复杂条件下薄板动力问题的一种近似解法
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摘要
介绍在各种复杂条件下，分析薄板振动特性的一个近似方法─—模态摄动法。这一方法是在等截面均匀板的模态子空间内实施，将复杂板的变系数偏微分方程的求解转化为代数方程组的求解。通过算例，表明这一方法简单实用，且能获得有良好精度的近似解
In this paper, a methed which may be called the methed of mode perturbation is developed to analyze the characteristics of complicated plates. In this method , the mode functions of the uniform plate with undetermined coefficients is substituted into the govening differntial equation with variable coefficients such that a solution of the algebric equations with undetermined coefficients is just required to solve for the problem. It is shown in several numerical examples that this method is simple, practicable and owns good precision.
In this paper, a methed which may be called the methed of mode perturbation is developed to analyze the characteristics of complicated plates. In this method , the mode functions of the uniform plate with undetermined coefficients is substituted into the govening differntial equation with variable coefficients such that a solution of the algebric equations with undetermined coefficients is just required to solve for the problem. It is shown in several numerical examples that this method is simple, practicable and owns good precision.
引文
1 铁木辛柯S.工程中的振动问题.胡人礼译.北京:人民出版社,1978
2 Hinton E. Nurmerical methods and software for dynamic analysis of plates and shells Swansea: Pineridge Press, 1988
3楼梦麟.线性广义特征值问题在模态子空间中的摄动解.同济大学学报,1994 22(3):263~ 273
4 楼梦麟 变参数土层的动力特性和地震反应分析同济大学学报,1997,25(2):155~160
5楼梦麟,吴京宁.复杂梁动力问题的近似分析方法上海力学,1997 18(3):234~ 240
6曹志远.板壳振动理论北京;中国铁道出版社,1989
2 Hinton E. Nurmerical methods and software for dynamic analysis of plates and shells Swansea: Pineridge Press, 1988
3楼梦麟.线性广义特征值问题在模态子空间中的摄动解.同济大学学报,1994 22(3):263~ 273
4 楼梦麟 变参数土层的动力特性和地震反应分析同济大学学报,1997,25(2):155~160
5楼梦麟,吴京宁.复杂梁动力问题的近似分析方法上海力学,1997 18(3):234~ 240
6曹志远.板壳振动理论北京;中国铁道出版社,1989
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