扇形板的富里哀—贝塞尔级数解

钱民刚; 严宗达

扇形板的富里哀—贝塞尔级数解

钱民刚¹,
严宗达²

1.
系统工程研究所;
2.
天津大学力学系

计量
- 文章访问数: 2224
- HTML全文浏览量: 138
- PDF下载量: 537
- 被引次数: 0
出版历程
- 收稿日期: 1983-12-02
- 刊出日期: 1985-04-15

Solution of Sector Plate by Fourier-Bessel Series

Qian Min-gang¹,
Yan Zong-da²

1.
Systems Engineering Institute, Beijing;
2.
Department of Mechanics, Tianjin University, Tianjin

摘要

摘要: 本文以加补充项的富里哀—贝塞尔双重级数的位移模式,对扇形弹性薄板在各种边界件条下的弯曲和振动问题,提出了一种应用范围比较广的、便于计算的、解析形式的解法.作为算例,文中给出了各种角度的径向边界简支或固定的扇形板在均布荷载或集中荷载作用下产生的挠度和弯矩的分布曲线,并与有关文献的数值结果进行了比较.本文推广了加补充项的富氏级数法的应用范围,并计算出各种角度的径向边界简支的扇形板的自振频率和节线的图表.

Abstract: In this paper a solution of deflection in the form of Fourier-Bessel double series with suplementary terms is proposed to analyse bending and vibration problems of thin elastic sector plate with various edge conditions, This solution is suitable to a wider range, convenient for calculation and it is in an analytical form, As computational examples, the distribution curves of deflection and bending moment of plates with various sector angles simply supported or clamped along the radial edges under uniform or concentrated load are obtained and the results are compared with the numerical results df related references, Thus the range of application of the Fourier series method with supple-mentary terms is extended, Frequencies and nodal lines in free vibration of plates with various sector angles simply supported along the radial edges are also given in this paper.

HTML全文

参考文献(20)

[1]	Г.П托尔斯托夫,《福里哀级数》,龙季和译,高等教育出版社(1957),
[2]	严宗达,《富氏级数在结构力学中的应用》,天津大学固体力学研究生讲义(1982).
[3]	S.铁摩辛柯、S沃诺斯基,《板壳理论》,科学出版社(1977).
[4]	徐芝纶,《弹性力学》(下册),人民教育出版社(1979).
[5]	Deverall, L, I, and C, J.Thorne, Bending of thin ring-sector plates, Trans, ASME,J.Appl, Mech,18 (1951),359-363.
[6]	Conway, H, D, and M, K, Huang, The bending of uniformly loaded sectorial plates with clamped edges, Trans, ASME, T.Appl.Mech,19 (1952),5-8.
[7]	Woinowsky-Krieger, S,Clamped semicircular plate under uniform bending load,Trans, ASME, 1, Appl, Mhch,22,1 (1955),129.
[8]	Ben-Amoz, M,Note on deflections and fleaurel vibrations of clamped sectorial plates, Trans, ASME, T.Appl, Meeh 26 (1959),136-137.
[9]	Morley, L, S, D,Variational of the clamped plate to two successive membrane problems with an application to uniformly loaded sectors, Quart, Lour, Mech, and Appl, Maths,16 (1963),451-471.
[10]	Ram,chandra Rao, B, S, and J, K, Sridhara,A bi-orthogonality relation for clamped sector plates, Journal of Engineering Mathematics, 4,4, Oct, (1970), 361-367.
[11]	Ramachandra Rao, B, S, and V.Kolathaya, Bending of a uniformly loaded clamped sector plate, Appl.Sci.Res,26,5 (1972),383-388.
[12]	Zerych, Stefan, Application of Fourier-Basset double series to analysis of circular and sector plates, Archiwum Inzynierii Ladowej, 18,1 (1972),3-21.
[13]	Rubin, C,Bending of ring and pie-shaped sectors, Traits, ASME,J.Appl, Mech,E42, 2 (1975),492-494.
[14]	Bhattacharya, A, P,Bending of sectorial plate having clam ped straight edge, Traps,ASME, J.Appl.Mech,42,1 (1975),229-230.
[15]	Bhattacharya, A, P, and K.N.Bhowmic, Note on the bending of an annular sector plate resting on an elastic foundation, T,Struct, Mech,4, 3 (1976),321-325.
[16]	Mukhopadhyay, Madhyjit, A semianalytic solutioa for radially supported curved plates in bending, Forsch.Ing,Wes,44, 6 (1978),187-196.
[17]	Mukhopadhyay, Madhyjit, A semianalytic solutioa for radially supported curved plates in bending, Forsch.Ing,Wes,44, 6 (1978),187-196.
[18]	Williams, M, L,Jr Surface stress singularities resulting from various boundary conditions in angular corners of plates under bending, Proceedings of the First U. S.National Congress of Applied Mechanics (1951),325-329.
[19]	Гонткевич В.С.,Собсmбенные Колебанuя Лласmuнок u Оболочек(1964).
[20]	钱民刚,用富里哀一贝赛尔级数解扇形、环扇形板,天津大学80级研究生毕业论文(1982).