矩形面导纳的理论计算与分析

研究面导纳在结构之间接触表面上振动能量传递时的特性，并利用复功率方法和振强的概念推导出无限大薄板的矩形而导纳在均布力作用下的解析表达式，为分析结构间接触表面上能量传递提供了理论工具．根据理论计算结果，研究并描述了接触面积的大小、边长和矩形面积的长宽比等参数对能量传递的影响，为研究隔振问题提供了有效的理论依据和方法．     

均布速度激励下矩形接触表面上力的分布与能量传递

研究无限大板受均布速度激励的矩形接触表面上的力的分布形式和振动能量传递的特性。利用离散的数学模型推导出了均布速度激励下力的计算方法,并计算了接触面积上力的分布。还研究了接触面积内各点及整个接触面积的能量传递特性以及激励频率和接触面积尺寸对其的影响。对如何减小结构之间振动能量的传递、提高隔振效果提出了相应的对策。     

无限大板上矩形面导纳的测量

研究在实验条件下测量均布速度激励下无限大板面导纳的方法．实验中利用有限板模拟无限大板，用具有矩形接触面积的刚性棱形锥产生均匀速度的激励，并建立消除附加质量影响的测量方法。实验结果与理论预测值一致，证明了实验模型与方法的可行。     

加筋板结构声导纳的面接触判据

通过采用有限元方法建立加筋板模型,计算不同边界条件下具有不同加筋形式的薄板在不同加载面尺寸下的导纳差值,进而得到与频率相关的加筋板面接触判据,揭示了加筋板面导纳和点导纳之间的相关关系,得到了“点”和“面”是否能够等效处理的面接触判据。进一步通过考察薄板的不同加筋形式和加载面形状以及加筋板的速度分布,可以发现:在不加筋、单加筋和十字加筋3种情况中不加筋平板的面接触判据最严格,而十字加筋板的面接触判据最宽松;单加筋板的速度差值与导纳差值的计算结果较为吻合;单加筋板的加载面沿垂直加筋方向的边长越长导纳差值越大。      

采用微分求积法分析薄板的气动弹性响应

为减轻结构重量，新一代飞行器的结构设计中更多地采用了薄壁结构，在超音速或超高音速飞行条件下，薄板的气动弹性响应相当剧烈。分析薄板的气动弹性响应方法主要有两类：第一类为经典的伽辽金方法；第二类为有限元方法。受薄板形状和边界条件的限制，伽辽金方法能够研究的问题是非常有限的，有限元方法虽然具有普适性，但本质上属于数值方法，其计算精度和收敛性必将受所选单元类型以及数值计算误差的影响。在薄板的气动弹性分析领域，文中采用一种全新的方法，即微分求积方法。     

非保守耦合系统的耦合损耗因子

研究利用子结构的导纳计算非保守耦合系统的耦合损耗因子的方法。首先,利用经典保守耦合系统统计能量分析能量平衡方程的形式,推导了非保守耦合系统中耦合损耗因子与结构振动能量比的关系;然后,给出了利用子结构的导纳计算结构振动能量比的方法;最后,实验测量了非保守耦合系统的耦会损耗因子,并与理论预测值比较。结果表明,理论预测和实验测量结果的一致性很好。     

复杂结构随机振动试验的响应控制再现

为了实现振动环境仿真系统中的振动响应的实时反馈，采用有限元计算获得激励响应。分析软件及计算方法的选取得当，是激励实时反馈环节实现的关键。在众多的实模态分析中，有两个算法很具代表性，它们是子空间迭代法和Lanczos算法。子空间迭代法广为使用，许多大型程序中都有配备，它稳定、可靠，然而速度较慢。Lanczos算法则被公认为快速高效，是求解大型矩阵特征值问题的一种最有效的方法，其计算量比子空间迭代法少数倍之多，特别适用于大型特征值求解问题，而且计算精度也很高，是现有模态计算方法最可取的。     

有效线导纳的仿真研究

利用有效导纳复功率流法研究了无限平板线激励下的功率传递规律,得出了线激励下的有效线导纳的理论公式,并对有效线导纳的功率传递特性进行了仿真研究。比较了有效线导纳理论公式和数值估计公式的计算结果,得到了数值估计公式的适用范围。然后研究了梁线激励作用下的功率传递特,并且对平板和梁上的功率传递规律进行了比较,结果为平板线激励的相对传递功率要略大于梁的相对传递功率。表明有效线导纳的理论公式在研究结构的功率传递上的灵活性和适用性。     

