【作者】 刘仁昌；

【导师】 任传波；

【作者基本信息】 山东理工大学 ， 固体力学， 2007， 硕士

【摘要】 无网格法具有只需节点信息无需划分单元的特性,近年来国内外学者对其进行了大量的研究,但在连续体的振动与控制中的研究还较少。本文将探索无网格伽辽金法在连续体的振动与控制中的应用情况。利用钟万勰教授提出的精细积分法求解动力学方程,具有无条件稳定,计算精度高的优点。本文通过数值方法研究一维结构的振动与控制。建立一维结构受控系统的动力学方程,利用无网格伽辽金法与精细积分法结合的方法求解此动力学方程,得到一维结构的动力响应,为数值方法解决结构振动与控制问题提供了一种较新的算法。本文主要工作:1推导了杆件、伯努力梁在静力学及振动与控制中的修正变分原理。2给出了weber权函数、指数权函数、形函数以及它们的一阶、二阶、三阶导数的公式。3推导了一维结构振动与控制的无网格-精细积分算法。4给出了弹簧摆、一维杆件、一维伯努力梁的振动与控制算例,并用解析解验证。由算例可以看到,用无网格-精细积分法解决一维结构的振动与控制问题是比较成功的。所以,我们以后可以在二维结构的振动与控制、断裂力学、大变形等其它领域做些工作。更多还原

【Abstract】 Element free Galerkin method (EFGM) has such meshless features as the need for nodes only without classified units. It is studied by scholars abroad in recent years, but there is still little research in vibration and control of continuous body. In this paper, research on vibration and control of continuous body with EFGM is done.Dynamic equations are solved with precise integration method which is advanced by professor Zhong. This method has the advantage of high precision and unconditionally stableness. In this paper, vibration and control of one dimensional structure is solved with numerical algorithms. Dynamic equation of one dimensional structure is founded, it is sovled with precise integration method which is combined with EFGM, and dynamic response of one dimensional structure is obtained. This is a new numerical algorithms to solve vibration and control of one dimensional structure.The chief work is:1 Modified variational principles in static and dynamic problems of one dimensional pole, bernoulli beam are derived.2 Formulas of weight function and shape function as well as their first order, second order, third order differential coefficient are given.3 Element free Galerkin-Precise Integration Method in the dynamic problems of one dimensional structure is derived.4 Examples of one spring pendulum, dimensional pole and bernoulli beam are applied and contrasted with exact solutions.We can see from calculating examples that, it is successful to solve vibration and control of one dimensional structure with element free-precise integration method. We can do some works in vibration and control of two dimensional structure, fracture mechanics, other fields such as being big and out of shape in the future.更多还原