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Base excited micro-cantilevers, also called as acoustically excited micro-cantilevers are commonly used for dynamic microscopy. Here, theoretical analysis of parametrically excited such cantilever, immersed in viscous fluids is shown. Parametric actuation is applied using feedback for the base excitation. The excitation induces nonlinearity in system due to nonlinearity in the detection method. Effect of hydrodynamic damping and loading on stability behavior has been examined. Mathematical model of the system is derived with consideration of electronic feedback and with the use of Galerkin’s method it has been converted in to ordinary differential equation. Further, analytical study is carried out using the method of multiple scales. For the stability analysis and amplitude behavior, numerical simulations are performed, which confirms the results of theoretical work. Application of perturbation methods, numerical simulations performed and also the experiments in the other works demonstrates sharp and high peak in frequency response of parametric excitation.
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