Nonlinear Oscillations of CNT Nano-resonator Based on Nonlocal Elasticity: The Energy Balance Method

Goharimanesh, Masoud; Koochi, Ali

doi:10.31181/rme200102041g

Cited by 36 publications

(9 citation statements)

References 31 publications

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“…So far there were many modifications of the homotopy perturbation method, see for examples, Refs. [22][23][24][25][26][27][28][29][30], and have many advantages over others in open literature [31][32][33][34][35].…”

Section: Introductionmentioning

confidence: 99%

Periodic Property and Instability of a Rotating Pendulum System

Amer

Elnaggar

et al. 2021

Axioms

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The current paper investigates the dynamical property of a pendulum attached to a rotating rigid frame with a constant angular velocity about the vertical axis passing to the pivot point of the pendulum. He’s homotopy perturbation method is used to obtain the analytic solution of the governing nonlinear differential equation of motion. The fourth-order Runge-Kutta method (RKM) and He’s frequency formulation are used to verify the high accuracy of the obtained solution. The stability condition of the motion is examined and discussed. Some plots of the time histories of the gained solutions are portrayed graphically to reveal the impact of the distinct parameters on the dynamical motion.

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Section: Introductionmentioning

confidence: 99%

Periodic Property and Instability of a Rotating Pendulum System

Amer

Elnaggar

et al. 2021

Axioms

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“…Diverse methods and approaches were used in modelling and analyzing nanostructures [29][30][31][32][33][34][35][36][37][38][39][40][41], nevertheless in the current literature survey is focused on dynamics of beam-like nanostructures. Wang and Varadan [42] presented effect of Eringen's nonlocal parameter on frequency of both single-walled and double-walled carbon nanotubes based on Euler-Bernoulli beam theory.…”

Section: Introductionmentioning

confidence: 99%

Detection of Nonlocal Calibration Parameters and Range Interaction for Dynamics of FGM Porous Nanobeams Under Electro-Mechanical Loads

Jankowski

2022

FU Mech Eng

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The present investigation examines the range of effect of nonlocal parameters on dynamic behavior of a smart beam-like nanostructure modeled as sandwich functionally graded porous nanobeam with piezoelectric layers. Therefore, the study is concentrated on determining length of the structure for which nonlocal effects are observed for vibration of nanobeam under in-plane electro-mechanical forces. The nanobeam-based NEMS device model is obtained based on assumptions of the nonlocal strain gradient theory in conjunction with Reddy higher-order shear deformation theory. The investigation present differences in obtained results for nanostructure’s free vibration based on classical and nonlocal assumptions. To study range of application of nonlocal parameters for different length of simply supported nanobeam, defined eigenvalue problem is solved in view of variation of length to thickness ratio, distribution of material properties, as well as electro-mechanical loads. What is more, the study attempts to determine and calibrate values of size-dependent coefficients based on expected natural frequencies, material properties, and applied loads. The results are completed with extensive discussion on the dependence of nonlocal parameters on nanobeam’s dynamic response, thus may be an important step forward to extend understanding of ultra-small structure’s behavior.

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“…¼ a, _ xð0Þ ¼ 0 oscillators (Qie et al, 17 Koochi A and Goharimanesh, 18 Anjum et al, 19,20 Rehman et al, 21 Suleman et al, 22 Anjum et al, 23 Li and Nadeem, 24 and Askari et al 25 ). The goal of this article is to present a combined technique of the LP and homotopy perturbation methods to solve some strongly nonlinear oscillators.…”

Section: Introductionmentioning

confidence: 99%

“…In a recent article, 7 Alam et al provided a generalized form of the modified LP 6 method and used it to solve various nonlinear oscillators. On the other hand, the homotopy perturbation method has been modified in some recent articles presented by Anjum et al, 12 He et al, 13 Anjum et al, 14 Ji et al, 15 and He et al 16 Moreover, some approximate techniques are available to solve strongly nonlinear oscillators (Qie et al, 17 Koochi A and Goharimanesh, 18 Anjum et al, 19,20 Rehman et al, 21 Suleman et al, 22 Anjum et al, 23 Li and Nadeem, 24 and Askari et al 25 ).…”

Section: Introductionmentioning

confidence: 99%

Combination of modified Lindstedt-Poincare and homotopy perturbation methods

Alam

Sharif

Molla

2022

Journal of Low Frequency Noise, Vibration and Active Control

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Some strongly nonlinear oscillators have been investigated with the help of combined modified Lindstedt–Poincare and homotopy perturbation methods. The solutions are more accurate than those obtained by the modified Lindstedt–Poincare method. Moreover, the determination of solutions is simpler than usual homotopy perturbation methods. Some similarities and dissimilarities between the present method and other existing methods have also been discussed.

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Nonlinear Oscillations of CNT Nano-resonator Based on Nonlocal Elasticity: The Energy Balance Method

Cited by 36 publications

References 31 publications

Periodic Property and Instability of a Rotating Pendulum System

Periodic Property and Instability of a Rotating Pendulum System

Detection of Nonlocal Calibration Parameters and Range Interaction for Dynamics of FGM Porous Nanobeams Under Electro-Mechanical Loads

Combination of modified Lindstedt-Poincare and homotopy perturbation methods

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