横观各向同性地基与矩形板动力相互作用解析研究
本文选题：Laplace变换 切入点：Laplace逆变换 出处：《西安建筑科技大学》2017年硕士论文 论文类型：学位论文
【摘要】：本文求解出在任意竖向移动荷载作用下横观各向同性弹性地基问题的通解。首先对胡海昌关于横观各向同性体的通解进行Laplace变换,再利用双重傅里叶变化及逆变换,求得横观各向同性弹性地基在直角坐标系下的Laplace形式通解,再进行Laplace逆变换可得其真实解。对于置于横观各向同性弹性地基上的四边自由正交各向异性薄板在移动荷载下的动力响应问题,先对薄板的边界条件以及控制方程进行Laplace变换,再对移动荷载以及未知的地基反力进行Laplace变换,最后进行双重傅里叶展开,引入变形协调方程,得出Laplace形式的通解,进行Laplace逆变换求得真实解。对于置于横观各向同性弹性地基上的四边自由正交各向异性的中厚板在移动荷载下的动力响应问题,先求得含有未知地基反力板的Laplace形式通解,引入变形协调方程,得出Laplace形式的通解,进行Laplace逆变换求得真实解。对于四边自由正交各向异性的中厚板的稳态振动问题,基于横观各向同性弹性地基模型的通解,结合板的稳态振动控制方程,引入变形协调方程,得出解析解。编制Matlab程序,通过Matlab程序计算算例,计算所得结果与文献吻合,证明本文方法的正确性。研究在移动荷载下地基的参数、板的参数对板挠度与板弯矩的影响情况;研究在简谐激励荷载作用下荷载的频率对板挠度和弯矩幅值的影响情况。
[Abstract]:In this paper, the general solution to the problem of transversely isotropic elastic foundation under arbitrary vertical moving load is solved. Firstly, the general solution of Hu Haichang's general solution to transversely isotropic body is carried out by Laplace transform, and then the double Fourier transform and inverse transformation are used to solve the problem of transversely isotropic elastic foundation. The general solution of Laplace form for transversely isotropic elastic foundation in rectangular coordinate system is obtained. The real solution can be obtained by using Laplace inverse transformation. For the dynamic response of four free orthotropic thin plates on transversely isotropic elastic foundation under moving loads, the boundary conditions and governing equations of thin plates are firstly transformed by Laplace transform. Then the moving load and the unknown foundation reaction are transformed by Laplace, and then the double Fourier expansion is carried out, and the deformation coordination equation is introduced, and the general solution of Laplace form is obtained. The real solution is obtained by inverse Laplace transform. For the dynamic response of a plate with free orthotropic anisotropy of four sides on a transversely isotropic elastic foundation under moving load, the general solution of Laplace form with unknown foundation is first obtained. The general solution of Laplace form is obtained by introducing the deformation coordination equation, and the real solution is obtained by Laplace inverse transformation. For the steady state vibration problem of moderately thick plate with free orthotropic anisotropy on four sides, the general solution of transversely isotropic elastic foundation model is obtained. Combined with the steady state vibration control equation of the plate, the deformation coordination equation is introduced, and the analytical solution is obtained. The Matlab program is compiled, and an example is calculated by the Matlab program. The calculated results are in good agreement with the literature. The validity of this method is proved. The influence of the parameters of the foundation and the plate on the deflection and bending moment of the plate under moving load is studied, and the influence of the frequency of the load on the deflection and the amplitude of bending moment of the plate under harmonic excitation is studied.
【学位授予单位】：西安建筑科技大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TU470
【参考文献】
相关期刊论文 前10条
1 王春玲;张科宇;郭莹;;层状地基与深置薄板静力相互作用解析研究[J];西安建筑科技大学学报(自然科学版);2016年02期
2 徐晓龙;何芳社;郭春霞;;非线性文克尔地基上四边自由板弯曲问题的伽辽金解[J];山东理工大学学报(自然科学版);2014年02期
3 王春玲;丁欢;刘俊卿;;层状横观各向同性地基上异性矩形薄板的弯曲解析解[J];计算力学学报;2014年01期
4 王春玲;周波;胡勇;;弹性半空间地基与四边自由异性矩形板相互作用的研究[J];应用力学学报;2013年04期
5 何芳社;郭春霞;;考虑地基摩阻时Timoshenko梁弯曲的Fourier级数解答[J];力学季刊;2012年03期
6 王春玲;张海霞;吴艳红;;半空间地基与正交异性矩形中厚板相互作用解析解[J];北京理工大学学报;2012年06期
7 王春玲;王爱勤;吴艳红;;弹性半空间地基上正交异性矩形中厚板的弯曲[J];长安大学学报(自然科学版);2012年02期
8 王春玲;张海霞;丁欢;;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年04期
9 何芳社;郭雅云;郭春霞;;弹性半空间地基与环形板的相互作用[J];西安建筑科技大学学报(自然科学版);2010年06期
10 王春玲;季泽华;;一种可适用于正交异性矩形薄板弯曲稳定振动的双重正弦傅立叶级数通解[J];应用力学学报;2010年03期
相关博士学位论文 前1条
1 王春玲;土与基础结构静、动力相互作用的弹性半空间理论[D];西安建筑科技大学;2006年
相关硕士学位论文 前3条
1 高典;横观各向同性弹性地基上各向异性矩形薄板的稳态振动解析解[D];西安建筑科技大学;2015年
2 刘晓梅;横观各向同性弹性半空间地基上圆板的弯曲[D];西安建筑科技大学;2009年
3 孙延芳;弹性半空间地基上四边自由矩形厚板的弯曲[D];西安建筑科技大学;2006年
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