Transverse Vibration for Non-uniform Timoshenko Nano-beams
In this paper, Eringen’s nonlocal elasticity and Timoshenko beam theories are implemented to analyze the bending vibration for non-uniform nano-beams. The governing equations and the boundary conditions are derived using Hamilton’s principle. A Generalized Differential Quadrature Method (GDQM) is u...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Semnan University
2015-04-01
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| Series: | Mechanics of Advanced Composite Structures |
| Subjects: | |
| Online Access: | https://macs.semnan.ac.ir/article_327_e19b0feb33c053f63c0ced02b44f9f4c.pdf |
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| Summary: | In this paper, Eringen’s nonlocal elasticity and Timoshenko beam theories are implemented to analyze the bending vibration for non-uniform nano-beams. The governing equations and the boundary conditions are derived using Hamilton’s principle. A Generalized Differential Quadrature Method (GDQM) is utilized for solving the governing equations of non-uniform Timoshenko nano-beam for pinned-pinned, clamped–clamped, clamped–pinned, clamped–free, clamped–slide, and pinned-slide boundary conditions. The non-dimensional natural frequencies and the normalized mode shapes are obtained for short and stubby nano-beams where influences varying cross-section area, small scale, shear deformation, rotational moment of inertia, acceleration gravity and the self-weight of the non-uniform Timoshenko nano-beam are discussed. The present study illus-trates that the small scale effects are more significant for smaller size of nano-beam, larger nonlocal parameter and higher vibration modes. Further, the compression forces due to gravity and the self-weight of the nano-beam also like the small scale effect are reduced the magnitude of the fre-quencies of the nano-beam. |
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| ISSN: | 2423-4826 2423-7043 |