This study analyzes the large-amplitude, nonlinear vibration of dielectric elastomer membrane disks with applied voltages through their thickness and mechanical loads applied radially around their outer circumferential surface. The material is modeled as an isotropic ideal dielectric, with the large-stretch mechanical stiffening captured using the Gent hyperelastic constitutive model. The fully nonlinear equation of motion for the coupled electromechanical system is derived using Hamilton’s principle. The disk comes to a steady equilibrium where the compressive stresses due to the applied voltage balance the tensile stresses from the applied radial loads. The equilibria are calculated numerically for a wide range of radial loads, applied voltages, and limiting stretches. It is possible for the disk to have two stable steady equilibria at given radial load and applied voltage, which gives rise to an instability where extreme stretches occur for infinitesimal changes in applied voltage. The equation of motion is determined for small vibrations of the system about equilibrium. Different from that for thin membrane disks, the vibrating mass of thick membrane disks depends on the steady equilibrium stretch. The natural frequency for membrane disks meaningfully decreases with increasing thickness due to the inertia associated with dynamic changes in the membrane thickness. The amount of axial inertia depends on the ratio of the nominal disk thickness to its radius and the steady equilibrium stretch. The limitations of the small vibration model are numerically determined in terms of the vibration amplitude, applied voltage, and membrane disk thickness. The linear model is less accurate for thick membrane disks than thin ones, where the inertia associated with changes in thickness is negligible. The linear model also suffers from inaccuracy in the vicinity of the bifurcation voltages where large stretches occur with small changes in voltage. Large amplitude vibrations are numerically investigated for a wide range of system parameters.


Nonlinear Vibration of Thick Dielectric Membrane Disks With Radial Loads

Division / Sponsors: 
Aerospace Division

Paper Proceedings: https://asmedigitalcollection.asme.org/SMASIS/SMASIS2020/volume/84027

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