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Analysis of pull-in instability of geometrically nonlinear microbeam using radial basis artificial neural network based on couple stress theory.

Heidari M, Heidari A, Homaei H - Comput Intell Neurosci (2014)

Bottom Line: 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.The results reveal significant influences of size effect and geometric parameters on the static pull-in instability voltage of MEMS.

View Article: PubMed Central - PubMed

Affiliation: Mechanical Engineering Group, Islamic Azad University, Aligudarz Branch, P.O. Box 159, Aligudarz, Iran.

ABSTRACT
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.

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An Euler-Bernoulli, loading, and coordinate system.
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fig1: An Euler-Bernoulli, loading, and coordinate system.

Mentions: In this section, the governing equation and corresponding classical and nonclassical boundary conditions of a nonlinear microbeam modeled on the basis of the couple stress theory are derived. The coordinate system and loading of an Euler-Bernoulli beam have been depicted in Figure 1. In this figure, F(x, t) and G(x, t) refer to the intensity of the transverse distributed force and the axial body force, respectively, both as force per unit length.


Analysis of pull-in instability of geometrically nonlinear microbeam using radial basis artificial neural network based on couple stress theory.

Heidari M, Heidari A, Homaei H - Comput Intell Neurosci (2014)

An Euler-Bernoulli, loading, and coordinate system.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4016879&req=5

fig1: An Euler-Bernoulli, loading, and coordinate system.
Mentions: In this section, the governing equation and corresponding classical and nonclassical boundary conditions of a nonlinear microbeam modeled on the basis of the couple stress theory are derived. The coordinate system and loading of an Euler-Bernoulli beam have been depicted in Figure 1. In this figure, F(x, t) and G(x, t) refer to the intensity of the transverse distributed force and the axial body force, respectively, both as force per unit length.

Bottom Line: 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.The results reveal significant influences of size effect and geometric parameters on the static pull-in instability voltage of MEMS.

View Article: PubMed Central - PubMed

Affiliation: Mechanical Engineering Group, Islamic Azad University, Aligudarz Branch, P.O. Box 159, Aligudarz, Iran.

ABSTRACT
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.

Show MeSH
Related in: MedlinePlus