扁薄锥壳在周边弯矩和横向载荷共同作用下的非线性振动

赵永刚; 王新志; 叶开沅

扁薄锥壳在周边弯矩和横向载荷共同作用下的非线性振动

1.
兰州理工大学理学院, 兰州 730050;
2.
兰州大学物理学院, 兰州 730000

基金项目: 甘肃省自然科学基金资助项目(ZS022-A25-022)

详细信息

作者简介:
赵永刚(1967- ),男,山西运城人,副教授,硕士(E-mail:mlszyg@263.net).

中图分类号: O405
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- 被引次数: 0
出版历程
- 收稿日期: 2002-08-25
- 修回日期: 2003-06-27
- 刊出日期: 2003-12-15

Nonlinear Vibration of Thin Shallow Conic Shells Under Combined Action of Peripheral Moment and Transverse Loads

1.
School of Sciences, Lanzhou University of Technology, Lanzhou 730050, P. R. China;
2.
Physical College, Lanzhou University, Lanzhou 730000, P. R. China

摘要

摘要: 从问题的变分方程和协调方程出发,选取扁锥壳中心最大振幅为摄动参数,采用摄动变分法,对周边简支的扁薄锥壳在周边弯矩和横向载荷共同作用下的非线性振动问题进行了求解.一次近似得到了扁薄锥壳在静载荷作用下的线性固有频率,二次近似得到了扁薄锥壳在静载荷作用下的精确度较高的非线性固有频率.并给出了小变形时固有频率与周边弯矩、横向载荷、振幅以及锥底角之间非线性关系的三次近似解析表达式,数值结果的图形反映了在一定范围内固有频率和各参数之间非线性关系的复杂性和规律性.
- 摄动变分法 /
- 非线性振动 /
- 固有频率 /
- 扁薄锥壳
Abstract: Based on the variation and harmonic equations and by taking the maximum amplitude of the shell center as the perturbation parameter, nonlinear vibration of thin shallow conic shells under combined action of peripheral moment and transverse loads was solved. The linear natural frequency can be got by the first-order approximation and the more accurate nonlinear frequency is got by the second-order approximation under the action of static loads. Meanwhile the third-order approximate analytic expression is given for describing the nonlinear relation between nature frequency and peripheral moment, transverse loads, amplitude, base angle under the small deformation. Within some range, the complex and regularity of the nonlinear relation can be directly observed from the numeric results.
- perturbation variation method /
- nonlinear vibration /
- natural frequency /
- thin shallow conical shell

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参考文献(10)

[1]	李世荣,宋曦,赵永刚.变厚度环板在面内变温条件下的固有频率[J].工程力学,1995,12(1):58-65.
[2]	王新志,赵永刚,叶开沅.扁薄锥壳非对称大变形问题[J].应用数学和力学,1998,19(10):847-858.
[3]	王永岗,吕英民.柔韧扁球壳在静荷载作用下的非线性振动[J].非线性动力学学报,1999,6(2):95-101.
[4]	周又和,郑晓静.受静载作用圆薄板的非线性振动[J].非线性动力学学报,1994,1(4):185-194.
[5]	赵永刚.圆薄板在复合载荷作用下的非线性振动问题[J].甘肃工业大学学报,1997,23(4):92-94.
[6]	赵永刚,马连生,王新志.扁薄锥壳在变温条件下的大振幅振动问题[J].兰州铁道学院学报,2001,20(4):21-26.
[7]	胡宇达.磁场中理想传导薄板的非线性振动一般方程[J].非线性动力学学报,1999,6(4):338-342.
[8]	杜国君.静载荷作用下柔韧圆板的大振幅振动[J].应用力学学报,1994,11(4):43-50.
[9]	王新志,王林祥,胡小方.波纹板的非线性振动[J].应用数学和力学,1987,8(3):237-245.
[10]	WANG Xin-zhi,MA Lian-sheng,ZHAO Yong-gang,et al.Nonlinear vibration of shallow conic shells subjected to static load[A].In:CHIEN Wei-zang Ed.Proceedings of the 3rd International Con ference on Nonlinear Mechanics[C].Shanghai:Shanghai University Press,1998,377-380.