Non-linear principal resonance of an orthotropic and magnetoelastic rectangular plate
| Autor: | Q.K. Han, Ernian Pan, C.X. Xue, S.Y. Zhang, Haijian Chu |
|---|---|
| Rok vydání: | 2011 |
| Předmět: |
Physics
Partial differential equation Applied Mathematics Mechanical Engineering Mathematical analysis Bending of plates Orthotropic material law.invention Magnetic field Physics::Fluid Dynamics symbols.namesake Mechanics of Materials law Ordinary differential equation Plate theory symbols Eddy current Lorentz force |
| Zdroj: | International Journal of Non-Linear Mechanics. 46:703-710 |
| ISSN: | 0020-7462 |
| DOI: | 10.1016/j.ijnonlinmec.2011.02.002 |
| Popis: | Based on the von Karman plate theory of large deflection, we have derived a non-linear partial differential equation for the vibration of a thin orthotropic plate under the combined action of a transverse magnetic field and a transverse harmonic mechanical load. The influence of the magnetic field is due to the magnetic Lorentz force induced by the eddy current. By employing the Bubnov–Galerkin method, the non-linear partial differential equation is transformed into a third-order non-linear ordinary differential equation. The amplitude-frequency equations are further derived by means of the multiple-scale method. As numerical examples for an orthotropic plate made of silver, the influence of the magnetic field, orthotropic material property, plate thickness, and the mechanical load on the principal resonance behavior is investigated. The higher-order effect and stability of the solution are also discussed. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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