【作者】 冯璐；

【导师】 额布日力吐；

【作者基本信息】 内蒙古大学 ， 数学， 2017， 硕士

【摘要】 本文将正交各向异性矩形薄板方程化为Hamilton系统,经过分离变量法计算,得到了相应的无穷维Hamilton算子,进而算出该无穷维Hamilton算子的本征值及对应的本征函数系,并分别证明了此本征函数系的辛正交性及完备性.之后利用辛叠加方法求出正交各向异性矩形薄板弯曲问题的解析解.最后通过算例,验证了所得解析解的正确性.更多还原

【Abstract】 The paper transformed the orthotropic rectangular thin plates equation into the Hamiltonian system,the corresponding infinite dimensional Hamiltonian operator is ob-tained by the method of separation of variables.Then the eigenvalues and corresponding eigenfunctions of the Hamiltoian operator are calculated,respectively.Furthermore,it,is proved the eigenfunctions system is symplectic orthogonal and complete.Then using the symplectic-superposition method,the analytical solutions of fully clamped orthotrop-ic rectangular thin plates bending problem are presented.Finally,the validation of the obtained analytical solutions is proved.更多还原