Showing 11 results for Pull-in
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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.
Amir R. Askari, Masoud Tahani,
Volume 14, Issue 8 (11-2014)
Abstract
Rrectangular plates-based resonant micro-sensors utilize the resonance frequency of electrically pre-deformed clamped micro-plates for sensing. Free vibration analysis of such systems in order to find their resonance frequency is the objective of present paper. For this aim, the modified couple stress theory (MCST) together with the Kirchhoff plate model is considered and the size-dependent equation of motion which accounts for the effect of axial residual stresses as well as the non-linear and distributed electrostatic force is derived using the Hamilton's principle. The lowest frequency of the system as the resonance frequency of these micro-plates is extracted using a single mode Galerkin based reduced order model (ROM). It is found that the fundamental frequency of the system is decreased with an increase of applied voltage and becomes zero when the input voltage reaches the pull-in voltage of the system. The findings of present paper are compared and validated by available results in the literature and an excellent agreement between them is observed. Also it is found that using the MCST in pull-in analysis of clamped rectangular micro-plates can remove the existing gap between the results of classical theory (CT) and available empirical observations. Furthermore, it is observed that accounting for the size-effect on free vibration analysis of electrostatically pre-deformed micro-plates is more essential than flat ones.
Ghader Rezazadeh, Morteza Sadeghi, Mohammad Fathalilou,
Volume 14, Issue 15 (3-2015)
Abstract
Size dependent behavior of materials appears for a structure when the characteristic size such as thickness or diameter is close to its internal length-scale parameter. In these cases, ignoring this behavior in modeling may leads to incorrect results. In this paper, strong effects of the size dependence on the static and dynamic behavior of the electrostatically actuated micro-beams have been studied. The equilibrium positions or fixed points of the gold and nickel micro-beams have been determined and shown that for a given DC voltage, there is a considerable difference between the fixed points gained using the classic beam theory and the modified couple stress theory. In addition, it has been shown that the static and dynamic pull-in voltages gained using the couple stress theory are several times higher than those gained using the classic beam theory. Some previous studies have applied the classic beam theory in their models and introduced a considerable hypothetical value of residual stress to match their experimental and incorrect theoretical results. It has been shown that using the modified couple stress theory decreases considerably the difference with the experimental results.
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.
Mohammad Fathalilou, Mojtaba Rezaee,
Volume 16, Issue 6 (8-2016)
Abstract
Electrostatic micro-sensors as a part of microelectromechanical systems (MEMS) play an important role in modern technology. So, precise modeling and suitable solutions for solving the governing mechanical and vibrational equations of them are of great importance. Due to the nonlinear nature of the electrostatic excitation, numerical methods are used to solve the governing equations. This paper presents a comparison between two Galerkin-based approaches to solve them. In the first approach, as used by many researchers in the literature, both sides of the equations are multiplied with the denominator of the electrical force term and then the Galerkin method is applied, whereas in the second approach, we apply direct Galerkin method to solve the equation. As a case study the nonlocal elasticity theory has been used to obtain the governing equation. The results show that for a given beam, although the both approaches predict same pull-in voltage in most cases, but the first approach cannot predict the pull-in instability in some cases and also misses some fixed points. So, the bifurcation diagrams and phase portraits have different quality in the two approaches. Also, the results show that the singular point which is the position of the substrate plate, acts as a strong attractor in the phase diagrams which the first approach is unable to predict it.
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.
Aminreza Noghrehabadi, Amir Haghparast,
Volume 16, Issue 11 (1-2017)
Abstract
In this paper, the modified couple stress theory is used to study static and dynamic pull-in instability of a general model of a nano-cantilever under a sudden applied DC voltage in the presence of the surface effects. A partial part of the nano-cantilever is subject to the electrostatic and capillary forces. Euler-Bernoulli theory is used to model the beam and the equation of motion is derived by using Hamilton’s principle. The governing equations are transformed into a non-dimensional form and then solved using finite element method (FEM). The results, obtained using FEM are compared with the data available in the literature and found in good agreement. Basic parameters for engineering design at the nanoscale, such as deflection and pull-in voltage have been calculated for both of the dynamic and static modes. The results of dynamic analysis of the beam show that as the voltage increases, the beam goes into an oscillating mode with large amplitudes just before pull-in phenomenon occurs and the beam collapses into the substrate (fixed electrode). Moreover, it is found that a decrease in the length of the fixed electrode (increase of the partially affecting parameter), and the increase of the fringing field effect, the size effect and the surface effect increases the pull-in voltage of the nano-cantilever beam.
Mohsen Bakhtiari Shahri, Hamid Moeenfard, Majid Moavenian,
Volume 17, Issue 1 (3-2017)
Abstract
Circular micro-plates are used in microelectromechanical systems (MEMS) such as micro-pumps and ultrasonic transducers due to their special geometry. One of the most important problems with electrostatic micro-actuators is pull-in instability which prevents large displacements. Stabilization in beyond pull-in displacements can be attained using an appropriate controller. This paper presents a position control problem for an electrostatic micro-actuator consisting two circular clamped micro-plates to enhance the stroke and speed up the input commands. To consider the modeling error and geometric uncertainties, a fuzzy controller is applied. First, the equation of the plates vibration is derived using Lagrange equation with single mode assumption. Fuzzy rule-base is constructed according to static and dynamic simulations. Genetic algorithm is utilized for finding the optimum parameters of the controller to accelerate accomplishing the commands. Finally, the maximum voltage of the plates is fitted with a function using the optimization results for full range gap commands. The performance of the fuzzy controller along with this function is depicted applying step, multiple step and chirp commands. The obtained results show that the objective has been met well.
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.
