scholarly journals Snap-through buckling of initially curved microbeam subject to an electrostatic force

2015 ◽  
Vol 471 (2177) ◽  
pp. 20150072 ◽  
Author(s):  
X. Chen ◽  
S. A. Meguid
Keyword(s):  
Electrostatic Force ◽  
Couple Stress Theory ◽  
Beam Theory ◽  
Intermolecular Forces ◽  
Modified Couple Stress Theory ◽  
Casimir Forces ◽  
Governing Equations ◽  
Stress Theory ◽  
Fringing Field ◽  
Curved Microbeam

In this paper, the snap-through buckling of an initially curved microbeam subject to an electrostatic force, accounting for fringing field effect, is investigated. The general governing equations of the curved microbeam are developed using Euler–Bernoulli beam theory and used to develop a new criterion for the snap-through buckling of that beam. The size effect of the microbeam is accounted for using the modified couple stress theory, and intermolecular effects, such as van der Waals and Casimir forces, are also included in our snap-through formulations. The snap-through governing equations are solved using Galerkin decomposition of the deflection. The results of our work enable us to carefully characterize the snap-through behaviour of the initially curved microbeam. They further reveal the significant effect of the beam size, and to a much lesser extent, the effect of fringing field and intermolecular forces, upon the snap-through criterion for the curved beam.

scholarly journals Vibration Characteristics of Piezoelectric Microbeams Based on the Modified Couple Stress Theory

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
R. Ansari ◽  
M. A. Ashrafi ◽  
S. Hosseinzadeh
Keyword(s):  
Boundary Conditions ◽  
Couple Stress ◽  
Natural Frequencies ◽  
Couple Stress Theory ◽  
Equations Of Motion ◽  
Modified Couple Stress Theory ◽  
Beam Model ◽  
Governing Equations ◽  
Stress Theory ◽  
Modified Couple Stress

The vibration behavior of piezoelectric microbeams is studied on the basis of the modified couple stress theory. The governing equations of motion and boundary conditions for the Euler-Bernoulli and Timoshenko beam models are derived using Hamilton’s principle. By the exact solution of the governing equations, an expression for natural frequencies of microbeams with simply supported boundary conditions is obtained. Numerical results for both beam models are presented and the effects of piezoelectricity and length scale parameter are illustrated. It is found that the influences of piezoelectricity and size effects are more prominent when the length of microbeams decreases. A comparison between two beam models also reveals that the Euler-Bernoulli beam model tends to overestimate the natural frequencies of microbeams as compared to its Timoshenko counterpart.

Static Deflection and Pull-In Instability of the Electrostatically Actuated Bilayer Microcantilever Beams

2015 ◽  
Vol 07 (06) ◽  
pp. 1550090 ◽  
Author(s):  
M. Mojahedi ◽  
M. Rahaeifard
Keyword(s):  
Scale Parameter ◽  
Couple Stress Theory ◽  
Beam Theory ◽  
Modified Couple Stress Theory ◽  
Length Scale Parameter ◽  
Length Scale ◽  
Static Deflection ◽  
Static Behavior ◽  
Stress Theory ◽  
Electrostatically Actuated

This paper deals with the static behavior of an electrostatically actuated bilayered microswitch on the basis of the modified couple stress theory. The beam is modeled using Euler–Bernoulli beam theory and equivalent elastic modulus and length scale parameter are presented for the bilayer beam. Static deflection and pull-in voltage of the beam is calculated using numerical and analytical methods. The numerical method is based on an iterative approach while the homotopy perturbation method (HPM) is utilized for the analytical simulation. Results show that there is a very good agreement between these methods even in the vicinity of the pull-in instability. Moreover, the effects of different parameters such as thicknesses of layers and length scale parameter on the static deflection and instability of the microcantilever are studied. Results show that for the cases with the equivalent length scale parameter comparable to the thickness of beam, the size-dependency plays significant roles in the static behavior of the bilayer microcantilevers.

Magnetic field effect on free vibration of smart rotary functionally graded nano/microplates: A comparative study on modified couple stress theory and nonlocal elasticity theory

2018 ◽  
Vol 29 (11) ◽  
pp. 2492-2507 ◽  
Author(s):  
Mohammad Hassan Shojaeefard ◽  
Hamed Saeidi Googarchin ◽  
Mohammad Mahinzare ◽  
Seyed Ahmad Eftekhari
Keyword(s):  
Elastic Material ◽  
Nonlocal Elasticity ◽  
Couple Stress ◽  
Couple Stress Theory ◽  
Nonlocal Elasticity Theory ◽  
Modified Couple Stress Theory ◽  
Functionally Graded ◽  
Governing Equations ◽  
Stress Theory ◽  
Modified Couple Stress

In this article, free vibration behavior of a rotating nano/microcircular plate constructed from functionally graded magneto-elastic material is simulated with the first-order shear deformation theory. For the sake of comparison, the nonlocal elasticity theory and the modified couple stress theory are employed to implement the small size effect in the natural frequencies behavior of the nano/microcircular plate. The governing equations of motion for functionally graded magneto-elastic material nano/microcircular plates are derived based on Hamilton’s principle; comparing the obtained results with those in the literature, they are in a good agreement. Finally, the governing equations are solved using the differential quadrature method. It is shown that the vibrational characteristics of functionally graded magneto-elastic material nano/microcircular plates are significantly affected by non-dimensional angular velocity, size dependency of the Eringen’s and the modified couple stress theories, and power law index for clamped and hinged boundary conditions. Results show that a critical point occurs by increasing the angular velocity and the effect of several parameters are changed after this point.

scholarly journals Pull-In and Snap-Through Analysis of Electrically Actuated Viscoelastic Curved Microbeam

