周界固定带裂纹薄圆板的振动基频

在将裂纹板挠度表示为正交多项式的基础上，用分区技术的瑞利一里兹方法求解了含不同长度径向裂纹和弧向裂纹的周界固定圆板的振动基频。实验上用小球撞击法测定了裂纹圆板的辐射声场频谱，并得出了谱的基频。此外用有限元法对裂纹板作了理论计算。三项结果基本符合。探究了裂纹长度对圆板基频的影响规律。     

裂纹及水介质对薄圆板振动辐射声场特性的影响

在有限元模态分析的基础上,提取了含人工裂纹的薄板各单元的相关参数,并将瑞利积分离散化,进而计算了裂纹薄板辐射声场的轴向声压分布和r=0．5 m球面上声场分布。结果表明,径向裂纹不仅使模态裂解为关于裂纹的对称模态和反对称模态,而且使声场分布有显著的变化。方法的有效性通过完整圆板辐射声场来验证。该方法可用于求解任意形状穿透裂纹薄板辐射声场的计算。还提出了一种简便计算置于无限大障板上的裂纹薄板水中振动频率以及辐射效率的计算方法。在假定薄板作小振幅振动、水中模态挠度近似为真空模态挠度的条件下,利用瑞利积分得到了因流体压而引起的附加质量密度。进而应用瑞利方法得到了薄板水中振动频率与真空中振动频率、无量纲附加虚质量增量之间的关系。在真空中模态的有限元方法分析数据以及采用适当方法处理奇点积分的基础上,应用离散积分计算了无量纲附加虚质量增量的值。从真空中模态特征频率出发用迭代法直到水中频率收敛为止而得到水中薄板的特征频率,进而计算了薄板的模态辐射效率。方法的有效性通过薄板的无量纲附加虚质量增量与Kwak的结果对比的一致性来验证。     

利用声辐射模态对声场进行重构

声辐射模态是定义在振动表面上的一组互相独立的基函数,描绘了振动表面的多极子辐射模式。本文利用声辐射模态对平板辐射的声场进行重构，并同时就频率和模态数对误差的影响进行了分析。针对复杂振动表面幅射的声场，重构时需正则化处理。数值计算结果和对应的理论值达到很好的吻合。     

非对称阻抗插入管消声器的Chebyshev-变分法建模与求解

针对非对称阻抗插入管消声器三维理论建模与求解问题,提出了一种半解析变分建模和求解方法,试验及有限元结果验证了理论模型和求解结果的正确性,开展了模态频率、声压响应及传递损失等声场特性的预测分析。首先构建插入管消声器内部子声场拉格朗日泛函,基于声压与质点振速连续性条件,得到插入管消声器三维理论模型。随后,将子声场声压展开为切比雪夫-傅里叶级数组合形式,按里兹法求得消声器三维声场模态信息。搭建了消声器传递损失试验平台,进行了刚性壁面和阻抗壁面消声器传递损失测试试验,对理论模型和计算结果进行了验证。通过算例分析了壁面阻抗的大小、阻抗面积和分布形式以及插入管偏置对消声器消声性能的影响。结果表明,提出的变分建模求解方法是有效的,对消声器壁面阻抗位置和形式的合理设置可有效降低输出声压。      

用有限元/边界元方法进行结构声辐射的模态分析

采用有限元方法和边界元方法建立了轻流体介质中复杂结构振动声辐射的模态分析模型,可计算结构的模态辐射效率、场点声压、结构辐射声功率和辐射效率等声场特性参数．文中以板和加筋板结构的振动声辐射为例进行了模态分析,并与用远场 Ｒａｙｌｅｉｇｈ积分计算所得结果进行了比较．研究了激励力作用位置对板结构声辐射的影响和加筋板与板的模态辐射效率特点,并指出板加筋后会改变板的模态辐射效率规律．     

