本文選題：干摩擦梁結(jié)構(gòu) + 非線性模態(tài)　； 參考：《天津大學》2015年博士論文

【摘要】：干摩擦阻尼廣泛應(yīng)用于摩擦葉片、空間結(jié)構(gòu)等機械結(jié)構(gòu)中,以達到減振或改變振動特性的目的。近些年來,干摩擦結(jié)構(gòu)的非線性動力學響應(yīng)得到了深入研究,但此類結(jié)構(gòu)的模態(tài)特性很少關(guān)注。干摩擦作用下結(jié)構(gòu)的非線性模態(tài)演化規(guī)律,以及采用模態(tài)的方法揭示減振機理等問題仍然沒有很好的解決。而這類研究對含干摩擦梁結(jié)構(gòu)的設(shè)計具有重要的理論意義。論文采用實驗方法、解析方法、數(shù)值方法研究摩擦梁結(jié)構(gòu)的模態(tài)特性,以揭示減振機理。實驗研究可初步了解干摩擦對梁結(jié)構(gòu)模態(tài)的影響規(guī)律;解析和數(shù)值研究主要獲得干摩擦對梁結(jié)構(gòu)模態(tài)的作用規(guī)律,以及如何依據(jù)模態(tài)特性開展基于干摩擦阻尼的減振設(shè)計。主要的研究工作和成果如下:(1)建立多點摩擦雙層梁實驗?zāi)Ｐ?采用LMS Polymax方法,獲得包含彈性體和剛體模態(tài)的16階模態(tài)參數(shù)。實驗表明,隨著無量綱激勵力(激勵力幅值與摩擦力比值)的增大,剛體模態(tài)頻率減小,而彈性體模態(tài)頻率略有增大;干摩擦系數(shù)對模態(tài)階數(shù)的影響程度不同。另外,為識別出系統(tǒng)較全面的模態(tài)參數(shù),確定出了激勵力幅值的合理范圍。(2)針對多點摩擦雙層梁模型,提出了一種適合于大型工程結(jié)構(gòu)的工作模態(tài)實驗方法。在20N法向壓力產(chǎn)生的干摩擦條件下,分別進行縱向、垂向的單向隨機激勵工況實驗,獲得的模態(tài)參數(shù)疊加結(jié)果與傳統(tǒng)模態(tài)實驗(錘擊法)獲得的結(jié)果一致。另外,研究了參考方向、采樣時間等參數(shù)對實驗效果的影響規(guī)律。(3)針對干摩擦懸臂梁,提出了求解非線性模態(tài)的能量等效方法。將干摩擦作用的懸臂梁模型,在模態(tài)方面等效為無干摩擦作用的懸臂梁模型。對干摩擦懸臂梁采用拉格朗日第一類方程建立運動方程,將干摩擦邊界條件考慮到運動方程中。采用拉格朗日第二類方程,對等效模型(單一懸臂梁)建立運動方程。獲得兩個模型的自然頻率和激勵能量的關(guān)系式,基于能量等效的原理,獲得干摩擦作用下的懸臂梁自然頻率解析式。隨后采用數(shù)值方法對1-5階自然頻率進行了驗證,結(jié)果具有較好的一致性。(4)研究了摩擦力大小、摩擦位置、激勵能量對含干摩擦懸臂梁自然頻率的影響規(guī)律,并揭示了這些參數(shù)對減振特性的影響規(guī)律。如改變摩擦位置可改變阻尼效率;若摩擦位置位于某階模態(tài)節(jié)點處,可對這階模態(tài)進行過濾,抑制其它階模態(tài)運動。另外,干摩擦非線性阻尼結(jié)構(gòu)的頻率能量依賴關(guān)系具有上臨界的特性。(5)研究了摩擦配置對非線性模態(tài)演變特性的影響規(guī)律。針對三次剛度非線性的兩自由度模型,考慮摩擦阻尼及接地和非接地摩擦配置模型,采用頻域方法(Hamilton FEP和瞬態(tài)FEP)和時域方法,研究1:1同相和反相非線性模態(tài)演變特性。雖然接地和非接地摩擦模型具有相同的Hamilton FEP,但模態(tài)演變特性不同。對于反相非線性模態(tài)演變,接地摩擦模型保持單一模態(tài)運動,非接地摩擦模型出現(xiàn)兩種非線性模態(tài)運動。同相非線性模態(tài)演變比較復(fù)雜,接地摩擦模型經(jīng)同相非線性模態(tài)、3:1非線性模態(tài),到反相非線性模態(tài)運動;非接地摩擦模型的同相非線性模態(tài)演變成3:1非線性模態(tài)運動。(6)通過非線性模態(tài)演變特性研究了非線性減振器的減振機理。不同類型的模態(tài)運動,非線性減振器減振特性不同。干摩擦阻尼配置決定著非線性模態(tài)演變特性及演變結(jié)果,非線性模態(tài)運動控制著非線性減振器的減振特性。兩種模型中,非接地摩擦模型的減振效果優(yōu)于接地摩擦模型;3:1非線性模態(tài)減振特性優(yōu)于反相非線性模態(tài)。通過上述研究工作,獲得了對含干摩擦結(jié)構(gòu)非線性模態(tài)的初步認識,豐富了非線性模態(tài)理論的研究成果,對基于干摩擦的非線性減振設(shè)計具有指導(dǎo)意義。
[Abstract]:Dry friction damping is widely used in the mechanical structures such as friction blades, space structures, to reduce vibration and change vibration characteristics. In recent years, the nonlinear dynamic response of dry friction structures has been studied deeply, but the modal characteristics of such structures are seldom concerned. It is still not well solved to reveal the mechanism of vibration damping by means of modal method. And this kind of research has important theoretical significance for the design of the structure of dry friction beam. The experimental method, analytical method and numerical method are used to study the modal characteristics of the friction beam structure to uncover the damping mechanism. The experimental study can understand the dry friction preliminarily. The influence law of the beam structure mode is rubbed. The analytical and numerical study mainly obtains the action law of the dry friction on the beam structure mode, and how to carry out the damping design based on the dry friction damping according to the modal characteristics. The main research work and results are as follows: (1) the experimental model of multi point friction double deck beam is established, and the LMS Polymax method is used to obtain the package. The 16 order modal parameters of the elastic body and the rigid body model show that the modal frequency of the rigid body decreases with the increase of the dimensionless excitation force (the ratio of the amplitude of the excitation force and the friction force), and the modal frequency of the elastomer increases slightly, and the influence of the dry friction coefficient on the modal order is different. In addition, the more comprehensive modal parameters are identified. A reasonable range of excitation amplitude is determined. (2) for multi point friction double deck beam model, a working mode experiment method suitable for large