权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

A study on the dynamic control of large flexible structures with BIEM

大型柔性结构BIEM动力控制研究

基本信息

批准号：
04650405
负责人：
NISHIMURA Naoshi
金额：
$ 1.22万
依托单位：
KYOTO UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for General Scientific Research (C)
财政年份：
1992
资助国家：
日本
起止时间：
1992 至 1993
项目状态：
已结题

项目摘要

1. Study of the control for the wave equation with BIEMA computer code for 2 dimensional wave equation in time domain is developed. This code is then modified into a program to obtain the exact control for the wave equation with the help of HUM (the Hilbert uniqueness method). This approach is in contrast to FEM in that it does not require the analysis of the backward problem. Also, the obtained code is remarkable in terms of its simplicity high speed and high accuracy. We found that the solution of axisymmetric problems can be obtained with this approach. In non-axisymmetric problems with many degrees of freedom for the unknown functions, however, the use of Tikhonov's regularisation is necessary.Although the original plan included control problems with constrains, we felt it would be more worth-while to consider minimization of the sum of L^2 norms of the field variable (pressure) and the boundary control. This is because one is interested in reducing the pressure level in noise control problems. Some theoretical consideration reduces this problem to a system of PDEs similar to the so called optimal system. As we found, however, the numerical calculation for this problem with BIEM is rather unstable, and could obtain numerical solutions only in simple problems.2. Study of the control for the plate equation with BIEMAn analysis similar to those in 1.was carried out in the context of the dynamical equation of plate. The Dirichlet control in this problem drives the plate to rest by prescribing appropriate boundary deflection and slope. A numerical study is carried out in an axisymmetric problem. It is found that the choice of the time shape functions controls the stability of the numerical analysis. We could obtain a good result with piecewise linear (constant) shape functions for the Dirichlet (Neumann) data, with the help of the Tikhonov regularisation.

1.本文利用二维波动方程的BIEMA程序，在时域内对波动方程的控制问题进行了研究。然后将该程序修改成一个程序，利用HUM（希尔伯特唯一性方法）获得波动方程的精确控制。这种方法与有限元法不同之处在于它不需要分析后向问题。同时，该编码具有简单、快速、高精度等特点.我们发现用这种方法可以得到轴对称问题的解。然而，在未知函数具有多个自由度的非轴对称问题中，使用吉洪诺夫正则化是必要的。虽然原计划包括有约束的控制问题，但我们认为考虑场变量（压力）和边界控制的L^2范数之和的最小化会更麻烦。这是因为人们对降低噪声控制问题中的压力水平感兴趣。一些理论上的考虑减少了这个问题的一个系统的偏微分方程类似于所谓的最优系统。然而，我们发现，用边界元法对这一问题进行数值计算是相当不稳定的，只能在简单问题上得到数值解.用边界元法研究板方程的控制问题在板的动力学方程中进行了类似于[1]的分析。这个问题中的狄利克雷控制通过规定适当的边界挠度和斜率来驱动板静止。数值研究进行了轴对称问题。结果表明，时间形函数的选择控制了数值分析的稳定性。我们可以得到一个很好的结果与分段线性（常数）形状函数的狄利克雷（诺依曼）数据，与帮助的Tikhonov正则化。