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。

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.