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.

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.

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.

A modified couple stress theory for buckling analysis of higher order inhomogeneous microbeams with porosities

2018 ◽  
Vol 233 (8) ◽  
pp. 2855-2866 ◽  
Author(s):  
Farzad Ebrahimi ◽  
Fateme Mahmoodi
Keyword(s):  
Boundary Conditions ◽  
Power Law ◽  
Couple Stress ◽  
Volume Fraction ◽  
Couple Stress Theory ◽  
Modified Couple Stress Theory ◽  
Functionally Graded ◽  
Stress Theory ◽  
Various Boundary Conditions ◽  
Modified Couple Stress

In this paper, buckling behavior of a higher order functionally graded microbeam with porosities is investigated based on the modified couple stress theory and the exact position of the neutral axis. Porosities are evenly and unevenly distributed inside the functionally graded microbeam. Material properties of the functionally graded microbeam are assumed to vary in the thickness direction through a modified form of power-law distribution in which the volume fraction of porosities is considered. The governing equations are derived by using Hamilton's principle and an analytical method is employed to solve these equations for various boundary conditions. The present formulation and numerical results demonstrate a good agreement with some available cases in the literature. Influences of several important parameters such as power-law exponent, porosity distributions, porosity volume fraction, slenderness ratio, and various boundary conditions on buckling loads of porous functionally graded microbeams are investigated and discussed in detail.

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.

Formulation for Static Behavior of the Viscoelastic Euler-Bernoulli Micro-Beam Based on the Modified Couple Stress Theory

2012 ◽  
Author(s):  
E. Taati ◽  
M. Nikfar ◽  
M. T. Ahmadian
Keyword(s):  
Size Effects ◽  
Couple Stress ◽  
Couple Stress Theory ◽  
Closed Form Solution ◽  
Modified Couple Stress Theory ◽  
Form Solution ◽  
Equilibrium Equations ◽  
Stress Theory ◽  
Modified Couple Stress ◽  
Micro Structures

In this work an analytical solution is presented for a viscoelastic micro-beam based on the modified couple stress theory which is a non-classical theory in continuum mechanics. The modified couple stress theory has the ability to consider small size effects in micro-structures. It is strongly emphasized that without considering these effects in such structures the solution will be wrong and not suitable for designing systems in micro-scales. In this study correspondence principle is used for deriving constitutive equations for viscoelastic material based on the modified couple stress theory. Governing equilibrium equations are obtained by considering an element of micro-beam. Closed-form solution for the static deflection of simply supported micro-beam is presented. Numerical results show that when the size of system is near the length scale parameter, the classical response will intensely be deviated from the correct solution observed in laboratories contrary to the modified couple stress which reflects the size effects.

Electro-thermal buckling of elastically supported double-layered piezoelectric nanoplates affected by an external electric voltage

2019 ◽  
Vol 15 (1) ◽  
pp. 50-78 ◽  
Author(s):  
Mohammad Malikan
Keyword(s):  
Thermal Stress ◽  
Critical Temperature ◽  
Boundary Conditions ◽  
Stress Function ◽  
Couple Stress Theory ◽  
Modified Couple Stress Theory ◽  
Thermal Buckling ◽  
Small Scale ◽  
Electric Voltage ◽  
Content Type

Purpose Thermal buckling of double-layered piezoelectric nanoplates has been analyzed by applying an external electric voltage on the nanoplates. The paper aims to discuss this issue. Design/methodology/approach Double-layered nanoplates are connected to each other by considering linear van der Waals forces. Nanoplates are placed on a polymer matrix. A comprehensive thermal stress function is used for investigating thermal buckling. A linear electric function is used for taking external electric voltages into account. For considering the small-scale effect, the modified couple stress theory has been applied. An analytical solution has been used by taking various boundary conditions. Findings EEV has a considerable impacted on the results of various half-waves in all boundary conditions. By increasing EEV, the reduction of critical buckling temperature in higher half-waves is remarkably slower than lower half-waves. By considering long lengths, the effect of EEV on the critical temperature will be markedly decreased. Originality/value This paper uses electro-thermal stability analysis. Double-layered piezoelectric nanoplates are analyzed. A comprehensive thermal stress function is applied for taking into account critical temperature.

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