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On 1:2 Internal Resonances in In-Plane Vibrations of Electrostrictive Plates

[+] Author Affiliations
Astitva Tripathi, Anil K. Bajaj

Purdue University, West Lafayette, IN

Paper No. DETC2014-35008, pp. V007T05A011; 8 pages
doi:10.1115/DETC2014-35008
From:
  • ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 7: 2nd Biennial International Conference on Dynamics for Design; 26th International Conference on Design Theory and Methodology
  • Buffalo, New York, USA, August 17–20, 2014
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-4640-7
  • Copyright © 2014 by ASME

abstract

Electrostrictive polymers are popular materials being employed in fabrication of high-strain actuators for use in new generation micro- and nano-scale devices along with applications such as artificial muscles. In this work, possibility of 1:2 internal resonances in in-plane vibrations of appropriately designed electrostrictive plates is investigated. The polymer is assumed to have mechanical response similar to that of a Mooney Rivlin material and the induced strain having a quadratic dependence on the applied external electric field. A Finite Element Method (FEM) formulation is used to develop mode shapes of a structure whose lowest two natural frequencies have been brought close to the ratio of 1:2. Using the mode shapes thus obtained, a more complete Lagrangian formulation is used to develop a nonlinear two-mode model of the electrostrictive plate structure. Application of a harmonic electric field results in in-plane parametric oscillations of the structure. The nonlinear response of the structure is developed using averaging on the two-mode model. The structure exhibits 1:2 internal resonance due to the large amplitude vibrations through the route of parametric excitation. The effects of material constitutive parameters on the nonlinear response are investigated.

Copyright © 2014 by ASME

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