NDLI: Near-grazing dynamics of base excited cantilevers with nonlinear tip interactions

Content Provider	Springer Nature Link
Author	Chakraborty, Ishita Balachandran, B.
Copyright Year	2012
Abstract	In this article, nonsmooth dynamics of impacting cantilevers at different scales is explored through a combination of analytical, numerical, and experimental efforts. For off-resonance and harmonic base excitations, period-doubling events close to grazing impacts are experimentally studied in a macroscale system and a microscale system. The macroscale test apparatus consists of a base excited aluminum cantilever with attractive and repulsive tip interactions. The attractive force is generated through a combination of magnets, one located at the cantilever structure’s tip and another attached to a high-resolution translatory stage. The repulsive forces are generated through impacts of the cantilever tip with the compliant material that covers the magnet on the translatory stage. The microscale system is an atomic force microscope cantilever operated in tapping mode. In this mode, this microcantilever experiences a long-range attractive van der Waals force and a repulsive force as the cantilever tip comes close to the sample. The qualitative changes observed in the experiments are further explored through numerical studies, assuming that the system response is dominated by the fundamental cantilever vibratory mode. In both the microscale and macroscale cases, contact is modeled by using a quadratic repulsive force. A reduced-order model, which is developed on the basis of a single mode approximation, is employed to understand the period-doubling phenomenon experimentally observed close to grazing in both the macroscale and microscale systems. The associated near-grazing dynamics is examined by carrying out local analyses with Poincaré map constructions to show that the observed period-doubling events are possible for the considered nonlinear tip interactions. In the corresponding experiments, the stability of the observed grazing periodic orbits has been assessed by constructing the Jacobian matrix from the experimentally obtained Poincaré map. The present study also sheds light on the use of macroscale systems to understand near-grazing dynamics in microscale systems.
Starting Page	1297
Ending Page	1310
Page Count	14
File Format	PDF
ISSN	0924090X
Journal	Nonlinear Dynamics
Volume Number	70
Issue Number	2
e-ISSN	1573269X
Language	English
Publisher	Springer Netherlands
Publisher Date	2012-08-01
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Grazing Cantilever dynamics Off-resonance excitations Period-doubling bifurcation Atomic force microscopy Mechanical Engineering Automotive Engineering Mechanics Vibration, Dynamical Systems, Control
Content Type	Text
Resource Type	Article
Subject	Ocean Engineering Applied Mathematics Control and Systems Engineering Mechanical Engineering Electrical and Electronic Engineering Aerospace Engineering

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