单向悬挂屋盖结构的风致气弹耦合效应数值模拟

综合运用计算流体力学和计算结构力学技术,建立了适用于索膜结构流固耦合风振分析的CFD数值模拟方法,并编制了相应的有限元计算程序。应用该程序对具有不同参数的大跨度单向屋盖结构进行了风振响应分析,探讨了来流风速、屋面质量和初始预张力等参数对结构流固耦合特性的影响。研究表明,由于屋盖前缘周期脱落的大尺度旋涡是诱导结构振动的主要原因,随着大尺度旋涡沿屋面向下游移动,其动能逐渐转化为结构变形能,使结构振动形态呈现明显的涡激振动特征。屋面质量、来流风速和初始预张力是影响结构流固耦合性能的主要参数。对于索膜结构,仅通过刚性模型来确定结构风压并进行风振响应分析,其结果是不可靠的。     

关于一类电-力振动模型的建模与分析

从电学、力学的基本原理出发,通过数学方法建立和分析了一种电-力振动模型。这是一种较复杂的电力混合作用的线性振动系统,由模型的特殊结构(类扬声器结构)作者确立了两种磁场,即感生磁场和外磁场两者正交独立,并规定了电学、力学两种不同物理量的坐标取向关系。该模型需要求得三阶正系数常微分方程的收敛解,再求得包含暂态、稳态项的完整解。另外,文章从能量和做功的角度,通过对电压电流间的相位差分析,对所建模型的正确性作了论证,同时也为这类建模引荐了一种论证手段。     

车辆-轨道系统垂向随机振动的辛方法分析

将轨道视为无限长的周期结构,建立车辆轨道垂向耦合模型. 使用虚拟激励法将随机的轨道不平顺激励转化为确定性的简谐激励,再用辛数学方法求解轨道结构的频率响应特性和耦合系统的响应功率谱. 整个计算模型只有26个自由度,求解过程快速而精确.数值算例中,将该方法与常规有限元方法进行了比较,验证了方法的高效性和正确性,讨论了车辆速度对系统随机响应的影响.      

压电结构的主动控制仿真与实验研究

结合有限元方法研究了直接负速度反馈和基于LQR(二次线性最优控制)的独立模态空间主动控制方法来控制结构的振动, 采用一种新的仿真方法：PATRAN与MATLAB联合仿真,对这两种方法进行主动控制数值仿真. 用MATLAB的xPC实时控制,进行了主动板的振动控制实验,验证了采用上述控制仿真方法的正确性. 各种结果表明用压电结构进行振动主动控制效果明显.     

具有随机路径的振动传递路径系统的随机响应分析

基于一般概率摄动有限元法,解决了具有随机路径的振动传递路径系统的响应分析问题.应用Kronecker代数,矩阵微分理论,向量值和矩阵值函数的二阶矩技术,矩阵摄动理论和概率统计方法,提出了振动传递路径系统的随机响应分析方法,在考虑工程中的不确定因素以后,在时域内清晰地描述了振动传递路径的随机响应.     

DEPENDENCE OF DAMPING CHARACTERISTICS OF A BEAM WITH DAMPING RUBBER MAGNETIC POWDER ON RUBBER PROPERTY

A cantilever beam with Damping Material Applying Rubber Magnetic Powder （DRM） has been investigated. Two methods are selected to hold DRM to a vibrating steel beam, one is to attach DRM by the magnetic attractive force （called DRM beam） and the other by adhesive bonding （called AB-DRM beam）. Different from the damping property of AB-DRM beam caused by shear deformation of damping material, the damping property of DRM beam is characterized by the sliding frictional loss together with the internal loss of damping material. The authors established a formulation to predict the damping characteristics of DRM beam, which was validated experimentally. It is found that rubber material loss factor β has a decisive influence on damping improvement of DRM beam versus AB-DRM beam. If β is smaller than the critical value around 0.8255, a valid range of vibratory amplitude always exists in which DRM beam can achieve better damping than AB-DRM beam; conversely, if β is bigger than the critical value, the valid range does not exist when slide occurs. Such results are used to determine the merits and limitations of DRM and develop design guidelines.     

