A sixth-order compact finite difference method for vibrational analysis of nanobeams embedded in an elastic medium based on nonlocal beam theory

In the present paper, the free vibration characteristics of nanobeams embedded in an elastic medium are investigated. Inclusion of size effects is considered in the analysis by incorporating Eringen’s nonlocal elasticity continuum into the classical Euler–Bernoulli beam theory. To include the surrou...

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Vydáno v:	Mathematical and computer modelling Ročník 54; číslo 11; s. 2577 - 2586
Hlavní autoři:	Ansari, R., Gholami, R., Hosseini, K., Sahmani, S.
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Kidlington Elsevier Ltd 01.12.2011 Elsevier
Témata:	Compact finite difference method elastic deformation Elastic foundation Exact sciences and technology Free vibration Mathematical analysis Mathematics Methods of scientific computing (including symbolic computation, algebraic computation) Nanobeams Nonlocal elasticity continuum Numerical analysis. Scientific computation prediction Sciences and techniques of general use vibration Elastic foundation Nonlocal elasticity continuum Free vibration Nanobeams Compact finite difference method Applied mathematics Boundary condition Mathematical model Discretization method Computer aided analysis Finite difference method
ISSN:	0895-7177, 1872-9479
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Abstract	In the present paper, the free vibration characteristics of nanobeams embedded in an elastic medium are investigated. Inclusion of size effects is considered in the analysis by incorporating Eringen’s nonlocal elasticity continuum into the classical Euler–Bernoulli beam theory. To include the surrounding elastic medium, the Pasternak elastic foundation model is utilized, including shear deformation of the elastic medium. A high-order compact finite difference method (CFDM) is employed for sixth-order discretization of the nonlocal beam model to obtain the fundamental frequencies of nanobeams corresponding to three commonly used boundary conditions, namely simply supported–simply supported, clamped–clamped, and clamped–free. Numerical results are presented to indicate the accuracy of the method based on the sixth-order discretization for predicting the vibrational response of embedded nanobeams subject to various boundary conditions.
AbstractList	In the present paper, the free vibration characteristics of nanobeams embedded in an elastic medium are investigated. Inclusion of size effects is considered in the analysis by incorporating Eringen’s nonlocal elasticity continuum into the classical Euler–Bernoulli beam theory. To include the surrounding elastic medium, the Pasternak elastic foundation model is utilized, including shear deformation of the elastic medium. A high-order compact finite difference method (CFDM) is employed for sixth-order discretization of the nonlocal beam model to obtain the fundamental frequencies of nanobeams corresponding to three commonly used boundary conditions, namely simply supported–simply supported, clamped–clamped, and clamped–free. Numerical results are presented to indicate the accuracy of the method based on the sixth-order discretization for predicting the vibrational response of embedded nanobeams subject to various boundary conditions.
Author	Gholami, R. Hosseini, K. Sahmani, S. Ansari, R.
Author_xml	– sequence: 1 givenname: R. surname: Ansari fullname: Ansari, R. email: r_ansari@guilan.ac.ir organization: Department of Mechanical Engineering, University of Guilan, P.O. Box 3756, Rasht, Iran – sequence: 2 givenname: R. surname: Gholami fullname: Gholami, R. organization: Department of Mechanical Engineering, University of Guilan, P.O. Box 3756, Rasht, Iran – sequence: 3 givenname: K. surname: Hosseini fullname: Hosseini, K. organization: Department of Mathematics, Islamic Azad University, Lahijan Branch, P.O. Box 1616, Lahijan, Iran – sequence: 4 givenname: S. surname: Sahmani fullname: Sahmani, S. organization: Department of Mechanical Engineering, University of Guilan, P.O. Box 3756, Rasht, Iran
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Keywords	Elastic foundation Nonlocal elasticity continuum Free vibration Nanobeams Compact finite difference method Applied mathematics Boundary condition Mathematical model Discretization method Computer aided analysis Finite difference method
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Snippet	In the present paper, the free vibration characteristics of nanobeams embedded in an elastic medium are investigated. Inclusion of size effects is considered...
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SubjectTerms	Compact finite difference method elastic deformation Elastic foundation Exact sciences and technology Free vibration Mathematical analysis Mathematics Methods of scientific computing (including symbolic computation, algebraic computation) Nanobeams Nonlocal elasticity continuum Numerical analysis. Scientific computation prediction Sciences and techniques of general use vibration
Title	A sixth-order compact finite difference method for vibrational analysis of nanobeams embedded in an elastic medium based on nonlocal beam theory
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