Nonlinear vibration of the piezoelectric nanobeams based on the nonlocal theory

Ke, Liao-Liang; Wang, Yue-Sheng; Wang, Zhengdao

doi:10.1016/j.compstruct.2012.01.023

Cited by 315 publications

(128 citation statements)

References 49 publications

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“…Asemi et al [79] derived the explicit expressions for the nonlinear frequencies when dealing with the nonlinear vibration problems of piezoelectric nanoelectromechanical resonators. The differential quadrature (DQ) method is employed by Ke et al [80] to conduct the nonlinear vibration simulation of the piezoelectric nanobeams based on the nonlocal theory.…”

Section: Vibrationmentioning

confidence: 99%

Nonlocal elasticity theory for graphene modeling and simulation: prospects and challenges

Liew

Zhang

2017

Journal of Modeling in Mechanics and Materials

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Abstract:This paper presents a literature review of recent research studies on the applications of nonlocal elasticity theory in the modeling and simulation of graphene sheets (GSs). The history, development and excellent properties of GSs are introduced. The details of nonlocal elasticity theory are also presented. A systematic introduction to the application of nonlocal elasticity on linear modeling and nonlinear modeling for single-layer graphene sheets (SLGSs) and multilayered graphene sheets (MLGSs) is also provided. The necessity of determining mechanical parameters and nonlocal parameters is discussed. Recommendations for future work are particularly presented. This work is intended to review the development of GSs, give an introduction to the research studies on nonlocal elasticity theory in the modeling of GSs, and provide recommendations for future research.

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Section: Vibrationmentioning

confidence: 99%

Nonlocal elasticity theory for graphene modeling and simulation: prospects and challenges

Liew

Zhang

2017

Journal of Modeling in Mechanics and Materials

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“…It was found that the applied continuum theory has an important role in finding more realistic values for the natural frequencies. Ke et al 22 investigated the nonlinear vibrations of a nanobeam by using nonlocal elasticity theory. The DQ method and a direct iterative method were used to obtain the nonlinear natural frequencies of the nanobeam.…”

Section: Introductionmentioning

confidence: 99%

Nanoscale piezoelectric vibration energy harvester design

2017

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Development of new nanoscale devices has increased the demand for new types of small-scale energy resources such as ambient vibrations energy harvesters. Among the vibration energy harvesters, piezoelectric energy harvesters (PEHs) can be easily miniaturized and fabricated in micro and nano scales. This change in the dimensions of a PEH leads to a change in its governing equations of motion, and consequently, the predicted harvested energy comparing to a macroscale PEH. In this research, effects of small scale dimensions on the nonlinear vibration and harvested voltage of a nanoscale PEH is studied. The PEH is modeled as a cantilever piezoelectric bimorph nanobeam with a tip mass, using the Euler-Bernoulli beam theory in conjunction with Hamilton’s principle. A harmonic base excitation is applied as a model of the ambient vibrations. The nonlocal elasticity theory is used to consider the size effects in the developed model. The derived equations of motion are discretized using the assumed-modes method and solved using the method of multiple scales. Sensitivity analysis for the effect of different parameters of the system in addition to size effects is conducted. The results show the significance of nonlocal elasticity theory in the prediction of system dynamic nonlinear behavior. It is also observed that neglecting the size effects results in lower estimates of the PEH vibration amplitudes. The results pave the way for designing new nanoscale sensors in addition to PEHs.

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“…Size-dependent thermal buckling behavior of nanocolumns was demonstrated. Arani et al (2012), Ke et al (2012) investigated the nonlinear vibration of the piezoelectric nanobeams based on the nonlocal theory and Timoshenko beam theory under the combination of electric and thermal fields. The nonlinear governing equations were derived by using Hamilton principle and the numerical solutions for the nonlinear frequency were determined employing differential quadrature method.…”

Section: Introductionmentioning

confidence: 99%

Large amplitude free vibration of micro/nano beams based on nonlocal thermal elasticity theory

Wang

Song

Lin

et al. 2015

Lat. Am. j. solids struct.

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This paper is concerned with the nonlinear free vibration of a heated micro/nano beam modeled after the nonlocal continuum elasticity theory and Euler-Bernoulli beam theory. The governing partial differential equations are derived from the Hamilton variational principle and von Kármán geometric nonlinearity, in which the effects of the nonlocality and ambient temperature are inclusive. These equations are converted into ordinary forms by employing the Kantorovich method. The solutions of nonlinear free vibration are then sought through the use of shooting method in spatial domain. Numerical results show that the proposed treatment provides excellent accuracy and convergence characteristics. The influences of the aspect ratio, nonlocal parameter and temperature rise parameter on the dimensionless radian frequency are carefully investigated. It is concluded that the nonlocal and temperature rise parameters lead to reductions of the nonlinear vibration frequency, while the influence of the nonlocal effect decreases with an increase in the aspect ratio.

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Nonlinear vibration of the piezoelectric nanobeams based on the nonlocal theory

Cited by 315 publications

References 49 publications

Nonlocal elasticity theory for graphene modeling and simulation: prospects and challenges

Nonlocal elasticity theory for graphene modeling and simulation: prospects and challenges

Nanoscale piezoelectric vibration energy harvester design

Large amplitude free vibration of micro/nano beams based on nonlocal thermal elasticity theory

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