Application of nonsmooth transformations to analyze a vibroimpact duffing system

The forced vibrations of an impact Duffing oscillator with one degree of freedom are studied using Zhuravlev's nonsmooth transformation and the multiple-scales method. Detailed consideration is given to the forced vibrations in the domain of resonance family. The stability and bifurcations of periodic vibrations are analyzed Translated from Prikladnaya Mekhanika, Vol. 44, No. 10, pp. 114–121, October 2008.     

PARALLEL FINITE ELEMENT ANALYSIS OF HIGH FREQUENCY VIBRATIONS OF QUARTZ CRYSTAL RESONATORS ON LINUX CLUSTER

Quartz crystal resonators are typical piezoelectric acoustic wave devices for frequency control applications with mechanical vibration frequency at the radio-frequency （RF） range. Precise analyses of the vibration and deformation are generally required in the resonator design and improvement process. The considerations include the presence of electrodes, mountings, bias fields such as temperature, initial stresses, and acceleration. Naturally, the finite element method is the only effective tool for such a coupled problem with multi-physics nature. The main challenge is the extremely large size of resulted linear equations. For this reason, we have been employing the Mindlin plate equations to reduce the computational difficulty. In addition, we have to utilize the parallel computing techniques on Linux clusters, which are widely available for academic and industrial applications nowadays, to improve the computing efficiency. The general principle of our research is to use open source software components and public domain technology to reduce cost for developers and users on a Linux cluster. We start with a mesh generator specifically for quartz crystal resonators of rectangular and circular types, and the Mindlin plate equations are implemented for the finite element analysis. Computing techniques like parallel processing, sparse matrix handling, and the latest eigenvalue extraction package are integrated into the program. It is clear from our computation that the combination of these algorithms and methods on a cluster can meet the memory requirement and reduce computing time significantly.     

ELECTRICALLY FORCED THICKNESS-SHEAR VIBRATIONS OF QUARTZ PLATE WITH NONLINEAR COUPLING TO EXTENSION

We study electrically forced nonlinear thickness-shear vibrations of a quartz plate resonator with relatively large amplitude. It is shown that thickness-shear is nonlinearly coupled to extension due to the well-known Poynting effect in nonlinear elasticity. This coupling is relatively strong when the resonant frequency of the extensional mode is about twice the resonant frequency of the thickness-shear mode. This happens when the plate length/thickness ratio assumes certain values. With this nonlinear coupling, the thickness-shear motion is no longer sinusoidal. Coupling to extension also affects energy trapping which is related to device mounting. When damping is 0.01, nonlinear coupling causes a frequency shift of the order of 10^-6 which is not insignificant,and an amplitude change of the order of 10^-8. The effects are expected to be stronger under real damping of 10^-5 or larger. To avoid nonlinear coupling to extension, certain values of the aspect ratio of the plate should be avoided.     

The destabilization paradox applied to friction-induced vibrations in an aircraft braking system

Mechanisms of friction are known as an important source of vibrations in a large variety of engineering systems, where the emergence of oscillations is noisy and can cause severe damage to the system. The reduction or elimination of these vibrations is then an industrial issue that requires the attention of engineers and researchers together. Friction-induced vibrations have been the matter of several investigations, considering experimental, analytical, and numerical approaches. An aircraft braking system is a complex engineering system prone to friction-induced vibrations, and is the subject herein. By considering experimental observations and by evaluating the mechanisms of friction involved, a complete nonlinear model is built. The nonlinear contact between the rotors and the stators is considered. The stability analysis is performed by determining the eigenvalues of the linearized system at the equilibrium point. Parametric studies are conducted in order to evaluate the effects of various system parameters on stability. Special attention will be given to the understanding the role of damping and the associated destabilization paradox in mode-coupling instabilities.