[1]王春玲1,2,张海霞1,等.弹性半空间地基上正交异性矩形薄板稳态振动通解[J].西安建筑科技大学学报:自然科学版,2011,43(04):474-479.[doi:DOI:10.15986/j.1006-7930.2011.04.001]
 ,,et al. General solutions to the steady vibration of orthotropic rectangularplates on the semi-infinite elastic foundatio[J].J.Xi’an Univ. of Arch. & Tech.:Natural Science Edition,2011,43(04):474-479.[doi:DOI:10.15986/j.1006-7930.2011.04.001]
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弹性半空间地基上正交异性矩形薄板稳态振动通解()
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西安建筑科技大学学报:自然科学版[ISSN:1006-7930/CN:61-1295/TU]

卷:
43
期数:
2011年04期
页码:
474-479
栏目:
出版日期:
2011-08-31

文章信息/Info

Title:
  General solutions to the steady vibration of orthotropic rectangular
plates on the semi-infinite elastic foundatio
文章编号:
1006-7930(2011)04-0474-06 .
作者:
王春玲1张海霞1丁 欢1
(1.西安建筑科技大学理学院,陕西西安710055;2.陕西循环经济工程技术院,陕西西安710055)
Author(s):
WANG Chun-ling1ZHANG Hai-xia1DING Huan1
(1.School of Science,Xi′an Univ.of Arch.& Tech.,Xi′an 710055,China;
2.Shaanxi Techno-institute of Recycling Economy,Xi′an 710055,China
关键词:
弹性半空间地基正交各向异性矩形板相互作用稳态振动解析解
Keywords:
the semi-infinite elastic foundationorthotropic rectangular plateinteractionsteady vibration analyticsolution
分类号:
O343.3
DOI:
DOI:10.15986/j.1006-7930.2011.04.001
文献标志码:
A
摘要:
先对边界任意约束的正交各向异性矩形薄板,构造了四次逐项可导的带有补充项的双重正弦傅里叶
级数通解.该解析解既不需要叠加,对不同的物性参数又不需要分类,而且待定系数少又具有明确的物理含
义,这使得正交各向异性矩形薄板的振动问题求解统一化、简单化、规律化.然后将该通解与弹性半空间受任
意竖向稳态荷载作用下的动力位移积分变换解相结合,得出弹性半空间地基上边界任意约束的正交各向异
性矩形板,在任意竖向稳态荷载作用下的稳态振动解析解.最后还给出了算例分析,其结果与文献吻合良好,
证明本文的方法是切实可行的.
Abstract:
General solution to the steady vibration which was constructed by double trigonometrically sine series with supplementary
 terms was introduced for the vibration analysis of orthotropic rectangular thin plates loaded with arbitrary
steady vertical force on the semi-infinite elastic foundation.This general solution is four-order derivative,and has less undetermined
 coefficients which has definite physical meaning.The solution can be used to sethe the problem of orthotropic
rectangular plates on the semi-infinite elastic foundation with neither a dassification by different property parameter nor a
superimposition.Such a solution has resulted in vibration analysis of orthotropic rectangular plates loaded with vertical
steady force on the semi-infinite elastic foundation,unionization,simplification and systematization.The analytic vibration
 solution to orthotropic rectangular plates loaded with vertical steady force on the semi-infinite elastic foundation was
given by combining the general solution of double trigonometrically sine series with supplementary terms with the dynamic
integral representations for displacements of the semi-infinite elastic foundation loaded with arbitrary vertical steady force.
The agreement is found satisfactory in proving the validity of the method in solving the problem.This new method would
be feasible in practical applications.

参考文献/References:

 References
[1] 杨端生,黄 炎.双参数弹性地基上的正交异性矩形板的弯曲[J].工程力学,2009,26(3):26-30.
YANG Duan-sheng,HUANG Yan.Bending of orthotropic rectangular plates on double-parametric elastic foundation
[J].Engineering Mechanics,2009,26(3):26-30.
[2] 王春玲,黄 义.弹性半空间地基上四边自由矩形板的弯曲解析解[J].岩土工程学报,2005,27(12):1402-1407.
WANG Chun-ling,HUANG Yi.Analytic solution of rectangular plates loaded with vertical force on an elastic half
space[J].Chinese Jounal of Geotechnical Engineering,2005,27(12):1402-1407.
[3] 王春玲,黄 义.弹性半空间地基上四边自由矩形板的弯曲解析解[J].应用数学和力学,2007,28(2):173-182.
WANG Chun-ling,HUANG Yi.Analytical solutions of steady vibration of a free rectangular plate on the semi-infinite
 elastic foundation[J].Applied Mathematics and Mechanics,2007,28(2):173-182.
[4] 王春玲,周 亮.弹性半空间地基上正交异性矩形板弯曲通解[J].力学季刊,2010,31(2):227-235.
WANG Chun-ling,ZHOU Liang.General solution of orthotropic rectangular plate under vertical force on semi-infinite
 elastic foundation[J].Chinese Quarterly of Mechanics,2010,31(2):227-235.
[5] 曲庆璋,章权,季求知,等.弹性板理论[M].北京:人民交通出版社,2000.
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备注/Memo

备注/Memo:
*收稿日期:2010-05-24  修改稿日期:2011-07-12
基金项目:陕西省自然科学基金资助项目(2010JM7015)
作者简介:王春玲(1964-),女,陕西礼泉人,博士,教授,主要从事地基与基础结构相互作用的研究.
更新日期/Last Update: 2015-11-05