頻率無關因果阻尼之研究

Abstract

本文考慮一質量-彈簧-阻尼振子, 建立耗散能量與頻率無關且符合因果律的結構阻尼的數學模型, 得到振子的運動方程式是由滑-定兩相線性系統互相切換.解出振子在簡諧外力下反應的正解, 導得兩相切換的準則式. 振子穩態的行為可以在頻率比-阻尼比的參數空間分成幾個類別.們也利用相平面法導得振子穩態反應的公式, 並與正解互相比較, 只要頻率比大於 1/3, 即可得到準確的結果. 接著改變原振子的組成力,入了一個彈簧元件, 建立雙線性結構振子, 得到運動方程式是由開-關兩相線性系統互相切換, 且振子在關閉相位不會產生定著, 並再次解出開關相位的正解與切換的準則式.後把結構阻尼元件放入多自由度架構, 發展出運動方程式的解題流程並導出滑-滑條件.

In this thesis we consider a mass-spring-damping oscillator, constructing a mathematical model of structural damping which is frequency-independentnd causal. It is found that the oscillator with the structural damping is a two-phase linear system with a slide-stick switch.he exact solutions of its responses to simple harmonic loading are obtained, and the criteria of the two-phase switch are derived.ith the aid of the long-term behavior of the exact solutions,he steady motions of the oscillator are categorized in the parametric space of the ratios of frequencies and dampings.ormulae for estimating the steady responses of the oscillator are also derived using the method of phase plane.he estimated results fit very well with the exact solutions when the ratio of frequencies is larger than 1/3.e further study an oscillator with bilinear structural damping, which is resulted from adding a spring element to the original oscillator.t is also a two-phase linear system but with an on-off switch; it never sticks even in the off phase.gain exact solutions and swithing criteria are obtained.t last we put the structural damping elements into a multi-degree-of-freedom frame and develop arocedure for solving its equations of motion and deriving the slide-slide condition.