夹层圆板的大幅度振动
Large Amplitude Vibration of Circular Sandwich Plates
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摘要: 本文利用哈密顿原理导出了夹层圆板轴对称大幅度自由振动的基本方程,并给出了表板很薄情况下的简化形式.作为算例,利用修正迭代法求出了具有滑动固定边界条件夹层圆板对轴称大幅度自由振动的一种解析解,并由此导出了夹层圆板振幅和振频的解析关系式.Abstract: In this paper,fundamental equations of the axisymmetric large amplitude.free vibration for circular sandwich plates are derived by means of Hamilion principle.Inmosi cases,the sandwich plates are composed of very thin faces,then the preceding fundamental equations are simplified considerably.For an illusirative example,a circu-lar sandwich plate with edge clamped but free to slip is considered,and then we gol a pure analytic solution of the axisvmmetric large amplitude free vibration with the aid of the modified iteration method.and derived an analytic relation for the amplitude-frequency response.
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Key words:
- circular sandwich plate /
- large amplitude /
- vibration
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[1] 刘人怀,夹层圆板的非线性弯曲,应用数学和力学,2(2)(1981),173. [2] 刘人怀、施云方,夹层圆板大浇育问题为精确解,应用玫学和力学,3(1)(1982),11. [3] 刘人怀.朱荡秋,夹层圆板大挠度问题的进一步研究,应用数学和力学,10(12)(1989),1041. [4] 李东,环形薄板大幅度振动,应用数学和力学,12(6)(1991),5.17. [5] 李东、刘人怀,修正迭代法在波纹圆板非线性振动问题中的应用,应用数学和力学.11(1)(1990).
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