基于裸光纤探头的双点光子多普勒测速系统

全光纤光子多普勒速度测量(PDV)系统是一种新型的激光测速系统,可广泛用于冲击波、爆轰波以及其他短时高速运动物体的速度测量。多点测量可以获得靶面不同位置的速度,以测量靶面的形变。为提高测量的空间分辨率,提出使用裸光纤束为PDV系统的探头,并在实验上实现了空间分辨率为375μm的双点速度测量。裸光纤探头的间距较小,一个探头的测量结果可能受到另一个探头反射光的干扰。理论和实验的研究结果表明,当靶面各点速度相同时,测量结果不受干扰光的影响;当各点速度不同时,其测速误差不但与两被测点的速度差有关,还与传感光和干扰光的光强和相位有关。     

载流弹性薄板结构吸声性能的研究

对弹性薄板吸声结构在水下的吸声性能进行了研究,推导了载流弹性薄板结构声阻抗的解析解。提出并计算了薄板结构的势能因子B_(nm)、动能因子A_(nm)和载流因子系数χ。得出薄板结构吸声性能严格的解析理论和幂级数近似表达式,本文获得的结果使薄板理论的吸声机理更加清晰,计算也更加简化。通过低频水声管对薄板结构进行了测试,测试结果和理论计算结果吻合得较好,验证了本文理论的正确性。     

Investigation of area mobility of a finite thin plate subject to a uniform velocity excitation

Methods for theoretically calculating area mobility of a finite thin plate are derived for a typical excitation pattern,uniform velocity excitation,over a contact area.In the derivation,the contact area is discretised into sub-regions and the excitation and response continuously distributed over these sub-regions are simplified as acting at the centers of the sub-regions.Therefore,according to the concept of effective point mobility,the theoretical formula for area mobility of a finite thin plate subject to a uniform velocity excitation is obtained.According to the relation between complex power and area mobility,the measurement method of a finite plate is also obtained by means of transfer point mobility.When comparing results generated by theoretical calculation to patterns measured in experiment,consistent patterns are found,suggesting that the proposed methods are practical.The results of calculation show that the accuracy of theoretical calculation increases with the number of sub-regions and is influenced by the moment caused by the experiment device,especially when the excitation frequency is high.     

VIBRATION POWER TRANSMISSION OVER A RECTANGULAR AREA OF AN INFINITE PLATE SUBJECT TO UNIFORM CONPHASE VELOCITY EXCITATION

In the study of vibration isolation, mobility is normally used to reflect the characteristics of power transmission over the contact region between the exciting machine and its supporting structure. However, recent investigations indicated that power transmission is influenced by the dimensions and shape of the contact region and the use of classical point mobility can lead to significant errors. The surface mobility of an infinite plate over a rectangular contact region subject to a uniform conphase velocity excitation has been derived using the effective point mobility concept for various aspect ratios of the contact region. Results show that power transmission is distributed in a ring-like manner, with the transmission in the central region and along the edges of the contact area being rather small. As the width-based Helmholtz number kw/2 increases, the ring-like region expands outward but less power is transmitted. The surface mobility decreases rapidly as Helmholtz number increases. For the same Helomholtz number, the surface mobility decreases as the aspect ratio of the contact region increases and for the same contact area, it is virtually independent of the shape of the contact region for aspect ratio less than 2 or at large Helmholtz numbers (greater than 4). Experimental measurements of a simulated infinite plate confirm the theoretical calculations. Unlike uniform conphase force excitation, the surface mobility due to uniform conphase velocity distribution does not oscillate with Helmholtz number.     

Energy transmission in finite coupled plates,part II: Application to an L shaped structure

The method presented in the first of these two companion papers is applied to the case of two thin plates coupled in an L shape. Numerical calculations yield values of the vibrational energies of each plate. The influences of damping, thickness and area of the plates and of the excitation type are presented and discussed. The theoretical results are compared with results from a computerized experiment, in which special attention was given to the number and position of point velocity measurements.     

