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- Title
Kirchhoff's Analogy between the Kapitza Pendulum Stability and Buckling of a Wavy Beam under Tensile Loading.
- Authors
Ramachandran, Rahul; Nosonovsky, Michael
- Abstract
The Kirchhoff analogy between the oscillation of a pendulum (in the time domain) and the static bending of an elastic beam (in the spatial domain) is applied to the stability analysis of an inverted pendulum on a vibrating foundation (the Kapitza pendulum). The inverted pendulum is stabilized if the frequency and amplitude of the vibrating foundation exceed certain critical values. The system is analogous to static bending a wavy (patterned) beam subjected to a tensile load with appropriate boundary conditions. We analyze the buckling stability of such a wavy beam, which is governed by the Mathieu equation. Micro/nanopatterned structures and surfaces have various applications including the control of adhesion, friction, wettability, and surface-pattern-induced phase control.
- Subjects
MECHANICAL buckling; INVERTED pendulum (Control theory); WETTING; ADHESION; BOUNDARY value problems
- Publication
Applied Mechanics, 2023, Vol 4, Issue 1, p248
- ISSN
2673-3161
- Publication type
Article
- DOI
10.3390/applmech4010014