桁架系統之非線性動力及混沌現象與機制

Nonlinear Dynamic and Chaotic Mechanism of Two-Member Truss

劉國瑞(Kou-Ruey Liu)

指導教授 ： 楊永斌

國立臺灣大學/工學院/土木工程學研究所/碩士(2004年)

https://doi.org/10.6342/NTU.2004.01760

摘要

在非線性動力系統中，隱含著一種特殊的行為，稱為混沌現象。儘管是處在決定性系統，但仍會出現類似隨機系統的不可預測性。而在各種領域中都可以發現這種系統，如大氣、生態甚至經濟、股市。我們關心在土木工程的範疇是否也有這樣的系統。
我們採用混沌理論的分析工具，包括里阿譜諾指數、龐加萊圖、分歧圖等，來分析雙桿件桁架系統的混沌現象。驗證在土木工程中最基本的桁架結構，具有混沌系統的共通特徵，如對起始條件的敏感性、奇異吸子、週期倍增混沌成形路徑等。
我們並進一步藉著結合靜力系統平衡路徑與動力系統加載曲線的概念，探討系統挫屈臨界外力與混沌邊界的關係，賦予混沌現象在工程面的意義。

關鍵字

混沌 ； 渾沌 ； 非線性動力 ； 桁架

並列摘要

In nonlinear dynamic systems, there exists a special behavior that is called chaos. Even in a deterministic system, we can find unpredictable characteristics similar to those in random systems. Such a phenomenon can be found in different fields, including the atmospheric science, ecology, economics, and even stock market. It is our concern that if it exists in the area of civil engineering.
We adopt various analysis measures commonly in chaotic theory, including the Lyapunov exponent, Poincaré maps, and bifurcation diagram, etc., to analyze the chaotic phenomenon of a two-member truss system. We intend to investigate if any chaotic characteristics can be found in such a simple truss structure in civil engineering, particularly the sensitivity to initial conditions, strange attractor and period-doubling route to chaos.
We further combine the concept of static equilibrium path with dynamic loading curve, to discuss the relation between the buckling external force and chaotic boundary. Emphasis has been placed on the physical interpretation of the chaotic phenomena encountered.

並列關鍵字

chaos ； nonlinear dynamic ； truss

參考文獻

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