engineering structures is proposed. Under the dry friction conditions produced by the 20N method, the longitudinal and vertical one-way random excitation conditions are carried out respectively, and the results of the superposition of modal parameters and the traditional modes are obtained. The results obtained by the state experiment (hammering) are the same. In addition, the influence of the reference direction, sampling time and other parameters on the experimental results is studied. (3) an energy equivalent method for solving the nonlinear mode is proposed for the dry friction cantilever beam. The cantilever beam model with dry friction is equivalent to a cantilever beam model with dry friction. The equation of motion of the dry friction cantilever beam is established by Lagrange's first type equation. The dry friction boundary condition is taken into consideration in the motion equation. The equation of Lagrange second is used to establish the equation of motion for the equivalent model (single cantilever beam). The relationship between the natural frequency and the excitation energy of the two models is obtained, based on the principle of energy equivalence. The natural frequency of the cantilever beam under dry friction is obtained. Then the numerical method is used to verify the natural frequency of the 1-5 order. The results have good consistency. (4) the influence of the friction force, the friction position and the excitation energy on the natural frequency of the dry friction cantilever beam is studied, and the vibration damping characteristics are revealed. If the friction position is changed, the damping efficiency can be changed. If the friction position is located at a certain modal node, this order mode can be filtered and other order modal motion can be suppressed. In addition, the frequency energy dependence of the dry friction nonlinear damping structure has a critical characteristic. (5) the characteristics of the friction configuration on the nonlinear modal evolution are studied. According to the three degree of stiffness nonlinear two degree of freedom model, considering the friction damping and the ground and non earthing friction configuration model, the frequency domain method (Hamilton FEP and transient FEP) and the time domain method are used to study the evolution characteristics of the 1:1 phase and the inverse phase nonlinear mode. Although the ground and non earthing friction models have the same Hamilton F EP, but the modal evolution characteristics are different. For the nonlinear modal evolution of the inverse phase, the ground friction model maintains a single mode motion, and the non earthing friction model has two nonlinear modal motions. The evolution of the phase nonlinear mode is more complex. The ground friction model is subjected to the phase nonlinear mode, the 3:1 nonlinear mode, the inverse nonlinear modal motion; The homogenous nonlinear mode of ground friction model evolves into 3:1 nonlinear modal motion. (6) the vibration damping mechanism of nonlinear damper is studied by nonlinear modal evolution characteristics. Different types of modal motion and nonlinear damper are different in damping characteristics. The nonlinear modal evolution characteristics and evolution results are determined by the dry friction damping configuration. In the two models, the damping effect of the non earthing friction model is superior to the ground friction model in the two models, and the nonlinear modal damping characteristics of the nonlinear modal are superior to the inverse nonlinear mode. The preliminary understanding of the nonlinear modal of the dry friction structure is obtained through the above research, and the nonlinearity is enriched. The research results of modal theory are of guiding significance to the nonlinear damping design based on dry friction.
【學位授予單位】：天津大學
【學位級別】：博士
【學位授予年份】：2015
【分類號】：O328

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