非均匀变厚度梁的动力响应的一般解

叶开沅; 童晓华; 纪振义

非均匀变厚度梁的动力响应的一般解

1.
兰州大学;
2.
多伦多大学;
3.
安徽建筑工程学院

计量
- 文章访问数: 1837
- HTML全文浏览量: 118
- PDF下载量: 647
- 被引次数: 0
出版历程
- 收稿日期: 1992-01-08
- 刊出日期: 1992-09-15

General Analytic Solution of Dynamic Response of Beams with Nonhomogeneity and Variable Cross Section

1.
Lanzhou University, Lanzhou;University of Toronto, Toronto, Canada;
2.
Zhejiang University, Hangzhou;University of Toronto, Toronto, Canada;
3.
Anhui Architectural Industry College, Hefei

摘要

摘要: 在本文中提出一个新方法——阶梯折算法来研究在任意载荷下任意非均匀和任意变厚度伯努利-欧拉梁的动力响应问题.研究了自由振动和强迫振动.新方法需要将区间离散为一定数目的元素,每个元素可看作是均匀和等厚度的.因此均匀、等厚度梁的一般解可在每个元素上应用.然后用初参数表示的整个梁的一般解使之满足相邻二元素间的物理和几何连续条件,这样就可以得到解析形式的自由振动的频率方程和解析形式的强迫振动的最终解,它化为求解二元线性代数方程,与离散元素的数目无关.现在的方法可推广应用至任意非均匀及任意变厚度有粘滞性和其他种类的梁以及其他结构元件问题上去.
- 非均匀 /
- 变厚度 /
- 伯努利-欧拉梁 /
- 离散 /
- 动力响应
Abstract: In this paper, a new method, the step-reduction method, is proposed to investigate the dynamic response of the Bernoulli-Euler beams with arbitrary nonhomogeneity and arbitrary variable cross-section under arbitrary loads. Both free vibration and forced vibration of such beams are studied. The new method requires to discretize the space domain into a number of elements. Each element can be treated as a homogeneous one with uniform thickness. Therefore, the general analytical solution of homogeneous beams with uniform cross-section can be used in each element. Then, the general analytic solution of the whole beam in terms of initial parameters can be obtained by satisfying the physical and geometric continuity conditions at the adjacent elements. In the case of free vibration, the frequency equation in analytic form can be obtained, and in the case of forced vibration, a final solution in analytical form can also be obtained which is involved in solving a set of simultaneous algebraic equations with only two unknowns which are independent of the numbers of elements divided. The present analysis can also be extended to the study of the vibration of such beams with viscous and hysteretic damping and other kinds of beams and other structural elements with arbitrary nonhomogeneity and arbitrary variable thickness.
- nonhomogeneity /
- variable thickness /
- Bernoulli-Euler beam /
- discretization /
- dynamic response

HTML全文

参考文献(21)

[1]	叶开沅,非均匀变厚度弹性体力学的若干问题的一般解Ⅳ,非均匀变厚度梁的弯曲,稳定性和自由振动问题,兰州大学学报,力学专号,(1)(1979),133-157.
[2]	Chu,C.H.and W.D.Pilkey,Transient analysis of structural members by the CSDT Riccati transfer matrix method,Computers and Structures,10(1979),599-611.
[3]	Finlayson,B.A.,The Methods of Weighted Residuals and Variational Principles,Academic Press,New York(1972).
[4]	Mikhlin,S.G.,Variational Methods in Mathematical Physics,Macmillan,New York(1964).
[5]	Laura,P.A.A.,B.Valerga De Greco,J.C.Vtjes and R.Carnicer,Numerical experiments on free and forced vibrations of beams of nonuniform cross-section,Journal of Sound and Vibration,120(1988),587-596.
[6]	Bathe,K.J.,Finite Element Procedures in Engineering Analysis,Prentice-Hall,Engliwood Cliffs,New Jersey(1982).
[7]	Ghali,A.and A.M.Neville,Structural Analysis,Intext Educational Publishers,Pennsylvania(1972).
[8]	Beskos,D.E.,Boundary element methods in dynamic analysis,Applied Mechanics Reviews,40(1987),1-23.
[9]	Just,D.J.,Plane frameworks of tapered box and I-section,Journal of the Structural Division,Proceedings of ASCE,108(1977),71-86.
[10]	Ovunk,B.A.,Dynamics of frameworks by continuous mass methods,Computers and Structures,5(1974),1061-1089.
[11]	Beskos,D.E.,Dynamics and stability of plane trusses with gusset plates,Computers and Structures,10(1979),785-795.
[12]	Beskos,D.E.and G.V.Narayanan,Dynamic response of frameworks by numerical Laplace transform,Computer Methods in Applied Mechanics and Engineering,117(1983),289-307.
[13]	Wang,H.C.,Generalized hypergeometric funetion solutions on transverse vibrations of a class of nonuniform beams,ASME Journal of Applied Mechanics,114(1968),702-708.
[14]	Taleb,N.J.and E.W.Suppiger,Vibration of stepped beams,Journal of Aerospace Science,28(1961),295-298.
[15]	Lindberg.G.M.,Vibration of nonuniform beams,The Aeronautical Quarterly,14(1963),387-395.
[16]	叶开沅、许剑云,在非均匀定常温度场下的非均匀变厚度高速度旋转圆盘的弹塑性应力分析,第15届ICTAM,Toronto(1980).
[17]	叶开沅、刘平,非均匀变厚度圆盘的定常热传导,应用数学和力学,5(5)(1984),619-621.
[18]	叶开沅、刘平,在定常温度场中非均匀变厚度高速旋转圆盘的等强度设计,应用数学和力学.
[19]	Yeh,K.Y.,Recent Investigations of structural optimization by analytic methods,Structural Optimization,edited by G.I.N.Rozvany & B.L.Karihaloo,Kluwer Academic Publishers(1988),379-386.
[20]	叶开沅、俞焕然,现行钢筋混凝土构件计算中存在的问题的探讨(一),(二),兰州大学学报(自然科学版),力学专号,10(1983),10-36.
[21]	叶开沅、许剑云,中心开孔圆ACC,扁薄球壳在任意分布横向载荷下的弯曲问题的一般解,应用数学和力学,1(3)(1980),319-334.