修正迭代法在波纹圆板非线性振动问题中的应用

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

李东¹,
刘人怀²

1.
上海工业大学;
2.
上海市应用数学和力学研究所

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出版历程
- 收稿日期: 1988-10-25
- 刊出日期: 1990-01-15

Application of the Modified Iteration Method to Nonlinear Vibration of Corrugated Circular Plates

Li Dong¹,
Liu Ren-huai²

1.
Shanghai University of Technology;
2.
Shanghai Institute of Applied Mathematics and Mechanics, Shanghai

摘要

摘要: 在本文中,我们将修正迭代法成功地推广运用于全波纹圆板的非线性振动问题的研究,获得了全波纹圆板的非线性振频和振幅的解析关系式.本文还讨论了波纹圆板的几何参量对其振动特性的影响,本文结果对精密仪器弹性元件的设计具有一定的实际意义.

Abstract: In this paper, the modified iteration method is successfully exended to investigate the nonlinear free vibration of corrugated circular plates with full corrugations. The analytical relation for the amplitude-frequency response of corrugated circular plates is obtained and discussions on the influences of geometrical parameters on vibration behaviours of corrugated circular plates are made. The present results arc practically important in the design of elastic elements in precision instruments.

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参考文献(15)

[1]	刘人怀,波纹国板的特征关系式,力学学报,1(1978), 47.
[2]	刘人怀,具有光滑中心的波纹圆板的特征关系式,中国科技大学学报,8, 2 (1979), 75.
[3]	Liu,R.H.,Large deflection of corrugaled circular plate with a plane central region under the action of concentrated loads at the center.International Journal of Noil-Linear Mechanics,19,5(1984),409.
[4]	Liu,R.H.,Large deflection of corrugated circular plate with plane boundary region,Solid Mechanics Archives,9,4(1984),383.
[5]	刘人怀,波纹环形板的非线性弯曲,中国科学,A辑,3(1984), 247.
[6]	刘人怀,在复合载荷作用下波纹环形板的非线性弯曲,中国科学,A辑,6(1986), 537.
[7]	Liu,R.H.,On large deflection of corrugated annular plates under uniform presssure,The Advances of Applied Mathematics and Mechanics in China,1(1987),138.
[8]	Liu,R.H.,The study on nonlinear bending problems of corrugated circular plates,The International Conference of Humboldt Foundation,Shanghai,(1987).
[9]	刘人怀.复合燕荷作用下波纹圆板的非线性分析,应用数学和力学,(1988),681.
[10]	叶开沅、刘人怀等,在对称线布载荷作用下的圆底扁薄球壳的非线性稳定问题,兰州大学学报,2 (1965), 10;科学通报,2 (1965), 142.
[11]	叶开沅、刘人怀等,圆底扁薄球壳在边缘力矩作用下的非线性稳定问题,科学通报,2(1965),145.
[12]	刘人怀,在内边缘均布力矩作用下中心开孔圆底扁球壳的非线性稳定问题,科学通报,3 (1965),253.
[13]	Liu,R.H.,and Li,D.,On the nonlinear bending and vibration of corrugated circular plates,International Journal of Non-Linear Mechanics,24(1989).(in press)
[14]	王新志等,波纹圆薄板的非线性振动,应用数学和力学,8. 3 (1987),237.
[15]	Huang,C.L.and B.E.Sandman,Large amplitude vibrations of rigidly clamped circular plates,International Journal of Non-Linear mechanics,6(1971),451.