Vibrations of carbon nanotubes and their composites: a review

Nanomechanical resonators with high aspect ratio, such as nanotubes and nanowires are of interest due to their expected high sensitivity. However, a strongly nonlinear response combined with a high thermomechanical noise level limits the useful linear dynamic range of this type of device. We derive the equations governing this behavior and find a strong dependence [[proportional]dsqrt((d/L)[sup 5])] of the dynamic range on aspect ratio.

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Dynamic range of nanotube- and nanowire-based electromechanical systems

In this letter we study the tip motion of a rectangular microcantilever in the proximity of a surface. The microcantilever has a hemispherical tip attached at its free end. The theoretical simulations led us to propose a method for mapping simultaneously the topography and the chemical composition of a sample surface in noncontact AM‐AFM. The method consists of exciting the first two modes of the microcantilever. The output signal of the first mode is used to image the topography of the sample while the second mode is used to map changes in the composition of the atoms or molecules under the tip. The simulations were performed by modeling the three dimensional microcantilever as a rectangular beam and applying the Newton equation. 25 Then the dynamic deflection function w(x,t) is described by

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Compositional mapping of surfaces in atomic force microscopy by excitation of the second normal mode of the microcantilever

Simulation of dynamics of beam structures with bolted joints using adjusted Iwan beam elements

This two-part review article presents an overview of mechanics of pipes conveying fluid and related problems such as the fluid-elastic instability under conditions of turbulence in nuclear power plants. In the first part, different types of modeling, dynamic analysis, and stability regimes of pipes conveying fluid restrained by elastic or inelastic barriers are described. The dynamic and stability behaviors of pinned-pinned, clamped-clamped, and cantilevered pipes conveying fluid together with curved and articulated pipes will be discussed. Other problems such as pipes made of viscoelastic materials and active control of severe pipe vibrations are considered. This part will be closed by conclusions highlighting resolved and nonresolved controversies reported in literature. The second part will address the problem of fluid-elastic instability in single- and two-phase flows and fretting wear in process equipment such as heat exchangers and steam generators. Connors critical velocity will be discussed as a measure of initiating fluid-elastic instability. Vibro-impact of heat exchanger tubes and the random excitation by the cross-flow can produce a progressive damage at the supports through fretting wear or fatigue. Antivibration bar supports used to limit pipe vibrations are described. An assessment of analytical, numerical, and experimental techniques of fretting wear problem of pipes in heat exchangers will be given. Other topics related to this part include remote impact analysis and parameter identification, pipe damage-induced by pressure elastic waves, the dynamic response and stability of long pipes, marine risers together with pipes aspirating fluid, and carbon nanotubes conveying fluid.

Overview of Mechanics of Pipes Conveying Fluids—Part I: Fundamental Studies

The nonlinear dynamic response of atomic force microscopy cantilevers tapping on a sample is discussed through theoretical, computational, and experimental analysis. Experimental measurements are presented for the frequency response of a specific microcantilever-sample system to demonstrate the nonlinear features, including multiple jump phenomena leading to reproducible hysteresis. We show that a comprehensive analysis using modern continuation tools for computational nonlinear dynamics and bifurcation problems reproduces all essential features of the data. A close connection is established between the features of the interaction potential well and the nonlinear forced tip response. In particular, the effects of the nonlinear van der Waals forces, the nanoscale contact nonlinearities, and microcantilever damping, as well as the effects of forced and parametric excitation on the bifurcations and instabilities of forced periodic motions of the microcantilever system, are discussed in detail. The results indicate that nonlinear system identification methods could be used as effective tools to extract detailed information about the tip‐surface interaction potential.

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Nonlinear dynamics of microcantilevers in tapping mode atomic force microscopy: A comparison between theory and experiment

The near‐resonant, nonlinear dynamic response of microcantilevers in atomic force microscopy is investigated through numerical continuation techniques and simulations of discretized models of the microcantilever interacting with a surface through a Lennard‐Jones potential. The tapping‐mode responses of two representative systems, namely a soft silicon probe‐silicon sample system and a stiff silicon probe‐polystyrene sample system, are studied. Van der Waals interactions are shown to lead to a softening nonlinearity of the periodic solution response, while the short‐range repulsive interactions lead to an overall hardening nonlinear response. Depending on the tip‐sample properties, the dynamics of the microcantilevers occur either in asymmetric single‐well potential regions or in asymmetric double‐well potential regions. In both cases, forced periodic motions of the probe tip destabilize through a sequence of period‐doubling bifurcations, while, in the latter, the tip can also escape the potential well to execute complex and unpredictable cross‐well dynamics. The results predict a broad range of nonlinear dynamic phenomena, many of which have been observed in the literature on experimental atomic force microscopy.

Nonlinear dynamics of atomic–force–microscope probes driven in Lennard–Jones potentials

https://tesla.physics.purdue.edu/~reifenbr/research/publications/ultramicroscopy_raman_lee_howell.pdf

Nonlinear dynamic perspectives on dynamic force microscopy

New non-linear modelling for vibration analysis of a straight pipe conveying fluid

The nonlinear dynamics of an atomic force microcantilever (AFM) with an attached multi-walled carbon nanotube (MWCNT) tip is investigated experimentally and theoretically. We present the experimental nonlinear frequency response of a MWCNT tipped microcantilever in the tapping mode. Several unusual features in the response distinguish it from those traditionally observed for conventional tips. The MWCNT tipped AFM probe is apparently immune to conventional imaging instabilities related to the coexistence of attractive and repulsive tapping regimes. A theoretical interaction model for the system using an Euler elastica MWCNT model is developed and found to predict several unusual features of the measured nonlinear response.

/pdf/nonlinear-tapping-dynamics-of-multi-walled-carbon-nanotube-14l1qobg5q.pdf

Soo-Il Lee

Papers

Nonlinear dynamics of microcantilevers in tapping mode atomic force microscopy: A comparison between theory and experiment

Nonlinear dynamics of atomic–force–microscope probes driven in Lennard–Jones potentials

Nonlinear dynamic perspectives on dynamic force microscopy

New non-linear modelling for vibration analysis of a straight pipe conveying fluid

Nonlinear tapping dynamics of multi-walled carbon nanotube tipped atomic force microcantilevers