Cauchy stresses and vibration frequencies for the instability parameters of dielectric elastomer actuators

• Published in: Journal of applied polymer science 2018-06, Vol.135 (21), p.n/a
• Main Authors: Kim, Tae‐Jong, Liu, Yanju, Leng, Jinsong
• Format: Article
• Language: English
• Subjects: Actuators; Bifurcations; Computational fluid dynamics; Deformation; Dynamic response; Dynamic stability; Elastomers; Electrical loads; Energy consumption; Equations of motion; Frequency response; Frequency stability; Galerkin method; Isotropic material; Materials science; Mathematical models; membranes; Nonlinear dynamics; Parametric analysis; Polymers; sensors and actuators; Stability analysis; Step voltage; Stresses; Vibration analysis
• ISSN: 0021-8995; 1097-4628
• DOI: 10.1002/app.46215

ABSTRACT An analysis of the effect of Cauchy stresses, vibration frequency response, and instability on the transient dynamic response of step‐voltage‐driven dielectric elastomer actuators (DEAs) is presented in this paper. Material nonlinearities associated with the hyperelastic constitutive law are taken into account, and the membrane is assumed to be made of an isotropic, homogeneous, and incompressible material. The results for the neo‐Hookean material model are further extended to analyze relatively complex multiparameter hyperelastic models (Mooney–Rivlin and Ogden) that are often employed for investigating the behavior of DEAs. The dynamic instability parameters are predicted using energy‐based extraction of static instability and validated by the response of the material in the vicinity of the dynamic instability. The natural modes of the membrane are used to approximate the nonlinear deformation field using the Galerkin method. A detailed parametric analysis of the equations of motion for the prestretched membrane shows the natural frequencies and mode shapes of the membrane and the strong influence of the stretching ratios and material parameters on the linear and nonlinear oscillations of the membrane. The results of the present investigation show the electric field–frequency relations, resonance curves, and bifurcation diagrams using the nonlinear dynamics of DEAs subjected to electrical loads. © 2018 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2018, 135, 46215.