This paper investigates the effect of dispersion (van der Waals and Casimir) forces on the pull-in instability of cantilever nano-actuators by considering their range of application. Adomian decomposition is introduced to obtain an analytical solution of the distributed parameter model. Dispersion forces decrease the pull-in deflection and voltage of a nano-actuator. However, the fringing field increases the pull-in deflection while decreasing the pull-in voltage of the actuator. The minimum initial gap and the detachment length of the actuator that does not stick to the substrate due to van der Waals and Casimir attractions were determined. Furthermore, the proposed approach is capable of determining the stress distribution of the actuator at the onset of instability. It is seen that Casimir and van der Waals attractions effectively reduce the maximum value of stress resultants at the onset of instability. The results indicate that Adomian decomposition is a reliable method for simulating nano-structures at submicrometer ranges.
An electromechanical beam-type nano-actuator is one the most important smart nanostructures. In this paper, modified couple stress theory is used to model the size effect on the static pull-in instability of electrostatic nanocantilevers in the presence of dispersion (Casimir/van der Waals) forces. The monotonically iterative method (MIM) and homotopy perturbation method (HPM) are employed to solve the nonlinear constitutive equation of the nanostructure as well as numerical methods. Furthermore, a lumped parameter model is developed to explain the size-dependent pull-in performance of the nano-actuator. The basic engineering design parameters such as critical tip deflection and pull-in voltage of the nanostructure are computed. It is found that dispersion forces decrease the pull-in voltage and deflection of the nano-actuator at sub-micrometer scales. On the other hand, the size effect can increase the pull-in parameters of the nano-actuators. The results indicate that the proposed analytical solutions are reliable for simulating nanostructures at sub-micrometer ranges.
While surface effects often play an important role in the pull-in performance of electromechanical nano-actuators, only a few works have been conducted that take these effects into account. In this paper, the influence of surface effects including residual surface stress and surface elasticity on the pull-in instability of a cantilever nano-actuator is investigated incorporating the influence of quantum vacuum fluctuations through the Casimir attraction. An analytical closed-form solution is obtained in terms of the modified Adomian decomposition (MAD) series and the obtained results are compared with those in the literature as well as the numerical solution. The instability parameters of the actuator are determined. The results demonstrate that surface effects cause the cantilever nano-actuator to behave as a softer structure. It is found that surface effects become more significant for low values of the actuator thickness as well as high values of the initial gap/width ratio. Furthermore, the influence of surface energy on the detachment length and the minimum gap of the freestanding actuator is discussed. Interestingly, the present MAD solution provides reliable results without the shortcomings of the previously proposed homotopy perturbation method.
A nano-scale continuum model is applied to investigating the effect of van der Waals (vdW) attraction on pull-in instability of nano-beams in the presence of electrostatic forces. Two cases including the cantilever and doubly-supported beams are considered. The modified Adomian decomposition (MAD) method is employed to solve the nonlinear constitutive equation of nano-beams in the presence of vdW and electrostatic forces for the first time. The results show that the effect of vdW attraction on the instability of the doubly-supported nano-beam is weak when compared to that of the cantilever due to the higher elastic stiffness of the former. Basic design parameters such as the critical deflection and pull-in voltage of the nano-beam are computed. The minimum initial gap and the detachment length of an actuator that does not stick to the substrate due to intermolecular attractions are determined. As a special case, the instability of freestanding nano-electromechanical systems (NEMS) due to vdW attraction is investigated. The MAD solutions are compared with the numerical ones and a proposed lumped model, as well as models available from the literature.
Herein, the torsion–bending coupled pull-in instability of rotational electromechanical nano–micro mirror is investigated using a two-degree-of-freedom (2-DOF) model. Two nano-scale phenomena (i.e., surface effect and molecular van der Waals attraction) are incorporated in the model. None of the previous 2-DOF models have taken these nano-scale effects into account. Results reveal that the influences of surface effects and intermolecular force on the coupled pull-in voltage of the nano–micro mirror highly depend on the geometrical characteristics of the system. It is found that if the mirror dimensions are of the order of the material length scale parameters, the pull-in characteristics computed via the present 2-DOF model will highly differ from those predicted by previous one-degree-of-freedom (1-DOF) models. Interestingly, the influence of surface effects on pull-in voltage of the system highly depends on the bending/torsion coupling ratio. Moreover, results show that the van der Waals force can reduce the pull-in voltage of the mirror. This deteriorating effect is more highlighted in the torsional mode than the bending mode.
It is well-established that mechanical behavior of nanoscale systems is size dependent. In this paper, strain gradient elasticity theory is used for mathematical modeling of size dependent electromechanical instability of cantilever nanoactuator. The nanoactuator is modeled using Euler–Bernoulli beam theory and equation of motion is derived using Hamilton's principle. In order to solve the nonlinear governing equation, reduced order method (ROM) is employed. The dynamic pull-in instability of the nanoactuator is investigated through plotting the time history and phase portrait of the system. Static and dynamic pull-in voltage of nanoactuator as a function of dimensionless length scale parameters is determined. The obtained results show that when thickness of the nanoactuator is comparable with the intrinsic material length scales, size effect can substantially influence the pull-in behavior of the system.
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