scholarly journals Estimation of Static Pull-In Instability Voltage of Geometrically Nonlinear Euler-Bernoulli Microbeam Based on Modified Couple Stress Theory by Artificial Neural Network Model

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Mohammad Heidari ◽  
Yaghoub Tadi Beni ◽  
Hadi Homaei
Keyword(s):  
Neural Network ◽  
Radial Basis Function ◽  
Basis Function ◽  
Couple Stress ◽  
Couple Stress Theory ◽  
Modified Couple Stress Theory ◽  
Beam Model ◽  
Stress Theory ◽  
Radial Basis ◽  
Modified Couple Stress

In this study, the static pull-in instability of beam-type micro-electromechanical system (MEMS) is theoretically investigated. Considering the mid-plane stretching as the source of the nonlinearity in the beam behavior, a nonlinear size dependent Euler-Bernoulli beam model is used based on a modified couple stress theory, capable of capturing the size effect. Two supervised neural networks, namely, back propagation (BP) and radial basis function (RBF), have been used for modeling the static pull-in instability of microcantilever beam. These networks have four inputs of length, width, gap, and the ratio of height to scale parameter of beam as the independent process variables, and the output is static pull-in voltage of microbeam. Numerical data employed for training the networks and capabilities of the models in predicting the pull-in instability behavior has been verified. Based on verification errors, it is shown that the radial basis function of neural network is superior in this particular case and has the average errors of 4.55% in predicting pull-in voltage of cantilever microbeam. Further analysis of pull-in instability of beam under different input conditions has been investigated and comparison results of modeling with numerical considerations show a good agreement, which also proves the feasibility and effectiveness of the adopted approach.

scholarly journals Analysis of Pull-In Instability of Geometrically Nonlinear Microbeam Using Radial Basis Artificial Neural Network Based on Couple Stress Theory

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Mohammad Heidari ◽  
Ali Heidari ◽  
Hadi Homaei
Keyword(s):  
Neural Network ◽  
Artificial Neural Network ◽  
Size Effect ◽  
Radial Basis Function ◽  
Basis Function ◽  
Couple Stress ◽  
Couple Stress Theory ◽  
Stress Theory ◽  
Radial Basis ◽  
Cantilever Microbeam

The static pull-in instability of beam-type microelectromechanical systems (MEMS) is theoretically investigated. Two engineering cases including cantilever and double cantilever microbeam are considered. Considering the midplane stretching as the source of the nonlinearity in the beam behavior, a nonlinear size-dependent Euler-Bernoulli beam model is used based on a modified couple stress theory, capable of capturing the size effect. By selecting a range of geometric parameters such as beam lengths, width, thickness, gaps, and size effect, we identify the static pull-in instability voltage. A MAPLE package is employed to solve the nonlinear differential governing equations to obtain the static pull-in instability voltage of microbeams. Radial basis function artificial neural network with two functions has been used for modeling the static pull-in instability of microcantilever beam. The network has four inputs of length, width, gap, and the ratio of height to scale parameter of beam as the independent process variables, and the output is static pull-in voltage of microbeam. Numerical data, employed for training the network, and capabilities of the model have been verified in predicting the pull-in instability behavior. The output obtained from neural network model is compared with numerical results, and the amount of relative error has been calculated. Based on this verification error, it is shown that the radial basis function of neural network has the average error of 4.55% in predicting pull-in voltage of cantilever microbeam. Further analysis of pull-in instability of beam under different input conditions has been investigated and comparison results of modeling with numerical considerations shows a good agreement, which also proves the feasibility and effectiveness of the adopted approach. The results reveal significant influences of size effect and geometric parameters on the static pull-in instability voltage of MEMS.

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.

FREE VIBRATION OF MICROTUBULES AS ELASTIC SHELL MODEL BASED ON MODIFIED COUPLE STRESS THEORY

2015 ◽  
Vol 15 (03) ◽  
pp. 1550037 ◽  
Author(s):  
YAGHOUB TADI BENI ◽  
M. KARIMI ZEVERDEJANI
Keyword(s):  
Cylindrical Shell ◽  
Shell Model ◽  
Couple Stress ◽  
Couple Stress Theory ◽  
Elastic Shell ◽  
Modified Couple Stress Theory ◽  
Experimental Results ◽  
Beam Model ◽  
Stress Theory ◽  
Modified Couple Stress

In this study, first, the thin cylindrical shell theory was derived from the modified couple stress theory and, afterwards, the vibration of protein microtubules (MTs) was investigated using the developed model. In order to model protein MTs more precisely, the cylindrical micro-shell model was used. Also, to take account of small size effects, equations of motion were obtained on the basis of the modified couple stress theory. For this purpose, first, using Hamilton's principle, vibration equations of cylindrical shell with boundary conditions were derived from the modified couple stress theory. Finally, the effects of size parameters, MT dimensions, and the medium surrounding on the axial and circumferential vibration frequency of the MT were examined. It should be noted that the results obtained from the cylindrical micro-shell model, unlike those from the beam model, have lower dependency on MT length, but they have extreme dependency on MT thickness and radius. In the end, it is worth noting that the model developed in this study can predict experimental results with greater precision compared to classic models. In other words, this model narrows the gap existing between experimental results and previous models and theories.

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.

Size-Dependent Postbuckling of Piezoelectric Microbeams Based on a Modified Couple Stress Theory

2017 ◽  
Vol 09 (04) ◽  
pp. 1750053 ◽  
Author(s):  
Xingjia Li ◽  
Ying Luo
Keyword(s):  
Couple Stress ◽  
Couple Stress Theory ◽  
Classical Model ◽  
Modified Couple Stress Theory ◽  
Beam Model ◽  
Postbuckling Behavior ◽  
Stress Theory ◽  
Size Dependent ◽  
Critical Buckling Force ◽  
Modified Couple Stress

This paper aims to investigate the postbuckling behavior of piezoelectric microbeams (PMBs) using a modified couple stress theory (MCST) and a Euler–Bernoulli–von Kármán beam model. The critical buckling force, voltage and the deformation amplitude were calculated for the buckling of the axially compressed microbeams with a clamp–clamp boundary condition. It is found that the stiffness of microbeams considering the MCST is higher than that given by the classical model when the feature size decreases to the microscale. Moreover, the microscale size effect has a strong influence on the critical buckling loads and the amplitude of postbuckling deformation. This study brings an improved understanding of the postbuckling behavior of PMBs, and offers useful guidance for the design of piezobeam-based sensors, actuators and stretchable microelectronics.

Size Effect on Natural Frequency of Cantilever Micro-Beams Based on a Modified Couple Stress Theory

2013 ◽  
Vol 694-697 ◽  
pp. 221-224 ◽  
Author(s):  
Sheng Li Kong
Keyword(s):  
Size Effect ◽  
Natural Frequency ◽  
Couple Stress ◽  
Natural Frequencies ◽  
Couple Stress Theory ◽  
Modified Couple Stress Theory ◽  
Beam Model ◽  
Stress Theory ◽  
Modified Couple Stress ◽  
The Difference

The natural frequency of cantilever micro-beams is solved analytically on the basis of modified couple stress theory. The governing equations are obtained by a combination of the basic equations of modified couple stress theory and Hamiltons principle. The size effect on natural frequencies of the cantilever micro-beams is analyzed. It is found that the natural frequencies of the cantilever micro-beams predicted by the newly model are size-dependent. The difference between the natural frequencies predicted by the newly established model and classical beam model is assessed.

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