Research On Vibration And Control Of One Dimensional Structure Using Element Free-Precise Integration Method

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.