Nonlinear and Nonplanar Dynamics of Suspended Nanotube and Nanowire Resonators

Conley, William G.; Raman, Arvind; Krousgrill, Charles M.; Mohammadi, Saeed

doi:10.1021/nl073406j

Cited by 81 publications

(100 citation statements)

References 26 publications

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“…We consider a nanowire of constant, circular cross-sectional area A (radius r) and apply the standard Euler-Bernoulli theory to obtain [14] the following set of PDEs governing the displacements Z(x,t) and Y (x,t) of the wire in the z and y directions, respectively:…”

Section: Model and Methodsmentioning

confidence: 99%

“…Their small size, extremely low power consumption, and ultrafast operational speed are among the virtues that have been exploited for significant applications ranging from single-electron spin detection [1] and Zeptogram scale mass sensing [2] to rf communications [3], semiconductor superlattice [4,5], and many others [6][7][8][9][10][11][12][13][14]. From the perspective of basic science, NEM systems represent a novel class of high-dimensional nonlinear dynamical systems.…”

Section: Introductionmentioning

confidence: 99%

“…To see why NEM systems are fundamentally nonlinear and thus chaos can arise, we take as an example an electrostatically driven nanowire [1,2,8,9,[12][13][14][20][21][22], a paradigm for investigating nonlinear behaviors in nanoscale systems [15,18,19]. When the nanowire moves, the amount of stretching can be expressed as an integral of nonlinear functions of the displacements (see Sec.…”

Section: Introductionmentioning

confidence: 99%

“…Because of the feasibility in applying noise to a nanowire system, e.g., by controlling the temperature of the surroundings, we expect that our idea of exploiting noise to regularize chaos in nanoscale systems to be experimentally verifiable and practically implementable. Figure 1 shows the device configuration of a suspended nanowire [14] in an environment of random thermal fluctuations. It is a solid structure with two ends bridging the sidewalls.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Regularization of chaos by noise in electrically driven nanowire systems

Hessari

Lai

et al. 2014

Phys. Rev. B

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The electrically driven nanowire systems are of great importance to nanoscience and engineering. Due to strong nonlinearity, chaos can arise, but in many applications it is desirable to suppress chaos. The intrinsically high-dimensional nature of the system prevents application of the conventional method of controlling chaos. Remarkably, we find that the phenomenon of coherence resonance, which has been well documented but for low-dimensional chaotic systems, can occur in the nanowire system that mathematically is described by two coupled nonlinear partial differential equations, subject to periodic driving and noise. Especially, we find that, when the nanowire is in either the weakly chaotic or the extensively chaotic regime, an optimal level of noise can significantly enhance the regularity of the oscillations. This result is robust because it holds regardless of whether noise is white or colored, and of whether the stochastic drivings in the two independent directions transverse to the nanowire are correlated or independent of each other. Noise can thus regularize chaotic oscillations through the mechanism of coherence resonance in the nanowire system. More generally, we posit that noise can provide a practical way to harness chaos in nanoscale systems.

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Section: Model and Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Regularization of chaos by noise in electrically driven nanowire systems

Hessari

Lai

et al. 2014

Phys. Rev. B

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“…We extended non-planar non-linear continuum theory which has once reported to explain the forced nonlinear motion of suspended SWNT in field effective transistor (FET) system [10]. In continuum dynamics, the main reasons of nonplanar and non-linear motion of 1D structure are supposed to be the longitudinal extensibility of structure and torsional motion.…”

Section: Theorymentioning

confidence: 98%

Non-linear and Non-planar Free Thermal Vibration of SWNT in Molecular Dynamic Simulation

Koh

Cannon

Chiashi

et al. 2012

Extended Abstracts of the 2012 International Conference on Solid State Devices and Materials

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IntroductionVibration of suspended and cantilevered nanotubes and nanowires has been studied extensively in electronics circuits such as transistor, mixer[1], sensors [2][3] and mesoscopic quantum theory [4]. Recently, it is reported that the power spectrum of the free thermal vibration of cantilevered single walled carbon nanotubes (SWNT) can be well expressed by Euler beam and Timoshenko beam theory and the continuous mechanics portion of the motion among the total thermal energy is about 97 percent [5][6]. The beam motion and thermal vibrational motion are strongly coupled for nanoscale structures. Vibrational motion or temperature can evolve to the beam motion. We observed that there is nonplanar motion with beating and bifurcation with long time span in NVE condition using molecular dynamics (MD) calculation. A few experiments are reported about free thermal vibration of the nanoscale cantilevered and suspended structure. Non planar motion of free vibration [7] and forced vibration [8] is measured using the field emission method (FEM) in silicon nanowire. We show that poincare distribution and frequency response in fine resolution shows this doffing (nonplanar) motion satisfies the solution of continuum non-linear equation which is derived by Hamilton's extended principle [9].

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A Comprehensive Categorization of Micro/Nanomechanical Resonators and Their Practical Applications from an Engineering Perspective: A Review

Ghaemi

Nikoobin

Ashory

2022

Adv Elect Materials

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Micro/nanoelectromechanical systems (M/NEMS), especially micro/nanomechanical resonators, provide an unprecedented platform for investigating a wide range of applications in both fundamental physical phenomena (such as quantum‐level problems) and engineering and applied sciences (like sensing physical quantities and signal processing). In sensing context, these tiny resonators are invaluable tools for detecting weak forces and single molecules. Measuring such small variations in sub‐nanometer amplitudes at high frequencies has created many practical challenges. Therefore, maximizing the responsivity to a specified input parameter and minimizing the responsivity to other inputs such as noise are considered as the optimal design for the excellent performance in nanoresonators. The present review aims to summarize some of the recent progress in this rapidly advancing field. Specifically, more attention is paid to the topics related to the dynamical behaviors of micro/nanoresonator and their practical applications. First, the theory behind micro/nanoresonators is described. Then a summary is presented of the basic concepts in resonant devices. In addition, several commonly dynamical techniques to enhance sensitivity are introduced. Finally, the devices are classified based on linear and nonlinear, single and array, symmetric and asymmetric, and frequency shift‐based and amplitude shift‐based resonators, along with the relative advantages and disadvantages of each one in engineering applications.

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Nonlinear and Nonplanar Dynamics of Suspended Nanotube and Nanowire Resonators

Cited by 81 publications

References 26 publications

Regularization of chaos by noise in electrically driven nanowire systems

Regularization of chaos by noise in electrically driven nanowire systems

Non-linear and Non-planar Free Thermal Vibration of SWNT in Molecular Dynamic Simulation

A Comprehensive Categorization of Micro/Nanomechanical Resonators and Their Practical Applications from an Engineering Perspective: A Review

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