Comparison of the accuracy of two different hyperelastic models for vibration of dielectric elastomer-based micro-beam resonators

Micro-beam resonator with material nonlinearity can be modeled with hyperelastic models but not all of these can introduce this nonlinearity properly. So we use two models in polynomial series: Neo-Hookean and Biderman. Governing equation of motion of these two models are developed separately with Hamilton principle. It is shown that Neo-Hookean model cannot derive the equation of micro-beam properly because of inadequate terms in comparison with Biderman model. It should be noted that the geometric nonlinearity is modelled with Von-Karman strain-displacement relationship. Deflection of the micro-beam based on Biderman model and parameterized perturbation method (PPM) is verified with fourth order Runge-Kouta numerical method for the first and third mode so that there is an excellent agreement. Also it is shown that increasing mode number leads to increasing of frequency