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Schematics of the 3-D FE mesh used for ANSYS simulations of the clamped–clamped beam. The domain in light gray is the dielectric, and the one in dark gray is the microbeam.
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A consistent one-dimensional distributed electromechanical model of an electrically actuated narrow microbeam with width/height between 0.5–2.0 is derived, and the needed pull-in parameters are extracted with different methods. The model accounts for the position-dependent electrostatic loading, the fringing field effects due to both the finite wid...
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... [34] on the accuracy of different simulation options, we used the tool ROM 144. We adapted the "Sample Miniature Clamped-Clamped Beam Analysis" [35, Example 6.6] to a narrow microbeam by extending the surrounding dielectric medium in order to accurately model the fringing fields. The region analyzed and its discretization into FEs are reported in Fig. 6 for the clamped-clamped microbeam; only half of the system is modeled due to symmetry conditions, and a refined mesh is employed in the gap region. In particular, the dielectric medium is considered as a block of length 100 , semi-width of 24 , and thickness of 24 . For the cantilever microbeam problem, the dielectric domain has been ...
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Citations
... In other simulations of coupled electromechanical problems [25,26,27,28] the electrostatic field was computed resorting to the Boundary Element approach, with a heavy computational burden. ...
This paper presents the first application of the direct parametrisation method for invariant manifolds to a fully coupled multiphysics problem involving the nonlinear vibrations of deformable structures subjected to an electrostatic field. The formulation proposed is intended for model order reduction of electrostatically actuated resonating Micro-Electro-Mechanical Systems (MEMS). The continuous problem is first rewritten in a manner that can be directly handled by the parametrisation method, which relies upon automated asymptotic expansions. A new mixed fully Lagrangian formulation is thus proposed which contains only explicit polynomial nonlinearities, which is then discretised in the framework of finite element procedures. Validation is performed on the classical parallel plate configuration, where different formulations using either the general framework, or an approximation of the electrostatic field due to the geometric configuration selected, are compared. Reduced-order models along these formulations are also compared to full-order simulations operated with a time integration approach. Numerical results show a remarkable performance both in terms of accuracy and wealth of nonlinear effects that can be accounted for. In particular, the transition from hardening to softening behaviour of the primary resonance while increasing the constant voltage component of the electric actuation, is recovered. Secondary resonances leading to superharmonic and parametric resonances are also investigated with the reduced-order model.
... Applying the Galerkin method [4] and after algebraic simplification, Eq. (12) is reduced to where (12) ...
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... In this theory, the long-range forces which lead to the dispersion phenomenon are captured in the propagation of short-wavelength waves in elastic continua [13][14][15]. In recent years, many researchers have addressed the mechanical analysis of micro-and nanostructures such as vibration [16][17][18][19], dynamic stability [20][21][22], buckling and postbuckling [23][24][25], pullin instability [26][27][28], and thermoelasticity behavior [29][30][31] using the non-classical continuum theories. A regime of intermolecular forces, namely the Casimir and van der Waals forces, is established in the proximity between two electrodes in electrostatically actuated NEMS [32][33][34]. ...
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... Pamidighantam et al. [50] refined this model by considering a nonlinear spring that improved the estimate of the pull-in voltage but required an empirical value of the pull-in displacement. In order to obtain better agreement with experimental observations, researchers have used a nonlinear beam equation to predict the pullin parameters [23,52]. If the mode shape corresponding to the fundamental frequency is taken as the basis function, then the one-degree of freedom ROM predicts pull-in parameters close to those given by solutions of three-dimensional equations by the finite element method [53]. ...
We present a new methodology to incorporate the Casimir forces within the molecular dynamics (MD) framework. At atomistic scales, the potential energy between two particles arising due to the Casimir effect can be represented as U(r
ij
) = C/r7. Incorporating the Casimir effect in MD simulations requires the knowledge of C, a problem hitherto unsolved. We overcome this by equating the total potential energy contributions due to each atomistic pair with the potential energy of continuum scale interacting bodies having similar geometries. After having identified the functional form of C, standard MD simulations are augmented with the potential energy contribution due to pairwise Casimir interactions. The developed framework is used to study effects of the Casimir force on the pull-in instability of rectangular and hollow cylindrical shaped deformable electrodes separated by a small distance from a fixed substrate electrode. Our MD results for pull-instability qualitatively agree with the previously reported analytical results but are quantitatively different. The effect of using longer-ranged Casimir forces in a constant temperature environment on the pull-in behaviour has also been studied.
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This paper presents a scheme for the study of dielectrics. For this purpose, fringing field is employed, which is usually considered an undesired effect. Two non-ideal capacitors are placed one beneath the other, which have a region of interlinking fringing fields. If the fringing fields are canceled out, it is called diminutive physically parallel orientation. This capacitor arrangement is placed in a Wheatstone bridge setup, so whenever a dielectric sample is placed within the main capacitor, then it creates distortion in the interlinking fringing fields. This is canceled out when the circuit is balanced, which happens at an optimum plate separation. Thus, the proposed scheme can be used to study fringing field intensity, sense the movement of a dielectric liquid, measure dielectric properties such as permittivity, study materials and biological substances, etc. This work is expected to find application in industrial sensing. Researchers will also find some interesting ideas to ponder upon.
