Surface and nonlocal effects on the nonlinear free vibration of non-uniform nanobeams
| Autor: | Mohamad Shojaee, Mohammad Shojaee, Parviz Malekzadeh |
|---|---|
| Rok vydání: | 2013 |
| Předmět: |
Timoshenko beam theory
Materials science Mechanical Engineering Mathematical analysis Infinitesimal strain theory Industrial and Manufacturing Engineering Vibration Cross section (physics) Nonlinear system Classical mechanics Rate of convergence Mechanics of Materials Ceramics and Composites Nyström method Boundary value problem Composite material |
| Zdroj: | Composites Part B: Engineering. 52:84-92 |
| ISSN: | 1359-8368 |
| Popis: | The surface and nonlocal effects on the nonlinear flexural free vibrations of elastically supported non-uniform cross section nanobeams are studied simultaneously. The formulations are derived based on both Euler–Bernoulli beam theory (EBT) and Timoshenko beam theory (TBT) independently using Hamilton’s principle in conjunction with Eringen’s nonlocal elasticity theory. Green’s strain tensor together with von Karman assumptions are employed to model the geometrical nonlinearity. The differential quadrature method (DQM) as an efficient and accurate numerical tool in conjunction with a direct iterative method is adopted to obtain the nonlinear vibration frequencies of nanobeams subjected to different boundary conditions. After demonstrating the fast rate of convergence of the method, it is shown that the results are in excellent agreement with the previous studies in the limit cases. The influences of surface free energy, nonlocal parameter, length of non-uniform nanobeams, variation of nanobeam width and elastic medium parameters on the nonlinear free vibrations are investigated. |
| Databáze: | OpenAIRE |
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