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題名 | Exact Solutions and Dynamic Responses of Sdof Bilinear Elastoplastic Structures=雙線性單自由度彈塑性結構的正解及動態反應 |
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作者 | 劉進賢; Liu, Chein-shan; |
期刊 | 中國工程學刊 |
出版日期 | 19970900 |
卷期 | 20:5 1997.09[民86.09] |
頁次 | 頁511-525 |
分類號 | 440.2 |
語文 | eng |
關鍵詞 | 動態分析; 雙線性結構; 非彈性反應譜; 調和載重; 塑性共振; Dynamic analysis; Bilinear structure; Inelastic response spectra; Harmonic loading; Plastic resonance; |
中文摘要 | 本文探討雙線性彈塑性單自由度結構在外加動態載重下的數學模式,推導得出塑 性不可逆開關的充分必要條件。經過深入的分析研究,本文指出描述雙線性彈塑性單自由度 結構的運動方程,可以轉換成兩相的線性微分方程及一個開關機制。因此任何外加動態載重 下結構的動態響應可以完全由求得的正解進行分析及計算。雙線性彈塑性結構的特點在於延 長結構的自然周期、增加阻尼比及塑性開關造成的非平滑修正載重。文中探討調和載重下雙 線性彈塑性結構的動態反應,給出塑性共振的必要條件,並進行彈塑性行為研究,發現雙線 性彈塑性結構有穩定的遲滯圈及極限環。文中亦探討調和載重下雙線性彈塑性結構的非彈性 反應譜,對自然頻率、降伏強度及走動勁度等參數的影響給予說明。 |
英文摘要 | The model of single degree of freedom bilinear elastoplastic structures under external loading is treated in this paper. Based on the model sufficient and necessary conditions for plastic irreversibility are derived. It is analyzed and pointed out that for the bilinear structure the equation of motion is nothing but a two-phase linear system with an on-off switch, which is operated in the pace of an intrinsic measure of plastic irreversibility. Then the exact solutions of the dynamic responses are derived for arbitrary external loading and, especially the explicit results are worked out for sinusoidal loading inputs. Comparison with the corresponding linear structure shows that the characteristics of the bilinear structure have three folds: longer natural period, larger damping ratio and non-smooth modified loading due to on-off switching. For harmonic loading the necessary condition for plastic resonance is derived, and the elastoplastic behavior is found to exhibit stable hysteresis loop and limit cycle. The inelastic response spectra are also given for harmonic loading, from which the influences of structural parameters, namely natural frequencies, yield strengths and kinematic stiffness, are analyzed and discussed. |
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