含干摩擦梁结构的非线性模态特性与减振机理研究

发布时间：2018-06-07 20:50

本文选题：干摩擦梁结构 + 非线性模态　；参考：《天津大学》2015年博士论文

【摘要】：干摩擦阻尼广泛应用于摩擦叶片、空间结构等机械结构中,以达到减振或改变振动特性的目的。近些年来,干摩擦结构的非线性动力学响应得到了深入研究,但此类结构的模态特性很少关注。干摩擦作用下结构的非线性模态演化规律,以及采用模态的方法揭示减振机理等问题仍然没有很好的解决。而这类研究对含干摩擦梁结构的设计具有重要的理论意义。论文采用实验方法、解析方法、数值方法研究摩擦梁结构的模态特性,以揭示减振机理。实验研究可初步了解干摩擦对梁结构模态的影响规律;解析和数值研究主要获得干摩擦对梁结构模态的作用规律,以及如何依据模态特性开展基于干摩擦阻尼的减振设计。主要的研究工作和成果如下:(1)建立多点摩擦双层梁实验模型,采用LMS Polymax方法,获得包含弹性体和刚体模态的16阶模态参数。实验表明,随着无量纲激励力(激励力幅值与摩擦力比值)的增大,刚体模态频率减小,而弹性体模态频率略有增大;干摩擦系数对模态阶数的影响程度不同。另外,为识别出系统较全面的模态参数,确定出了激励力幅值的合理范围。(2)针对多点摩擦双层梁模型,提出了一种适合于大型工程结构的工作模态实验方法。在20N法向压力产生的干摩擦条件下,分别进行纵向、垂向的单向随机激励工况实验,获得的模态参数叠加结果与传统模态实验(锤击法)获得的结果一致。另外,研究了参考方向、采样时间等参数对实验效果的影响规律。(3)针对干摩擦悬臂梁,提出了求解非线性模态的能量等效方法。将干摩擦作用的悬臂梁模型,在模态方面等效为无干摩擦作用的悬臂梁模型。对干摩擦悬臂梁采用拉格朗日第一类方程建立运动方程,将干摩擦边界条件考虑到运动方程中。采用拉格朗日第二类方程,对等效模型(单一悬臂梁)建立运动方程。获得两个模型的自然频率和激励能量的关系式,基于能量等效的原理,获得干摩擦作用下的悬臂梁自然频率解析式。随后采用数值方法对1-5阶自然频率进行了验证,结果具有较好的一致性。(4)研究了摩擦力大小、摩擦位置、激励能量对含干摩擦悬臂梁自然频率的影响规律,并揭示了这些参数对减振特性的影响规律。如改变摩擦位置可改变阻尼效率;若摩擦位置位于某阶模态节点处,可对这阶模态进行过滤,抑制其它阶模态运动。另外,干摩擦非线性阻尼结构的频率能量依赖关系具有上临界的特性。(5)研究了摩擦配置对非线性模态演变特性的影响规律。针对三次刚度非线性的两自由度模型,考虑摩擦阻尼及接地和非接地摩擦配置模型,采用频域方法(Hamilton FEP和瞬态FEP)和时域方法,研究1:1同相和反相非线性模态演变特性。虽然接地和非接地摩擦模型具有相同的Hamilton FEP,但模态演变特性不同。对于反相非线性模态演变,接地摩擦模型保持单一模态运动,非接地摩擦模型出现两种非线性模态运动。同相非线性模态演变比较复杂,接地摩擦模型经同相非线性模态、3:1非线性模态,到反相非线性模态运动;非接地摩擦模型的同相非线性模态演变成3:1非线性模态运动。(6)通过非线性模态演变特性研究了非线性减振器的减振机理。不同类型的模态运动,非线性减振器减振特性不同。干摩擦阻尼配置决定着非线性模态演变特性及演变结果,非线性模态运动控制着非线性减振器的减振特性。两种模型中,非接地摩擦模型的减振效果优于接地摩擦模型;3:1非线性模态减振特性优于反相非线性模态。通过上述研究工作,获得了对含干摩擦结构非线性模态的初步认识,丰富了非线性模态理论的研究成果,对基于干摩擦的非线性减振设计具有指导意义。
[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.
【学位授予单位】：天津大学
【学位级别】：博士
【学位授予年份】：2015
【分类号】：O328

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