A Study on Optimization for Vibration Properties of Thin Plates using Locally Rolling

局部轧制薄板振动特性优化研究

基本信息

批准号：
11650248
负责人：
KURATANI Fumiyasu
金额：
$ 1.86万
依托单位：
Hyogo University of Teacher Education
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1999
资助国家：
日本
起止时间：
1999 至 2000
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-11650248/
关键词：
Vibration Property Thin Plate Optimization Problem Finite Element Method Circular Saw Rolling Initial Stress Stiffness Matrix

项目摘要

When thin plates are locally compressed with opposing rollers, residual stresses are induced within the thin plates and then their vibration properties change. This research presents an optimization technique for the vibration properties of thin plates using locally rolling. Optimal rolling conditions are determined in the optimization problem assisted by computer instead of an experimental approach. A circular saw is given an actual example of a thin plate, which is widely used in cutting wood.1. A Search Algorithm for Optimal Rolling Conditions of Circular SawsA search algorithm based on gradient projection method is proposed for determining optimal rolling conditions (rolling position and rolling load) to maximize the lowest frequency of backward traveling wave of a rotating circular saw. In some examples, the optimal conditions are determined for several rotation speeds of a disk as a simple model of a circular saw. The results show that (1) the lowest frequency of backward traveling wave of an optimally rolled disk increases considerably, (2) the optimal conditions for the maximization of the lowest frequency of backward traveling wave vary with the rotation speed of the disk.2. An Efficient Method for Estimating Natural Frequencies of Rolled Circular SawsAn efficient method is proposed for estimating natural frequencies of circular saws locally compressed by rolling. The proposed method easily estimates the natural frequencies of a circular saw after rolling from the natural frequencies and mode shapes of the circular saw before rolling and the initial stress stiffness matrix after rolling without eigenvalue analysis. Some examples show that (1) the natural frequencies are accurately estimated from one-dimensional eigenvalue problem when rolling loads are small, (2) when the difference between the mode shapes before and after rolling is large, the coupled eigenvalue problem must be solved. In this case, the small-sized eigenvalue problem can be sufficient.

当薄板被相对的滚子局部压缩时，在薄板内诱导残余应力，然后其振动特性会发生变化。这项研究提出了一种使用本地滚动的薄板振动特性的优化技术。最佳滚动条件是在计算机辅助的优化问题中确定的，而不是实验方法。给出了一个圆形锯的实际例子的薄板，该板被广泛用于切割木材。1。提出了一种基于梯度投影方法的循环滚动条件的搜索算法，以确定最佳的滚动条件（滚动位置和滚动负载），以最大程度地提高旋转圆形锯的向后流动波的最低频率。在某些示例中，确定磁盘的多个旋转速度作为圆形锯的简单模型的最佳条件。结果表明，（1）最佳滚动磁盘向后行驶波的最低频率大大增加，（2）最大化向后行驶波最低频率的最佳条件随磁盘的旋转速度而变化。2。提出了一种有效的方法来估计滚动锯齿有效方法的固有频率，以估算滚动局部压缩的圆形锯的固有频率。提出的方法很容易估算从旋转旋转锯和滚动前的圆形锯中滚动后圆形锯的固有频率，而在没有特征值分析的情况下滚动后滚动后的初始应力刚度矩阵。一些示例表明，（1）滚动负载小时，从一维征值问题中准确估算了固有频率，（2）当滚动前后的模式形状之间的差异很大时，必须解决耦合特征值问题。在这种情况下，小型特征值问题就足够了。