Sundar

doi:10.1177/0954406219866467

Cited by 4 publications

(4 citation statements)

References 52 publications

(60 reference statements)

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“…Figs. [19][20][21][22][23][24][25] show that when the detuning parameter is positive, with increasing temperature of the top surface, the amplitude response increases too and while the detuning parameter is negative, this behaviour changed. It means that with increasing temperature, the amplitude response decrease.…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

“…By utilizing nonlocal strain gradient theory, the oscillation properties of the nanotube with fractional-order derivative damping are studied. The results indicate that fundamental frequency and time response are impressing by the fractional-order derivative damping [24]. Bending characteristics of perforated microbeams subjected to various loading pattern are investigated.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Nonlinear Vibration and Stability Analysis of Functionally Graded Nanobeam Subjected to External Parametric Excitation and Thermal Load

Shayestenia

Janmohammadi

Sadatsakkak

et al. 2021

NHC

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Analysis of vibration stability of simply supported Euler-Bernoulli functionally graded (FG) nanobeam embedded in viscous elastic medium with thermal effect under external parametric excitation is presented in this work. An attempt has been made for the first time is investigating the effect of thermal load on dynamic behavior, amplitude response, instability region and bifurcation points of functionally graded nanobeam. Thermal loads are supposed to be uniform, linear or nonlinear distribution along the thickness direction. Nonlocal continuum theory and the principle of the minimum total potential energy are applied to derive the governing equations. The partial differential equations (PDE) are transported to the ordinary differential equations (ODE) by using the Petrov-Galerkin method and the multiple time scales method are manipulated to solve the motion equation. To study the effect of external parametric excitation and thermal effect, different temperature distributions along the thickness such as uniform, linear, and nonlinear distribution are considered. Moreover, stable and unstable regions and bifurcation points are determined. It is obtained that the thermal load can affect the amplitude response of FG nanobeam. Also, it is observed that the instability of the system is affected by the detuning parameter and the parametric excitation amplitude plays great role in the instability of system. Nanobeams are used in many devices like nanoresonators, nanosensors and nanoswitches. This paper is helpful for designing and manufacturing nanoscale structures specially nanoresonators under different thermal loads.

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Section: Numerical Results and Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Nonlinear Vibration and Stability Analysis of Functionally Graded Nanobeam Subjected to External Parametric Excitation and Thermal Load

Shayestenia

Janmohammadi

Sadatsakkak

et al. 2021

NHC

View full text Add to dashboard Cite

show abstract

“…To achieve the numerical results, they used Hamilton, Bolotin, and fourth-order Runge-Kutta approach. Jha and Dasgupta 50 reported the dynamic analysis of a hinged-hinged Nanobeam using the nonlocal theory. Among the parameters affecting the response of the beam, it was the damping that mostly influenced the free oscillation characteristics of the beam.…”

Section: Introductionmentioning

confidence: 99%

Dynamic instability analysis of timoshenko FG sandwich nanobeams subjected to parametric excitation

Zanjanchi Nikoo,

Lezgi,

Sabouri Ghomi

et al. 2023

Proceedings of the Institution of Mechanical Engineers, Part C:

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According to the nonlocal theory, the dynamic instability and vibration of functionally graded (FG) porous sandwich nanobeams resting on a visco-elastic foundation under axial harmonic load are studied. In this paper the Timoshenko and nonlocal continuum theory are employed to take shear deformation, rotational bending and small-scale effects into account. The governing equations of motion are extracted using the nonlinear Von-Karman, and Hamilton approaches. Then, to turn the partial differential equations (PDEs) into ordinary differential equations (ODEs) in the case of equations of motion, the method of Galerkin is employed, followed by the use of the multiple time scale method to solve the resulting equations. According to the results of this study, it can be claimed that the porosity ratio is more effective than porosity distribution and nonlocal parameters on the amplitude response and dynamic instability regions. Moreover, to examine thermal increments, foundation characteristics, slenderness, and thickness ratios, the bifurcation diagrams are drawn and discussed. It is found that foundation and geometric characteristics are of the highest significance in the nonlinear response of the Timoshenko nanobeams. The main intention of this study is to present a holistic idea about the porous materials used in sandwich structures which can be used in many composite structures in aircraft and automobiles.

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“…Farhatnia et al [30] studied buckling of FG plate resting on Pasternak elastic layer using differential transform method. Jha and Dasgupta [31] used the approximate averaging method to found the analytical solution of the Duffing-type differential equation obtained for the nonlinear fractionally damped nanobeam structure. The authors adopted the Galerkin method to discretize the governing equation of the system.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear superharmonic resonance analysis of a nonlocal beam on a fractional visco-Pasternak foundation

Nešić¹,

Cajić

Karličić

et al. 2020

Proceedings of the Institution of Mechanical Engineers, Part C:

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This paper investigates the dynamic behavior of a geometrically nonlinear nanobeam resting on the fractional visco-Pasternak foundation and subjected to dynamic axial and transverse loads. The fractional-order governing equation of the system is derived and then discretized by using the single-mode Galerkin discretization. Corresponding forced Mathieu-Duffing equation is solved by using the perturbation multiple time scales method for the weak nonlinearity and by the semi-numerical incremental harmonic balance method for the strongly nonlinear case. A comparison of the results from two methods is performed in the validation study for the weakly nonlinear case and a fine agreement is achieved. A parametric study is performed and the advantages and deficiencies of each method are discussed for order two and three superharmonic resonance conditions. The results demonstrate a significant influence of the fractional-order damping of the visco-Pasternak foundation as well as the nonlocal parameter and external excitation load on the frequency response of the system. The proposed methodology can be used in pre-design procedures of novel energy harvesting and sensor devices at small scales exhibiting nonlinear dynamic behavior.

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Mathematical modeling of a fractionally damped nonlinear nanobeam via nonlocal continuum approach

Cited by 4 publications

References 52 publications

Nonlinear Vibration and Stability Analysis of Functionally Graded Nanobeam Subjected to External Parametric Excitation and Thermal Load

Nonlinear Vibration and Stability Analysis of Functionally Graded Nanobeam Subjected to External Parametric Excitation and Thermal Load

Dynamic instability analysis of timoshenko FG sandwich nanobeams subjected to parametric excitation

Nonlinear superharmonic resonance analysis of a nonlocal beam on a fractional visco-Pasternak foundation

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