Structural Dynamic Modification for Continuous Systems

連體系統的結構動態修改理論

陳溪泉(Hsi-Chuan Chen) ； 周元昉(Yuan-Fang Chou) ； 張純節(Churn-Jier Jang)

《中華民國振動與噪音工程學會論文集》 1998 (1998/05) Pp. 215-224

https://doi.org/10.30028/CSSVANNUAL.199805.0215

摘要

當一物體的物理特性改變時，其動態特性也將隨之改變。為不失一般性，本文所探討的對象為一受初始預應力、非均勻、非等向性的連體結構為對象，研究其結構動態特性的修改理論。對於修改後結構若仍利用數值法或模態測試來獲得其動態特性，則其時間和金錢的花費將相當可觀。一般修改過程常為小量且局部，可將此修改過程視為原結構在材料特性或在控制邊界上的擾動，利用邊界擾動法(BPM, Boundary Perturbation Method)可推導出其擾動統御方程式，若能得知其擾動解，也就可預估修改後結構的動態特性。利用原結構特徵函數的正交性，使用特徵函數展開法可求其擾動解。本文亦推導出尤拉樑的動態特性修改方法，以便於檢視本理論的精確性和說明其使用方法。假如修改的量很大。擾動法求解的收劍性將受限制，可考慮將此大修改量分成數個小修改量，以疊代方式將可降低擾動解的估算誤差。以一些實際的例子來比較利用BPM和FEM所估算的修改後系統的結構動態特性的差異和效率。BPM更可有效率的使用於結構動態特性修改的逆問題上。假如原系統的結構動態特性是透過模態測試獲得的，則以此模態測試的結果為基礎，利用BPM亦可估算修改系統的結構動態特性。

並列摘要

A structural dynamic modification approach for continuous systems, which can be initially stressed, nonhomogeneous, anisotropic, and arbitrary in shape, is presented in this paper. The modified system is treated as the original system with some perturbations on material properties or on control boundary. The governing equations of the modified system are derived by the boundary perturbation method (BPM). If the perturbation solutions can be found, the dynamic behavior of the modified system can be predicted. When the modal parameters of the original system arc known, the eigenfunction expansion method is employed to find out perturbation solutions. The dynamic modification approach for Euler- Bernoulli beam is derived to check its accuracy and to illuminate, its application. If the modifications are too large to apply the perturbation method, the BPM with updating approach can reduce the errors. Two sets of solutions based on the BPM and the FEM for some realistic examples will be compared to demonstrate the effectiveness of the proposed method. The BPM method can also apply for inverse problems of structural dynamicmodification. When the structural dynamic characteristics arc obtained via modal testing, the B1A can be used to predict the perturbed solutions.