Nonlinear free and forced vibrations of a dielectric elastomer-based microcantilever for atomic force microscopy

The majority of atomic force microcode (AFM) probes work based on piezoelectric actuation. However, some undesirable phenomena such as creep and hysteresis may appear in the piezoelectric actuators that limit their applications. This paper proposes a novel AFM probe based on dielectric elastomer actuators (DEAs). The DE is modeled via the use of a hyperelastic Cosserat model. Size effects and geometric nonlinearity are included utilizing the modified couple stress theory and the von-Kármán strains. A non-contact interaction condition is adopted for AFM, which is taken into account via the van der Waals force. Governing equations are derived employing Hamilton’s principle, and a reduced model is obtained using an extended Galerkin scheme. The free vibration of the system is formulated when a static voltage is applied to the elastomer. The forced vibration is then formulated when the system is under a combination of static and dynamic voltages. The ordinary differential equations of the free and forced vibrations are numerically and analytically solved by the backward differentiation method and multiple time scales method, respectively. Results are presented in time histories, phase portraits, Poincaré maps, fast Fourier transforms, and frequency amplitude curves. Overall, the obtained information displays that the system undergoes quasiperiodic and periodic motions. Moreover, the resonant response of the DE-based AFM is softening-type.