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Monday, July 8 • 15:50 - 16:10
FREQUENCIES OF A CANTILEVERED NANOBEAM WITH ARBITRARY BOUNDARY CONDITIONS INCLUDING SURFACE EFFECTS.

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This investigation is about the motion of a cantilevered beam used in tapping mode atomic force microscopy (AFM) which can be utilized in scanning the topographical features of biological samples or "pliable" samples in general. These cantilevered beams can be used to modify samples by using high frequency oscillations to remove material or shape nano structures. A cantilever nanobeam with arbitrary boundary conditions is studied to investigate different configurations and the effects on the relevant parameters. The nano structure is modelled using the Euler-Bernoulli theory. Eringen's theory of non-local continuum is incorporated to simulate the dynamics of the system. This theory is effective at nano-scale because it takes into account the small-scale effects of the structure. The scanning process is achieved by tapping/contact with the sample surface to determine the topographical profile of the sample. The tapping contact force can also be used to deform the sample surface or remove material using high frequency oscillations. The fixed end is modelled as a torsional spring with zero transverse displacement instead of the "ideal" or clamped boundary condition. The torsional boundary condition can be tuned, by changing the torsional spring stiffness, such that the compliance of the system matches that of the sample to prevent mechanical damage of both the cantilever tip and the sample. The boundary condition at the free end is a tip-mass attached to a transverse linear spring which models a contact force. At nano scale, the surface area to bulk ratio increases and surface effects becomes a significant factor when determining the natural frequencies of the system. The motions of the tip of the beam and the tip-mass is investigated to frequency response and force. The tip response frequency includes information about the maximum displacement amplitude and therefore the sample penetration depth.

Moderators
EP

Elsa Piollet

Dr, Polytechnique Montréal
avatar for Mohammad Rafiee

Mohammad Rafiee

Postdoctoral Fellow, Polytechnique Montréal
Mohammad Rafiee received his Ph.D. degree in Mechanical Engineering from the University of Ottawa in 2018. Currently, he is a Postdoctoral Fellow at Polytechnique Montreal in Canada. His research interests are primarily focused on the development of advanced composite materials, smart... Read More →
AR

Annie Ross

Professor, Polytechnique Montreal

Authors

Monday July 8, 2019 15:50 - 16:10 EDT
St-Laurent 8
  T07 Struct. dyn. & nonlin. vib., RS02 Vibr & cntrl of nonlin mech syst

Attendees (7)