Tuning inertial nonlinearity for passive nonlinear vibration control

  • Samuel C. StantonEmail author
  • Dean Culver
  • Brian P. Mann
Original paper


This paper examines the viability of completely passive control approach based on multiple timescale perturbation methods to elicit desired dynamic cancellation or suppression of nonlinear vibration characteristics. Without appeal to feedback, auxiliary oscillating systems, or nonlinear energy sinks, we demonstrate how inertial nonlinearity balancing can more simply realize distortion-free vibrational responses that are robust to very strong forcing amplitudes across resonant, super-harmonic, and sub-harmonic excitation frequencies as well as opportunities to passively suppress hysteresis, cusp-fold bifurcations, and higher harmonics. Of particular merit are the variegated results concerning critical design points for passive control of sub-harmonic resonances. To most simply capture the essence and broad relevance of the approach, we focus upon a variant of the Duffing oscillator that describes moderately large amplitude vibration of a cantilever beam, various link systems, and kinematically constrained particle motion. The results herein are anticipated to be the most relevant to NEMS/MEMS- based sensing research and technology as well as vibration-based mechanical energy harvesting or mechanical filtering.


Inertial nonlinearity Method of multiple scales Passive vibration control Mechanical filter 



The views expressed are those of the writer and not the Army, DoD, or its components. This material is based upon work supported by, or in part by, the U. S. Army Research Laboratory and the U. S. Army Research Office under contract/Grant Number W911NF-12-R-0012-04.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Human and animal rights

No animals or human subjects were used during the course of the research.


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Copyright information

© US Government 2019

Authors and Affiliations

  1. 1.Engineering Sciences DirectorateUS Army Research OfficeAdelphiUSA
  2. 2.Vehicle Technology DirectorateUS Army Research LaboratoryAdelphiUSA
  3. 3.Mechanical Engineering and Material Science DepartmentDuke UniversityDurhamUSA

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