A Semi-Analytic Modeling of Nonlinearities for Nano-robotic Applications, Macro and Micro Sized Systems

Hysteresis effects on the macro, micro and nano sized piezo-driven systems are presented using a semi-analytical approach. After deriving the equations of motion and related boundary conditions using the Hamilton principle, they have been discretized using the Generalized Differential Quadrature Method (GDQM). Validation with exact and existent numerical methods provided and a good agreement has been observed for linear and nonlinear responses. As a pioneer, the hysteresis loops are provided with present distributed semi-analytical approach. Then, applicability of the obtained hysteresis loop in a nano-manipulation scheme has described exactly. It has shown that an expensive nano-manipulation scheme may be failed in the presence of hysteresis loops. In addition, the effects of the lamination on the hysteresis loop have been investigated. However, lamination strongly changes the linear response of micro and nano electro mechanical systems, nonlinear response shape (hysteresis loops) toward the lamination has not considerably affected.