Porous Dielectric Hydrogel In MEMS Capacitive Sensors: Static And Dynamic Nonlinear Analysis

Abstract

This study investigates the static and non-linear behavior of a circular microplate resting on a porous polymeric/elastomeric dielectric hydrogel foam, which fills the gap of the capacitive accelerometer sensor and is simultaneously subjected to transverse harmonic base acceleration excitation and static bias excitation. Based on the von-Karman relations and the Hamilton’s principle and introducing the Airy stress function, the governing nonlinear coupled partial differential equations of the problem under fully clamped edge boundary conditions are derived and using the Galerkin’s procedure are reduced to a set of nonlinear ODEs with time. Then, the validity of the formulation for analyzing the pull-in behavior of the problem achieved by comparing the obtained results with those of the literature. The static pull-in behavior of an electrostatically actuated microplate is investigated with respect to variations of the hydrogel layer parameters by solving the governed equations of multi-degree of freedom equilibrium states. In a following using the perturbation method and considering the nonlinear approximate solution of third order, the primary resonance of the problem is analyzed under the base excitation by transverse acceleration. This is done by deriving the modulation equations for the frequency response and the basic acceleration response under steady-state conditions. The existence and stability conditions of Mult-coexisting non-trivial solutions for nonlinear responses are discussed and the bifurcation points of the related characteristic curves are derived and it is shown that changes in different parameters can lead to the jump phenomenon. Performing 2-Dim and 3_Dim bifurcation diagrams and through a comprehensive analysis, the influences of the problem parameters such as bias voltage, acceleration amplitude, acceleration frequency, damping and initial volume fraction of porosity, dielectric coefficient and initial Young's modulus of the hydrogel on the nonlinear behavior of the sensor are studied and it is shown that the porosity of the hydrogel has a significant influence on the resonance amplitude.