| 复合载荷作用下夹层圆板的非线性振动和屈曲 |
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| 引用本文： | 杜国君,马建青.复合载荷作用下夹层圆板的非线性振动和屈曲[J].应用数学和力学,2007,28(8):967-975. |
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| 作者姓名： | 杜国君 马建青 |
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| 作者单位： | 燕山大学,建筑工程与力学学院,河北,秦皇岛,066004 |
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| 摘 要： | 基于von Karman薄板理论,建立了均布载荷和周边面内载荷联合作用下夹层圆板非线性振动问题的控制方程和滑动固定边界条件,给出了相应静力问题的精确解及其数值结果.基于时间模态假设和变分法,得到了空间模态的控制方程,并使用修正迭代法求解该方程,得到夹层圆板幅频-载荷特征关系.讨论了两种载荷对夹层圆板振动特性的影响规律.当周边面力使夹层圆板的最低固有频率为零时,就可获得临界载荷的值.
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| 关 键 词： | 夹层圆板 非线性振动 屈曲 复合载荷 幅频-载荷特征关系 |
| 文章编号： | 1000-0887（2007）08-0967-09 |
| 修稿时间： | 2006-11-20 |
Nonlinear Vibration and Buckling of Circular Sandwich Plate Under Complex Load |
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| DU Guo-jun,MA Jian-qing.Nonlinear Vibration and Buckling of Circular Sandwich Plate Under Complex Load[J].Applied Mathematics and Mechanics,2007,28(8):967-975. |
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| Authors: | DU Guo-jun MA Jian-qing |
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| Institution: | School of Civil Engineering and Mechanics, Yanshan University, Qinhuangdao , Hebei 055004, P. R. China |
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| Abstract: | The nonlinear vibration fundamental equation of circular sandwich plate under uniformed load and circumjacent load and the loosely clamped boundary condition were established by yon plate theory, and then accordingly exact solution of static load and its numerical results is given. Based on time mode hypothesis and the variational method, the control equation of the space mode was derived, and then the amplitude fi-equency-load character relation of circular sandwich plate was obtained by the modified iteration method. Consequently the rule which the two kinds of load affected the vibration character of the circular sandwich plate was investigated. When circurnjacent load makes the lowest natural frequency zero, critical load is obtained. |
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| Keywords: | circular sandwich plate nonlinear vibration buckling complex load amplitude frequency-load character relation |
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