轨道板中超声兰姆波传播的有限元计算和实验*

该文针对我国高速铁路轨道板缺陷的非接触动态检测问题,研究了空气耦合超声兰姆波在轨道板中的传播规律。首先,给出了轨道板中超声兰姆波的相速度和群速度频散曲线,结果表明:随着频厚积的增加,频散现象越明显,并且A0相速度收敛于Rayleigh波的波速。然后,建立轨道板中波传播的有限元模型,计算得到兰姆波传播的群速度为2220 m/s,且二维傅里叶变换系数的较大值沿Rayleigh波的频散曲线分布。最后,在沪杭高铁嘉兴南站进行了现场测试,以8.8°倾斜角向轨道板激励产生超声兰姆波,激发产生的兰姆波模态群速度为2325 m/s,且二维傅里叶变换分析其系数的较大值沿Rayleigh波的频散曲线分布。有限元计算结果和实验结果均与理论计算结果一致。该研究为后续轨道板缺陷的非接触动态检测提供了理论依据和实验方法。     

THE ENERGY MOBILITY

The energy mobility method is presented and applied both numerically and experimentally to thin plates of high modal density. The energy mobility is defined as the ratio of the frequency averaged quadratic velocity at one point of a structure to the frequency averaged active power injected at one point of the structure. It can be calculated using only classic input and transfer mobilities. The property of energy additivity of the contributions of several external loads is shown to be a good approximation in the case of a single structure. To quantify the approximations on typical structures one is interested in, numerical simulations are presented on plates. A good agreement is found between the predictions using the energy mobility and the exact calculations. An experiment conducted on a plate with a real excitation confirms that the prediction of the energy mobility approach can be quite satisfactory. Finally, a remarkable property for the energy mobility (contrary to standard mobility) is noted: the insensitivity to the presence of a mass heterogeneity at driving points. This property allows one to simplify considerably the characterization of industrial structures that have in general a lot of heterogeneities. The energy mobility concept is further applied to the vibrational behaviour of an assembly. For each subsystem the connection is described by adding injected power and coupling power into the energy additivity. The equality of the frequency averaged quadratic velocity and the power flow balance at each coupling point allows one to calculate the coupling power at connection points with energy mobilities of uncoupled subsystems. A system of two plates has been used to compare the energy mobility calculation and the exact one given by the classic mobility method. The comparison shows that a connectivity factor must be introduced to keep the same formalism generally used with classic mobilities. A generalized definition for the energy mobility is then established.     

Sound radiation from a thin infinite plate in contact with a layered inhomogeneous fluid

In this paper the sound radiation from a thin infinite plate in contact with a layered inhomogeneous fluid subjected to single point excitation is studied. Sources contributing to the inhomogeneity are discussed, and the fluid is analytically expressed as a layered inhomogeneous field. Using Hankel transform, the equations governing the fluid-structure interaction are solved. The asymptotic form of the radiation pressure at far field is obtained using the method of stationary phase. Numerical examples show that the sound radiation patterns from a plate in contact with an inhomogeneous fluid is much more complicated than that in a homogeneous fluid. Three different radiation patterns (bell, disc, and their combination) were observed in the numerical examples, and the radiation patterns are sensitive to the field parameters. Depending on frequency, the sound pressure at far field is either magnified or reduced compared with that in a homogeneous fluid. And beyond some frequency the sound pressures are almost zero.     

An approximation for the point mobility at the intersection of two perpendicular plates

The problem of point excitation at a T-intersection of two perpendicular plates is studied in order to establish expressions for the point mobility. It is found that the theory for point excitation of the free surface of a semi-infinite elastic solid is applicable in the frequency range associated with structure-borne sound transmission. From this theory the mobility for an infinite system is derived. Based on this model and on an experimental investigation an estimation procedure for the point mobility in the finite dimension case is developed. The agreement with measurements performed in situ is quite acceptable. Both the theoretical and the experimental investigations reveal that the real part of this mobility is small, although it is larger in the experimental results. This indicates that other components of excitation are difficult to eliminate and may contribute to the power input in practice. Because of the small real part of the mobility it is advantageous with respect to the reduction of structure-borne sound power transmission to locate the contact points between a source and the receiver at such intersections. Corrections are deduced for the measured magnitude of the mobility for the case when separate force and motion transducers are used.     

Waves propagating along a periodic set of point inhomogeneities in a thin elastic plate

Waves localized along a periodic set of point inhomogeneities in a thin elastic plate are studied. The cases of point masses and the cases of small-radius holes in an isolated plate and in a plate that is in contact with an acoustic medium are considered. The holes are modeled with the use of generalized point models.