Nonlinear vibration analysis of Timoshenko nanobeams based on surface stress elasticity theory
In this article, the nonlinear free vibration behavior of Timoshenko nanobeams subject to different types of end conditions is investigated. The Gurtin–Murdoch continuum elasticity is incorporated into the Timoshenko beam theory in order to capture surface stress effects. The nonlinear governing equ...
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| Published in | European journal of mechanics, A, Solids Vol. 45; pp. 143 - 152 |
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| Main Authors | , , , , |
| Format | Journal Article |
| Language | English |
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Elsevier Masson SAS
01.05.2014
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| Subjects | |
| Online Access | Get full text |
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| Abstract | In this article, the nonlinear free vibration behavior of Timoshenko nanobeams subject to different types of end conditions is investigated. The Gurtin–Murdoch continuum elasticity is incorporated into the Timoshenko beam theory in order to capture surface stress effects. The nonlinear governing equations and corresponding boundary conditions are derived using Hamilton's principle. A numerical approach is used to solve the problem in which the generalized differential quadrature method is applied to discretize the governing equations and boundary conditions. Then, a Galerkin-based method is numerically employed with the aim of reducing the set of partial differential governing equations into a set of time-dependent ordinary differential equations. Discretization on time domain is also done via periodic time differential operators that are defined on the basis of the derivatives of a periodic base function. The resulting nonlinear algebraic parameterized equations are finally solved by means of the pseudo arc-length continuation algorithm through treating the time period as a parameter. Numerical results are given to study the geometrical and surface properties on the nonlinear free vibration of nanobeams.
•Performing nonlinear vibration analysis of nanobeams including surface stress effects.•Developing a Timoshenko beam model within the framework of the Gurtin-Murdoch continuum elasticity.•Proposing a novel numerical solution methodology for solving the nonlinear problem.•Exploring the geometrical and surface properties on the nonlinear vibration of nanobeams. |
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| AbstractList | In this article, the nonlinear free vibration behavior of Timoshenko nanobeams subject to different types of end conditions is investigated. The Gurtin-Murdoch continuum elasticity is incorporated into the Timoshenko beam theory in order to capture surface stress effects. The nonlinear governing equations and corresponding boundary conditions are denved using Hamilton's principle. A numerical approach is used to solve the problem in which the generalized differential quadrature method is applied to discretize the governing equations and boundary conditions. Then, a Galerkin-based method is numerically employed with the aim of reducing the set of partial differential governing equations into a set of time-dependent ordinary differential equations. Discretization on time domain is also done via periodic time differential operators that are defined on the basis of the derivatives of a periodic base function. The resulting nonlinear algebraic parameterized equations are finally solved by means of the pseudo arc-length continuation algonthm through treating the time penod as a parameter. Numerical results are given to study the geometrical and surface properties on the nonlinear free vibration of nanobeams. In this article, the nonlinear free vibration behavior of Timoshenko nanobeams subject to different types of end conditions is investigated. The Gurtin–Murdoch continuum elasticity is incorporated into the Timoshenko beam theory in order to capture surface stress effects. The nonlinear governing equations and corresponding boundary conditions are derived using Hamilton's principle. A numerical approach is used to solve the problem in which the generalized differential quadrature method is applied to discretize the governing equations and boundary conditions. Then, a Galerkin-based method is numerically employed with the aim of reducing the set of partial differential governing equations into a set of time-dependent ordinary differential equations. Discretization on time domain is also done via periodic time differential operators that are defined on the basis of the derivatives of a periodic base function. The resulting nonlinear algebraic parameterized equations are finally solved by means of the pseudo arc-length continuation algorithm through treating the time period as a parameter. Numerical results are given to study the geometrical and surface properties on the nonlinear free vibration of nanobeams. •Performing nonlinear vibration analysis of nanobeams including surface stress effects.•Developing a Timoshenko beam model within the framework of the Gurtin-Murdoch continuum elasticity.•Proposing a novel numerical solution methodology for solving the nonlinear problem.•Exploring the geometrical and surface properties on the nonlinear vibration of nanobeams. |
| Author | Gholami, R. Rouhi, H. Mohammadi, V. Ansari, R. Faghih Shojaei, M. |
| Author_xml | – sequence: 1 givenname: R. surname: Ansari fullname: Ansari, R. email: r_ansari@guilan.ac.ir – sequence: 2 givenname: V. surname: Mohammadi fullname: Mohammadi, V. – sequence: 3 givenname: M. surname: Faghih Shojaei fullname: Faghih Shojaei, M. – sequence: 4 givenname: R. surname: Gholami fullname: Gholami, R. – sequence: 5 givenname: H. surname: Rouhi fullname: Rouhi, H. |
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| Snippet | In this article, the nonlinear free vibration behavior of Timoshenko nanobeams subject to different types of end conditions is investigated. The Gurtin–Murdoch... In this article, the nonlinear free vibration behavior of Timoshenko nanobeams subject to different types of end conditions is investigated. The Gurtin-Murdoch... |
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| SubjectTerms | Boundary conditions Differential equations Free vibration Mathematical analysis Mathematical models Nanobeam Nanostructure Nonlinear free vibration Nonlinearity Stresses Surface stress elasticity |
| Title | Nonlinear vibration analysis of Timoshenko nanobeams based on surface stress elasticity theory |
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