Browsing by Author "Eason, Richard Parker"

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    Numerical investigation of coexisting high and low amplitude responses and safe basin erosion for a coupled linear oscillator and nonlinear absorber system
    (Elsevier, 2014) Eason, Richard Parker; Dick, Andrew James; Nagarajaiah, Satish
    Over the last half century, numerous nonlinear variants of the tuned mass damper have been developed in order to improve attenuation characteristics. In the present study, the performance of a linear oscillator and an absorber with a strongly nonlinear cubic stiffness is evaluated by using numerical methods. This configuration has been of recent interest due to its capability of wide-band energy absorption. However, high amplitude solutions, which would amplify the response of the system, have been shown to often coexist with the low amplitude solutions. The present research is focused on numerically determining the relative strength of the coexisting solutions. Erosion profiles are presented, quantifying the integrity of the system, i.e. the likelihood of converging to a safe, low amplitude response, and providing an indication of the structural safety of a practical absorber system. The results indicate that the high amplitude solutions not only exist but significantly influence the response of the system within the range of expected operating conditions, particularly at excitation frequencies lower than the natural frequency of the linear oscillator. The erosion profiles indicate a 20-40% increase in system integrity for the case of zero damping compared to a small amount of damping, no significant integrity change when adding a small linear stiffness component to the nonlinear absorber, and no significant change in integrity between the midpoint and extreme of the bi-stable range. Additional higher-period solutions are also discovered and evidence of a chaotic response is presented.
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    Optical Lever Measurement Accuracy for Off-Resonance Atomic Force Microscopy
    (2011) Eason, Richard Parker; Dick, Andrew J.
    This research evaluates measurement accuracy in optical lever-based atomic force microscopy (AFM) for off-resonance conditions and parameter variations. Under controlled conditions and correct calibration, AFM provides researchers with the ability to accurately observe and manipulate matter on the micro- and nano-scale. Accuracy of imaging and nano-manipulation operations are directly correlated to the accuracy with which the displacement of the probe is measured. The optical lever method, a common displacement measurement technique employed in AFM, calculates probe displacement based on a calibration that assumes a consistent response profile throughout operation. Off-resonance excitation and tip-sample interaction forces during intermittent contact mode AFM can alter this response profile. Standard tapping-mode operation at the fundamental frequency is observed to be robust to changes in effective stiffness, maintaining accurate measurements for all laser spot positions considered. A nominal laser spot position between Xp = 0.5 and 0.6 is determined to most accurately predict displacement for off-resonance excitation during both free response and intermittent contact condit ions. Measurement accuracy for off-resonance tapping- mode is more directly correlated to changes introduced to the interaction force profile than choice of spot position.