Electrostriction is a recent actuation mechanism which is being explored for a variety of new micro- and millimeter scale devices along with macroscale applications such as artificial muscles. The general characteristics of these materials and the nature of actuation lend itself to possible production of very rich nonlinear dynamic behavior. In this work, principal parametric resonance of the second mode in in-plane vibrations of appropriately designed electrostrictive plates is investigated. The plates are made of an electrostrictive polymer whose mechanical response can be approximated by Mooney Rivlin model, and the induced strain is assumed to have quadratic dependence on the applied electric field. A finite element model (FEM) formulation is used to develop mode shapes of the linearized structure whose lowest two natural frequencies are designed to be close to be in 1:2 ratio. Using these two structural modes and the complete Lagrangian, a nonlinear two-mode model of the electrostrictive plate structure is developed. Application of a harmonic electric field results in in-plane parametric oscillations. The nonlinear response of the structure is studied using averaging on the two-mode model. The structure exhibits 1:2 internal resonance and large amplitude vibrations through the route of parametric excitation. The principal parametric resonance of the second mode is investigated in detail, and the time response of the averaged system is also computed at few frequencies to demonstrate stability of branches. Some results for the case of principal parametric resonance of the first mode are also presented.
Skip Nav Destination
Article navigation
September 2018
Research-Article
Analysis of Parametric Resonances in In-Plane Vibrations of Electrostrictive Hyperelastic Plates
Astitva Tripathi,
Astitva Tripathi
School of Mechanical Engineering,
Purdue University,
West Lafayette, IN 47907
e-mail: astitva.tripathi@gmail.com
Purdue University,
West Lafayette, IN 47907
e-mail: astitva.tripathi@gmail.com
Search for other works by this author on:
Anil K. Bajaj
Anil K. Bajaj
Search for other works by this author on:
Astitva Tripathi
School of Mechanical Engineering,
Purdue University,
West Lafayette, IN 47907
e-mail: astitva.tripathi@gmail.com
Purdue University,
West Lafayette, IN 47907
e-mail: astitva.tripathi@gmail.com
Anil K. Bajaj
1Corresponding author.
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received August 1, 2017; final manuscript received February 25, 2018; published online July 26, 2018. Assoc. Editor: Hiroshi Yabuno.
J. Comput. Nonlinear Dynam. Sep 2018, 13(9): 090911 (11 pages)
Published Online: July 26, 2018
Article history
Received:
August 1, 2017
Revised:
February 25, 2018
Citation
Tripathi, A., and Bajaj, A. K. (July 26, 2018). "Analysis of Parametric Resonances in In-Plane Vibrations of Electrostrictive Hyperelastic Plates." ASME. J. Comput. Nonlinear Dynam. September 2018; 13(9): 090911. https://doi.org/10.1115/1.4040261
Download citation file:
176
Views
Get Email Alerts
Cited By
Irrational Nonlinearity Enhances the Targeted Energy Transfer in a Rotary Nonlinear Energy Sink
J. Comput. Nonlinear Dynam (June 2024)
Investigation of Gear Meshing Vibration and Meshing Impact Resonance Intensity Assessment
J. Comput. Nonlinear Dynam (May 2024)
Hand Vibration Reduction Using Nonlinear Vibration Absorber for the Vibro-Impact Hammer Model
J. Comput. Nonlinear Dynam
Related Articles
Study of Train Derailments Caused by Damage to Suspension Systems
J. Comput. Nonlinear Dynam (May,2016)
Hybrid Delayed Synchronizations of Complex Chaotic Systems in Modulus-Phase Spaces and Its Application
J. Comput. Nonlinear Dynam (July,2016)
Takagi–Sugeno Fuzzy Predictive Control for a Class of Nonlinear System With Constrains and Disturbances
J. Comput. Nonlinear Dynam (September,2015)
Dynamic Response Optimization of Complex Multibody Systems in a Penalty Formulation Using Adjoint Sensitivity
J. Comput. Nonlinear Dynam (May,2015)
Related Proceedings Papers
Related Chapters
Dynamic Behavior in a Singular Delayed Bioeconomic Model
International Conference on Instrumentation, Measurement, Circuits and Systems (ICIMCS 2011)
Two-Dimension Simulation of a Red Blood Cell Partitioning in Microvascular Bifurcation
International Conference on Software Technology and Engineering (ICSTE 2012)
A Perturbation Solution for Interlaminar Stresses In Bidirectional Laminates
Composite Materials: Testing and Design (Fourth Conference)