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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Bibliographic Details
Published in:Mathematical and computer modelling Vol. 54; no. 11; pp. 2577 - 2586
Main Authors: Ansari, R., Gholami, R., Hosseini, K., Sahmani, S.
Format: Journal Article
Language:English
Published: Kidlington Elsevier Ltd 01.12.2011
Elsevier
Subjects:
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
Online Access:Get full text
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Summary: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.
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ISSN:0895-7177
1872-9479
DOI:10.1016/j.mcm.2011.06.030