SDOF碰撞衝擊動力系統兩邊阻擋受二個不同頻率激振之理論解析

Responses on the SDOF Impacting System with Two Fenders Subjected to Double Excitations

簡守謙(Shoou-Chian Jen)

《中華民國振動與噪音工程學會論文集》 2011 (2011/06) Pp. 184-189

https://doi.org/10.30028/CSSVANNUAL.201106.0184

摘要

本文旨在對單自由度SDOF(Single-Degree-of-Freedom)有兩邊阻擋之碰撞衝擊動力系統，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，繪出響應時序圖(waveform)和相圖(Phase portrait)，比較兩者相當吻合。數值分析在不同初始狀態，利用穩態解的起始值是以基本週期交替出現之特性，繪出分歧圖可以分辨頻率互鎖與類週期之響應，出現週期倍增至混沌現象，並有週期三響應出現。

關鍵字

碰撞衝擊 ； 二頻激振 ； 混沌

並列摘要

This study investigates the transient and steady state solutions of an single-degree-of-freedom (SDOF) impacting system with two fenders subjected to double excitations that the frequencies are nonmultiple ratio. Based on the analytical solution and the numerical simulation of the 4th order Runge-Kutta method, both waveform and phase portrait are plotted in good agreement with steady state response of the piecewise-linear system with different parameters. As integral bifurcation are plotted, frequency-locked oscillations with period 3 motions are found. This bifurcations exhibit the jump phenomenon, moreover, all possible subharmonics and period-doubling bifurcations to chaos are sought.

並列關鍵字

Impacting ； Double excitations ； Chaos