本文選題：橫向自由振動 + 軸向繩移系統(tǒng)��； 參考：《合肥工業(yè)大學(xué)》2017年碩士論文

【摘要】：在工程設(shè)備中廣泛應(yīng)用的軸向繩移系統(tǒng)以其振動問題,尤其是橫向振動,而備受關(guān)注。不同的邊界條件,系統(tǒng)的橫向振動形式也不相同,本文針對四種不同的典型邊界條件研究了軸向繩移系統(tǒng)的橫向自由振動。本文以軸向繩移系統(tǒng)為研究對象,首先建立了兩端固定、固定-自由、阻尼-固定和固定-移動四種邊界條件下的物理模型,分別用兩種不同的方法建立了軸向繩移系統(tǒng)的數(shù)學(xué)模型,第一種是基于拉格朗日方程和形函數(shù)建立的有限元動力學(xué)方程;第二種是基于哈密頓變分原理建立的偏微分運(yùn)動方程。其次,針對傳統(tǒng)有限元法對于高速移動繩橫向振動計(jì)算誤差大、易發(fā)散的問題,基于行波在不同邊界的反射疊加技術(shù),提出一種有限長度軸向移動繩橫向振動計(jì)算方法。接著結(jié)合其初始條件以及四種邊界條件分別獲得反射波的表達(dá)式,從而將移動繩的橫向自由振動等效為不同速度的行波及其反射波的疊加,推導(dǎo)出其理論表達(dá)式,并根據(jù)行波的運(yùn)動規(guī)律分別獲得了定繩長和變繩長系統(tǒng)的運(yùn)動周期。最后以能量反射系數(shù)為切入點(diǎn)分析了能量變化的周期性,并分析了不同邊界條件下系統(tǒng)的能量變化規(guī)律以及繩在通過邊界處的能量轉(zhuǎn)換機(jī)制。
[Abstract]:The axial rope moving system, which is widely used in engineering equipment, has attracted much attention for its vibration problem, especially transverse vibration. For different boundary conditions, the transverse vibration forms of the system are also different. In this paper, the transverse free vibration of the axial rope moving system is studied for four different typical boundary conditions. In this paper, the axial rope moving system is taken as the research object. Firstly, the physical models under four boundary conditions of fixed, fixed free, damping fixed and fixed moving are established. The mathematical models of the axial rope moving system are established by two different methods, the first is the finite element dynamic equation based on Lagrange equation and the form function, and the second is the partial differential motion equation based on Hamiltonian variational principle. Secondly, aiming at the problem that the traditional finite element method has a large error in calculating the lateral vibration of high speed mobile rope, based on the reflection superposition technique of traveling wave at different boundaries, a finite length axial moving rope lateral vibration calculation method is proposed. Then combined with the initial conditions and the four boundary conditions, the expressions of the reflected waves are obtained respectively, so that the lateral free vibration of the moving rope is equivalent to the stacking of the traveling waves and the reflected waves with different velocities, and the theoretical expressions are derived. According to the moving law of traveling wave, the motion periods of fixed rope length and variable rope length system are obtained respectively. Finally, the periodicity of energy change is analyzed with the energy reflection coefficient as the starting point, and the energy variation law of the system under different boundary conditions and the energy conversion mechanism of the rope passing through the boundary are analyzed.
【學(xué)位授予單位】：合肥工業(yè)大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：TH113.1

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本文編號：1934730