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單自由度分段線性動力系統受雙頻率激振的理論分析

The Analytical Study of an SDOF Piecewise-Linear System Subjected to Double Excitations

摘要


本文旨在對單自由度SDOF分段線性動力系統,承受二個不同外力簡諧激振頻率時,暫態與穩態響應的理論解析與數值模擬之研究。藉由理論分析與四階Runge-Kutta方法之數值模擬,分段線性動力系統為週期響應時,響應時序圖和相圖兩種方法幾乎無誤差。配合以相圖、頻譜圖、Poincarè切面圖、響應時序圖和Lyapunov指數,分辨分歧圖在參數變化之穩態響應之型態。

並列摘要


This study investigates the transient and steady state solutions of a single-degree-of-freedom (SDOF) piecewise-linear system subjected to double excitations with the frequencies of rational ratio. Based on theoretical analysis and numerical simulation of the 4th order Runge-Kutta method, both waveform and phase portrait are plotted in good agreement with periodic motions of the piecewise-linear system in different steady state parameters when periodic motion and chaotic motion are distinguished by bifurcation diagrams with characteristics of phrase portraits, frequency spectrum, Poincaré sections and Lyapunov exponent.

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