Showing 6 results for Pull-In Instability
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Volume 12, Issue 3 (8-2012)
Abstract
In this paper, stress gradient theory is used to model the static pull-in instability and size effect of electrostatic nanocantilevers in the presence of electrostatic and dispersion (Casimir/van der Waals) forces. The Differential transformation method (DTM) is employed to solve the nonlinear constitutive equation of the nanostructure as well as numerical methods. The basic engineering design parameters such as critical tip deflection and pull-in voltage of the nanostructure are computed. It is found that in the presence of dispersion forces, both pull-in voltage and deflection of the nanobeam increase with increasing the size effect. Compared to the pull-in voltage, the pullin deflection of the beam is less sensitive to the size effect at sub-micrometer scales. On the other hand, the size effect can increase the pull-in parameters of the nano-actuators only in sub-micrometer scales. The results indicate that the proposed analytical solutions are reliable for simulating nanostructures at sub-micrometer ranges.
Iman Karimipour, Ahmad Reza Karimipour, Yaghoub Tadi Beni,
Volume 15, Issue 2 (4-2015)
Abstract
In recent decade, modeling the instability of nanostructures has attracted many attentions in nanomechanics. Nanomechanical switches are fundamental building blocks for the design of NEMS applications, such as nanotweezers and nanoscale actuators. One common type of NEMS including nano-bridge in micro mirrors is used. At nano-scales, the decreasing gap between the two electrodes makes surface traction due to molecular interaction such as van der Waals that must be taken into account in the analysis of NEMS. In this study, strain gradient theory has been used to investigate the size dependent pull-in instability of beam-type (NEMS)where is an inherent instability in them. The von-Karman nonlinear strain has been applied to derive the constitutive equation of the system. Effect of intermolecular force have been included in the nonlinear governing equations of the systems. Homotopy perturbation method (HPM) has been employed to solve the nonlinear equations. Effect of intermolecular attraction and the size dependency and the importance of coupling between them on the instability performance i.e. critical deflection and instability voltage have been discussed. According the findings of this research, one can conclude that intermolecular forces decrease pull-in voltage and size effect parameter in nano scale leads to increase of pull-in parameters. Also HPM method can be applied as efficient method to analyze beam type nano structures.
Soroosh Malihi, Yaghoub Tadi Bani,
Volume 16, Issue 5 (7-2016)
Abstract
Consideration of dynamic and static behavior of structures in nano and micro scale for analysis and predicting of their performance and accuracy have more importance. In this study, the effect of size and intermolecular van der Waals force on dynamic behavior of torsional nanomirror considering bending-torsion two degree of freedom model using the higher order modified couple stress theory has been investigated. First considering the higher order modified couple stress theory and intermolecular van der Waals force, equation of motion of system is developed, afterwards using Rung-Kuta method, this equations is solved and dynamic performance of nanomirror and its phase portraits have been obtained. Also translational and torsional natural frequencies of system considering applied voltage are investigated. So pull-in instability parameters of system are considered and their dependency upon van der Waals force and size effects are determined. Results demonstrate that equilibrium points of system include center points and focus points that phase portraits related to these points exhibit periodic orbits and heteroclinic orbits. Also size effect and modified couple stress model on amplitude and frequency of vibration of system have been investigated. Proposed model in this study is able to predict experimental results with higher precision than previous classic models and reduce the difference between past theories and empirical results.
Vahid Marefat,
Volume 16, Issue 10 (1-2017)
Abstract
In this paper a nonlinear controller is going to be designed for micro-beam’s deflections under mechanical shock effects. The micro-beam is supposed to undergo mechanical shocks. Mechanical shocks are one of the failure sources and the controller is to considerably suppress shock’s unfavorable effects. Half-Sine, rectangular and triangular pulses are chosen as reference shock signals to represent true complicated shock signals in nature which consist of different harmonics. Two layers of electrodes are placed in both sides of the micro-beam and they are used to actuate the micro-beam by different voltage levels. Upper layer is specifically meant for control purpose. Nonlinear equations governing micro-beam’s deflection dynamics are derived, discretized by Galerkin method to a set of nonlinear duffing type ODE and used to investigate micro-beams response to each shock input signal. Controller design is based on a simple nonlinear model formed by micro-beam’s first mode shape. Proper second order behavior is generated by feedback linearization method as controller logic. Finally controller performance and shock rejecting capability is evaluated by numerical simulations. Controller is shown to be very effective in diminishing shock unfavorable effects and postponing pull-in instability by numerical simulations.
Mohammad Ali Mokhtari Amir Majdi, Masoud Tahani,
Volume 18, Issue 1 (3-2018)
Abstract
The aim of the proposed study is to investigate the size dependent behavior of the micro-bridge gyroscopes under the combined effects of instantaneous DC voltage and harmonic base excitation. To do so, modified couple stress theory is utilized to model the size-dependent behavior of the micro-gyroscope. To avoid resonance, viscous damping is used. Hamilton’s principle is then employed to derive the governing equations of motion. Afterwards, to convert the partial differential equations of motion to ordinary differential equations of motion, a Galerkin based single mode approximation is made. Then fourth-order Range-Kutta method is used to solve the governing equations of motion. To check the accuracy of the present model, the results are then validated through comparison with the available results in the literature and the comparison shows good agreements. In addition to the previous comparison, the present results are the validated through comparison with the results of COMSOL simulation. Furthermore, the effects of different parameters on the dynamic pull-in instability and amplitude of the vibrations are investigated. The observation shows that for the case of the harmonic base excitation, the system will be excited on two frequencies.
E. Akrami Nia, H. Ekhteraei Toussi,
Volume 19, Issue 10 (10-2019)
Abstract
Microbeams are one of the most important members of microelectromechanical systems (MEMS) which contrast of electrical and mechanical forces in them cause pull-in instability. One of the proposed mechanisms for controlling this instability and enlarging the stable range of system are initially curved microbeams. Despite studying various pull-in instability in straight elastic or viscoelastic microbeams, the instability of curved microbeams has been investigated only within the range of elastic behavior. Therefore in the present study, assuming a clamped-clamped viscoelastic initially curved microbeam, the effect of viscoelastic behavior on the instabilities called snap-through and pull-in, was investigated. The viscoelastic behavior was simulated by the standard anelastic linear solid model. The governing differential equation was obtained based on the modified couple stress theory and by use of Hamilton’s pull-in instability principle. By using the Galerkin method, the governing equation was converted to a nonlinear ordinary differential equation and solved by MATLAB sofware. The structure behaviors are compared in two extreme situations before and after the viscoelastic relaxation by drawing diagrams. The results show when the time of structure relaxation increases, viscoelastic behavior causes more decreasing in instabilities voltage, but its effect on the position of instability will depend on the axial load. In this way, in the presence of tensile load, viscoelastic behavior increases the snap-through position and decreases the pull-in position, but in the presence of compressive load, snap-through occurs at smaller deflections and pull-in occurs at larger deflections.
