MODELING OF SURFACE STRESS EFFECTS ON THE DYNAMIC BEHAVIOR OF ACTUATED NON-CLASSICAL NANO-BRIDGES

2015 ◽  
Vol 39 (2) ◽  
pp. 137-151 ◽  
Author(s):  
Hamid M. Sedighi
Keyword(s):  
Surface Stress ◽  
Initial Conditions ◽  
Couple Stress Theory ◽  
Actuation Voltage ◽  
Homoclinic Orbits ◽  
Modified Couple Stress Theory ◽  
Small Scale ◽  
Actuator Dynamics ◽  
Stress Theory ◽  
In Series

The influence of surface stress and small scale on the dynamic pull-in behavior of nano-bridges is investigated in this paper. For this purpose, the governing equation of motion is derived based on the modified couple stress theory and Homotopy Perturbation Method with an auxiliary term is employed to produce the approximate solution of nano-beam vibrations. The effects of actuation voltage, initial conditions, surface energy and length scale parameter on the pull-in instability and fundamental frequency of the system are studied. The accuracy of proposed asymptotic approach is validated with numerical simulations. The obtained results from asymptotic analysis reveal that two terms in series expansions are sufficient to produce an acceptable approximation. The nano-actuator dynamics exhibit periodic and homoclinic orbits.

Natural vibrations of micro beams with nonrigid supports

2016 ◽  
Vol 23 (19) ◽  
pp. 3233-3246 ◽  
Author(s):  
Diana V Bambill ◽  
Graciela I Guerrero ◽  
Daniel H Felix
Keyword(s):  
Boundary Conditions ◽  
Couple Stress Theory ◽  
Continuum Theory ◽  
Modified Couple Stress Theory ◽  
Free Vibrations ◽  
Small Scale ◽  
Stress Theory ◽  
Edge Conditions ◽  
Micro Systems ◽  
Micro Structures

The present study aims to provide some new information for the design of micro systems. It deals with free vibrations of Bernoulli–Euler micro beams with nonrigid supports. The study is based on the formulation of the modified couple stress theory. This theory is a nonclassical continuum theory that allows one to capture the small-scale size effects in the vibrational behavior of micro structures. More realistic boundary conditions are represented with elastic edge conditions. The effect of Poisson’s ratio on the micro beam characteristics is also analyzed. The present results revealed that the characterization of real boundary conditions is much more important for micro beams than for macro beams, and this is an assessment that cannot be ignored.

Size-dependent in vibration analysis of magnetostrictive sandwich composite micro-plate in magnetic field using modified couple stress theory

2017 ◽  
Vol 21 (2) ◽  
pp. 580-603 ◽  
Author(s):  
A Ghorbanpour Arani ◽  
H Khani Arani ◽  
Z Khoddami Maraghi
Keyword(s):  
Magnetic Field ◽  
Couple Stress Theory ◽  
Composite Fiber ◽  
Modified Couple Stress Theory ◽  
Sandwich Composite ◽  
Small Scale ◽  
Dimensionless Frequency ◽  
Stress Theory ◽  
Fiber Angle ◽  
Modified Couple Stress

In the present study, free vibration of magnetostrictive sandwich composite micro plate with magnetostrictive core and composite face sheets are investigated. The modified couple stress theory is taken into account so as to consider the small scale effects. The surrounding elastic medium is simulated as visco-Pasternak foundation to study the effects of both damping and shear effects. Using energy method, Hamilton’s principle and first-order shear deformation theory, the governing equations of motion and related boundary conditions are obtained. Finally, the differential quadrature method is employed to analysis the vibration of magnetostrictive sandwich composite micro plate. In this regard, the dimensionless frequency are plotted to study the effects of small scale parameter, surrounding elastic medium, magnetic field, composite fiber angle, aspect ratio, thickness ratio, and boundary conditions. The results indicate that the magnetic field and composite fiber angle play a key role in the dimensionless frequency of magnetostrictive sandwich composite micro plate. The obtained results in this article can be used to design sensors and actuators, aerospace industry, and control of vibration response of systems.

Size-Dependent Dynamic Behavior and Instability Analysis of Nano-Scale Rotational Varactor in the Presence of Casimir Attraction

2016 ◽  
Vol 08 (02) ◽  
pp. 1650018 ◽  
Author(s):  
Hamid M. Sedighi ◽  
Meisam Moory-Shirbani ◽  
Mohammad Shishesaz ◽  
Ali Koochi ◽  
Mohamadreza Abadyan
Keyword(s):  
Dynamic Behavior ◽  
Casimir Force ◽  
Scale Parameter ◽  
Dynamic Instability ◽  
Couple Stress Theory ◽  
Modified Couple Stress Theory ◽  
Small Scale ◽  
Stress Theory ◽  
Size Dependent ◽  
Casimir Attraction

