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作者应用拉格朗日乘子法,提出了一种在已知各子结构模态信息条件下求解加筋圆板一类组合结构动特性的有效方法。该方法将以往求解这类结构动特性的非线性特征值问题转化为广义特征值问题,从而避免了在搜根中可能遇到的奇异性。作为算例,作者应用该法求解了某化工厂丙烯酸吸收塔塔盘的固有频率。其结果表明,这一方法具有计算精度高,求解特征值问题规模小等优点。这种方法还可推广到求解工程中其它常见板、梁组合结构的动态特性。
Using Lagrange multiplier method, the author proposes an effective method to solve the dynamic characteristics of a kind of composite structure with stiffened circular plates under the condition of known modal information of each substructure. This method converts the nonlinear eigenvalue problem that has been used to solve this kind of structural dynamics into a generalized eigenvalue problem, so as to avoid the singularities that may be encountered in the search for the root. As an example, the author used this method to solve the natural frequency of a chemical plant acrylic absorber tray. The results show that this method has the advantages of high computational accuracy and small problem of solving eigenvalue problems. This method can also be extended to solving the dynamic characteristics of other common plate and beam composite structures in engineering.