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Nonlinear vibrations of nano-beams accounting for nonlocal effect using a multiple scale method |
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| Authors: | YANG XiaoDong & C.W.LIM |
| Affiliation: | YANG XiaoDong1 & C.W.LIM2 1 Department of Engineering Mechanics,Shenyang Institute of Aeronautical Engineering,Shenyang 110136,China,2 Department of Building , Construction,City University of Hong Kong,Hong Kong 999077 |
| Abstract: | The nonlinear free transverse vibrations of a nano-beam on simple supports are investigated based on nonlocal elasticity theory.The governing equation is proposed by considering geometric nonlinearity due to finite stretching of the beam.The method of multiple scales is applied to the governing equation to evaluate the nonlinear natural frequencies.Numerical examples are presented to demonstrate the analytical results and highlight the contributions of the nonlinear term and nonlocal effect. |
| Keywords: | nonlocal elasticity theory nanobeam natural frequency method of multiple scales |
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