When the size of structures approaches to the sub-micron scale, physical responses of such systems become size-dependent, hence, classic theories may not be able to predict the behavior of the miniature structures. In the present article, the modified couple stress theory (MCST) is employed to account for the effect of the size-dependency on the dynamic instability of torsional nano-electromechanical systems (NEMS) varactor. By incorporating the Coulomb, Casimir and damping forces, the dimensionless governing equations are derived. The influences of Casimir force, applied voltage and length scale parameter on the dynamic behavior and stability of fixed points are investigated by plotting the phase portrait and bifurcation diagrams. It is found that the Casimir force reduces the instability threshold of the systems and the small-scale parameter enhances the torsional stability. The pull-in instability phenomenon shows the saddle-node bifurcation for torsional nano-varactor.

Nonlinear Vibration of Size Dependent Microresonators with an Electrostatically Actuated Proof Mass

2018 ◽  
Vol 18 (04) ◽  
pp. 1850057 ◽  
Author(s):  
Ehsan Sharifinsab ◽  
Mahdi Mojahedi
Keyword(s):  
Nonlinear Vibration ◽  
Microelectromechanical Systems ◽  
Proof Mass ◽  
Multiple Scales ◽  
Initial Conditions ◽  
Couple Stress Theory ◽  
Modified Couple Stress Theory ◽  
System Response ◽  
Stress Theory ◽  
Size Dependent

In this paper, the dynamic and nonlinear vibration responses of a microresonator containing a microbridge with a proof mass located at its middle are studied. The proof mass of the microresonator is actuated by the electrostatic field in such a way that a direct voltage finds a certain equilibrium position and then be prompted to vibration under the alternative voltage. Due to the importance of the size dependency effect in analysis of the performance of microelectromechanical systems, the size dependent theory is used in the modeling of the microstructure. By adopting the modified couple stress theory and considering electrostatic actuation, the dynamic equation of motion is derived using the extended Hamilton’s principle. Further, with the approximation by Galerkin’s method, the governing equation for the static and oscillatory motion is reduced and the resultant equation is solved by analytical (multiple-scales) and numerical methods. In the analytical and numerical results, the effects of various parameters on the system response, including the midplane stretching and size dependent effects, and dependency of vibration response to initial conditions, are analyzed in detail.

scholarly journals Free Vibration Analysis of Shear Deformable Small-Scale Tubes

2020 ◽  
Vol 3 (1) ◽  
pp. 418-427
Author(s):  
Reza Aghazadeh
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Couple Stress ◽  
Couple Stress Theory ◽  
Free Vibration Analysis ◽  
Modified Couple Stress Theory ◽  
Small Scale ◽  
Tube Model ◽  
Stress Theory ◽  
Modified Couple Stress

This study presents an approach for investigating free vibration problem of small-scale tubes based on modified couple stress theory in conjunction with higher order shear deformation tube model. The size effect is captured through utilization of a length scale parameter involved in modified couple stress theory. A newly developed refined tube model is employed to satisfy friction-free conditions on inner and outer surfaces of micro-tubes. Hamilton’s principle is used as a variational technique for derivation of governing system of equations. For axial vibrations, an analytical procedure is conducted, while for transverse vibrations differential quadrature method is used as a numerical technique. The correctness of numerical results are verified through comparisons made with results which are available in the literature for limiting cases. The analyses reveal the effects of size and transverse shear deformation on the natural frequencies of micro-tubes.

Effects of couple stresses on the in-plane vibration of micro-rotating disks

2020 ◽  
Vol 26 (13-14) ◽  
pp. 1246-1259
Author(s):  
Emadoddin Bagheri ◽  
Mostafa Jahangiri ◽  
Mohsen Asghari
Keyword(s):  
Free Vibration ◽  
Mechanical Behavior ◽  
Couple Stress ◽  
Scale Effects ◽  
Couple Stress Theory ◽  
Modified Couple Stress Theory ◽  
Small Scale ◽  
Rotating Disks ◽  
Stress Theory ◽  
Modified Couple Stress

Micro-rotating disks are extensively used in micro-electromechanical systems such as micro-gyroscopes and micro-rotors. Because of the sensitivity of these elements, enough knowledge about the mechanical behavior of these structures is an essential matter for designers and fabricators. The small-scale effects on the in-plane free vibration of such micro-disks present an important aspect of the mechanical behavior of these elements. The small-scale effects on the in-plane free vibration of these micro-disks are investigated in this study using the modified couple stress theory. By using the Hamilton principle, the partial differential equations governing the coupled radial and tangential motion of the disk particles with their corresponding boundary conditions are derived. Then, the solution for the boundary value problem is analytically presented. The effects of the angular speed of the micro-disks and the length scale parameter of the modified couple stress theory on the steady radial and tangential displacements, and on the natural frequencies are investigated. Those results are compared with the ones previously obtained from the classical continuum mechanics analysis.

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