2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Ehsan Akrami-Nia ◽  
Hamid Ekhteraei-Toussi
Keyword(s):  
Governing Equation ◽  
Couple Stress Theory ◽  
Viscoelastic Behavior ◽  
Modified Couple Stress Theory ◽  
Stress Theory ◽  
Viscoelastic Parameters ◽  
Relaxation Coefficient ◽  
Electromechanical Instability ◽  
Curved Microbeam ◽  
Viscoelastic Microbeam

Microbeams are key elements in most of the micro-electromechanical systems (MEMS). Electromechanical instability of microbeams in turn plays an important role in their applications. The shape and mechanical properties of microbeams dictate their functional characteristics. Focusing on their instability-based working mechanism, one can appreciate that viscoelasticity of MEMS materials cannot be neglected. Consequently, the analysis of instability in viscoelastic curved microbeams is an essential demand. In this research, assuming a clamped-clamped initially curved microbeam, the effects of viscoelastic behavior on the snap-through and pull-in instabilities are investigated. The standard inelastic linear solid model is used for the simulation of viscoelastic behavior. Integrodifferential governing equation of the curved viscoelastic microbeam is obtained by assuming modified couple stress theory and using Hamilton’s principle. By applying the Galerkin method, the obtained governing equation is discretized, converted to a nonlinear differential equation, and solved by MATLAB software. Through a quasi-static analysis, the voltage and location of snap-through and pull-in instabilities are identified. The effects of different viscoelastic parameters including the creep moduli and relaxation coefficient upon the snap-through and pull-in instabilities are investigated. The effects of different short- and long-term creeping characteristics of viscoelastic microbeam are studied and discussed in detail.

Application of Modified Couple Stress Theory and Homotopy Perturbation Method in Investigation of Electromechanical Behaviors of Carbon Nanotubes

2016 ◽  
Vol 9 (1) ◽  
pp. 23-42 ◽  
Author(s):  
Mir Masoud Seyyed Fakhrabadi
Keyword(s):  
Carbon Nanotubes ◽  
Perturbation Method ◽  
Couple Stress ◽  
Homotopy Perturbation Method ◽  
Couple Stress Theory ◽  
Modified Couple Stress Theory ◽  
Governing Equations ◽  
Stress Theory ◽  
Homotopy Perturbation ◽  
Modified Couple Stress

AbstractThe paper presents the size-dependant behaviors of the carbon nanotubes under electrostatic actuation using the modified couple stress theory and homotopy perturbation method. Due to the less accuracy of the classical elasticity theorems, the modified couple stress theory is applied in order to capture the size-dependant properties of the carbon nanotubes. Both of the static and dynamic behaviors under static DC and step DC voltages are discussed. The effects of various dimensions and boundary conditions on the deflection and pull-in voltages of the carbon nanotubes are to be investigated in detail via application of the homotopy perturbation method to solve the nonlinear governing equations semi-analytically.

Vibration Analysis of Nano-Beam with Consideration of Surface Effects and Damage Effects

2015 ◽  
Vol 4 (1) ◽  
Author(s):  
Fan Yin ◽  
Chang Ping Chen ◽  
De Liang Chen
Keyword(s):  
Harmonic Balance ◽  
Couple Stress Theory ◽  
Harmonic Balance Method ◽  
Beam Theory ◽  
Governing Equations ◽  
Bernoulli Beam ◽  
Stress Theory ◽  
Beam Thickness ◽  
The Galerkin Method ◽  
Euler Bernoulli Beam

AbstractOn the basis of Euler-Bernoulli beam theory, surface elastic theory, the strain equivalent assumption and modiffed couple stress theory, the nonlinear governing equations of the nano-beam are derived. In addition, the Galerkin method and the Harmonic Balance Method are adopted so as to give a solution to the equations. In the example, the effects of nano-beam length, nano-beam thickness, damage factor and surface efect to curves of amplitude-frequency response of the nano-beam are discussed. The results show that damage effects should be taken into consideration and the frequency can be controlled by load and structure size of nano-beam.

Free Vibration of Edge Cracked Functionally Graded Microscale Beams Based on the Modified Couple Stress Theory

2017 ◽  
Vol 17 (03) ◽  
pp. 1750033 ◽  
Author(s):  
Şeref Doğuşcan Akbaş
Keyword(s):  
Couple Stress ◽  
Scale Parameter ◽  
Couple Stress Theory ◽  
Beam Theory ◽  
Modified Couple Stress Theory ◽  
Functionally Graded ◽  
Beam Model ◽  
Cracked Beam ◽  
Stress Theory ◽  
Modified Couple Stress

In this study, the free vibration analysis of edge cracked cantilever microscale beams composed of functionally graded material (FGM) is investigated based on the modified couple stress theory (MCST). The material properties of the beam are assumed to change in the height direction according to the exponential distribution. The cracked beam is modeled as a modification of the classical cracked-beam theory consisting of two sub-beams connected by a massless elastic rotational spring. The inclusion of an additional material parameter enables the new beam model to capture the size effect. The new nonclassical beam model reduces to the classical one when the length scale parameter is zero. The problem considered is investigated using the Euler–Bernoulli beam theory by the finite element method. The system of equations of motion is derived by Lagrange’s equations. To verify the accuracy of the present formulation and results, the frequencies obtained are compared with the results available in the literature, for which good agreement is observed. Numerical results are presented to investigate the effect of crack position, beam length, length scale parameter, crack depth, and material distribution on the natural frequencies of the edge cracked FG microbeam. Also, the difference between the classical beam theory (CBT) and MCST is investigated for the vibration characteristics of the beam of concern. It is believed that the results obtained herein serve as a useful reference for research of similar nature.

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