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Nonlinear dynamics of miniaturized dielectric elastomer actuators with surface effects

##article.authors##

  • Akhil Pratap Singh Soft Active Materials and Structures Laboratory, Department of Mechanical Engineering, Indian Institute of Technology Jodhpur 342030, India
  • Gal Shmuel Faculty of Mechanical Engineering, Technion-Israel Institute of Technology, Haifa 32000, Israel
  • ATUL KUMAR SHARMA IIT Jodhpur 0000-0001-9086-8441

Abstract

Dielectric elastomer actuators (DEAs) have attracted considerable attention for applications requiring lightweight, compliant, and large-strain electromechanical transduction. However, the reduction of operating voltage through miniaturization introduces pronounced surface and interfacial effects that can significantly alter the dynamic response and stability characteristics of these systems. In this work, a dynamic electromechanical framework is developed to investigate the nonlinear dynamics of miniaturized dielectric elastomer actuators while explicitly incorporating surface elasticity, intrinsic surface energy, and surface tension. The dielectric elastomer is modeled as an incompressible neo-Hookean ideal dielectric, and the governing nonlinear equation of motion is derived using an Euler-Lagrange formulation under finite deformation. An energy-based approach is further employed to predict the onset of dynamic pull-in instability and the associated critical conditions. The dynamic response under both DC and AC voltage excitations is examined through transient time-history analysis, phase portraits, Poincaré maps, and frequency-response characteristics. Particular attention is devoted to dynamic pull-in instability and its dependence on surface parameters. The predictions of critical instability parameters are verified through direct numerical integration of the nonlinear governing equation, showing close agreement. A comprehensive parametric study reveals how surface elasticity, intrinsic surface energy, and surface tension modify the effective stiffness, resonance behavior, and critical instability thresholds of miniaturized DEAs. The results demonstrate that surface effects substantially shift dynamic pull-in voltages and alter nonlinear oscillatory characteristics, highlighting their critical role in the design and development of miniaturized dielectric elastomer actuators operating under transient electromechanical loading.

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Posted

2026-05-28