Nonlinear Multi-Mode Dynamics of a Microbeam for Noncontact Atomic Force Microscopy in Ultra-High Vacuum
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We study the nonlinear multi-mode dynamics of a microbeam for noncontact atomic force microscopy in ultra-high vacuum. A boundary-value problem that includes a coupled linear thermo- and viscoelastic field with a localized nonlinear atomic interaction force, augmented by the linearized heat equation, is reduced to a modal dynamical system via Galerkin’s method. An equivalent linear thermoelastic quality factor is obtained and compared with a closed form solution. A numerically obtained escape curve defines valid operating parameters for low damping conditions. Primary, secondary and coupled internal resonances of a three-mode system are examined to reveal a rich bifurcation structure.
1997 ◽
Vol 384
(1-3)
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pp. L828-L835
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1994 ◽
Vol 52
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pp. 1064-1065
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2016 ◽
Vol 7
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pp. 432-438
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