期刊
EUROPEAN JOURNAL OF MECHANICS A-SOLIDS
卷 75, 期 -, 页码 142-155出版社
ELSEVIER
DOI: 10.1016/j.euromechsol.2019.01.021
关键词
Axially accelerating plate; Longitudinally varying tension; Irregular instability boundary; Parametric and internal resonances; Nonhomogeneous boundary condition
类别
资金
- National Natural Science Foundation of China [11672186, 11502147, 11602146, 11232009, 11572182]
- Innovation Program of Shanghai Municipal Education Commission [2017-01-07-00-09-E00019]
- Shanghai Municipal Education Commission
- Shanghai Education Development Foundation [14CG57]
In this paper, instability boundaries of axially accelerating plates with internal resonance are investigated for the first time. The relation between the acceleration and the longitudinally varying tensions are introduced. The governing equation and the corresponding boundary conditions are derived from the generalized Hamilton principle. The effects of internal resonances and the nonhomogeneous boundary conditions on the instability boundaries are highlighted. By the method of multiple scales, the modified solvability conditions in principal parametric and internal resonances are established. The Routh-Hurwitz criterion is introduced to determine the instability boundaries. The effects of the viscoelastic coefficient and the viscous damping coefficient on the instability boundaries are examined. Abnormal instability boundaries are detected when the internal resonance is introduced. The phenomenon of local zigzag and V-shape boundaries are explained from the viewpoint of modal interactions. The numerical calculations of the differential quadrature schemes about the first four complex frequencies, the first four complex modes, and the stability boundaries are used to confirm the results of the analytical method.
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