Dynamics and stability of a non - linear controlled system subject to parametric excitation 參數(shù)激勵下非線性受控系統(tǒng)的動力學和穩(wěn)定性
Investigation to quadratic nonlinearities and two - time superharmonic vibrations of plates in parametric excitation 參數(shù)激勵薄板平方非線性與2倍超諧振動
A detailed model of non - linear parametric excitation vibration coupling the stay cable and the girder , in which the static sag as well as the geometric non - linearity are considered , is proposed in this paper . based on several numeric examples investigated by the galerkin method composed with the integration strategy , several kinds of factors effecting stay cable parameter vibration are studied . another parameter vibration model by the axial excitation is presented and the corresponding nonlinear equations are derived 本文創(chuàng)新地提出了斜拉橋拉索-橋面耦合參數(shù)振動模型,推導了索-橋耦合非線性參數(shù)振動方程組,聯(lián)合galerkin法及數(shù)值積分方法,對各種特性的拉索進行了數(shù)值求解,得出了影響拉索參數(shù)振動的各種因素;提出了斜拉索受軸向端激勵參數(shù)振動模型,導出了模型的非線性振動方程,使用諧波平衡法得出了產(chǎn)生參數(shù)振動需要的最小激勵幅值、共振時瞬態(tài)及穩(wěn)態(tài)的振動幅值及索拉力的變化特性,并用數(shù)值積分方法對實際斜拉橋拉索進行了計算,分析了拉索阻尼對參數(shù)振動的影響。
According to the finite element method result , the parametric vibration of cables in cable - stayed arch bridge becomes prone to be exhibited . then a model of non - linear parametric excitation vibration coupling the stayed cable and the girder , namely , the mode of cable - stayed beam , is proposed in the thesis . and the nonlinear dynamical 3 、首先利用有限元分析方法,得出了斜拉索發(fā)生參數(shù)共振的可能,然后建立了斜拉拱橋拉索-橋面耦合參數(shù)振動模型,即索-梁組合結(jié)構(gòu)模型,推導了索-梁組合結(jié)構(gòu)非線性運動方程,利用多尺度方法研究斜拉索的參數(shù)共振和亞諧波共振,并對穩(wěn)態(tài)解的穩(wěn)定性進行了分析。