声场重构的声辐射模态阶数分析

利用声辐射模态法对椭球状声源辐射声场进行重构,分析了模态阶数对相对误差的影响,以及模态阶数与频率的关系;同时深入探讨了声源形状变化对模态阶数选取的影响。研究发现利用较少的模态阶数即可得到很好的重构效果,且声源形状的变化对重构所需模态阶数的影响较小,因此可将该方法用于任意形状声源的重构,体现了此方法在声场重构中的优越性。     

非规则封闭空间声场建模的Chebyshev-变分法及其固有声学特性分析

针对非规则封闭空间声场建模问题,提出了一种基于Chebyshev-变分原理的声场建模方法。该方法首先选取包络非规则声场的矩形空间并将此矩形空间内的声压函数展开成三重Chebyshev级数形式,然后通过坐标变换得到定义域空间中的声场势能和声场动能,最后按照里茨方法对声场的拉格朗日泛函进行求解,得到声场的特征方程并求得声场固有频率和模态。通过与曲面声场的数值结果对比,验证了本建模方法的正确性和有效性。在此基础上研究具有不同倾角的梯形声场固有特性,分析内部凹槽深度对"凹"型声场频率和模态的影响。结果表明,梯形声场模态会随着倾角增大而逐步演变;"凹"型声场低阶频率随凹槽深度的增加而逐渐减小,但第一阶频率却呈现先减小后增大的特点。      

利用源强密度声辐射模态重建声场

为了利用声场中少量测点声压数据精确重建复杂结构的辐射声场,提出了源强密度声辐射模态分析理论和声场重建公式.在结构表面定义的空间上,利用以源强密度分布函数为参量的结构辐射声功率泛函表达式定义了一个线性自伴正辐射算子,该算子的特征函数为结构的源强密度声辐射模态.然后通过对矩形平板和带有半球帽的圆柱体的源强密度声辐射模态的分析,证明了源强密度声辐射模态具有空间滤波特性,并利用该性质建立了声场重建公式.球体仿真和平板实验验证了所提出的声场重建方法的可行性和稳健性.基于源强密度声辐射模态的声场重建方法简单,利用较少测点数据就可以获得较高的声场重建精度,特别适合于复杂结构的低频声场重建.     

螺旋型电磁超声辐射声场对缺陷检测影响的 计算机模拟*

电磁超声(EMAT)作为一种非接触超声检测技术，已得到了普遍的关注和研究。然而，EMAT目前只得到了一些有限的应用，尤其在缺陷探伤应用方面还不能替代压电超声，深入探究其原因并加以改进，对推动EMAT在缺陷检测方面的应用具有重要意义。利用有限元方法建立了螺旋型EMAT模型，分析了其辐射声场和声场特征；通过将有限元计算所得到的洛伦兹力分布简化为门函数，并结合格林函数法，得到了螺旋型EMAT辐射声场的简化解析结果。这些方法可用于计算螺旋型EMAT辐射声场指向性以及在缺陷检测中比较关心的一些特征参数，如扩散角、偏离角等参数。通过螺旋型EMAT辐射声场实验，验证了理论分析结果。通过与压电超声检测理论与实验的对比，研究认为：螺旋型EMAT辐射声场的具有横波和纵波等多种波模及多种模态转换的特点，以及相对复杂的异型声场几何分布等复杂特性，使其在缺陷检测应用方面受到局限。这些研究方法对改进EMAT设计，优化控制EMAT辐射声场，拓展EMAT在缺陷检测方面的应用具有参考价值。     

基于声辐射模态讨论声能量辐射与传递

声辐射模态表示了振动声源表面的辐射模式。基于声辐射模态讨论了振动声源表面声能量辐射和声场中声能量传递的性质,给出声能量辐射和传递的模式。采用表面声强描述振动声源表面的声能量辐射,采用声强描述声能量在声场中的传递。表面声强和声强可分解成两部分,一部分将辐射的声能量传递到远场;另一部分表现为振动声源与声场之间的能量交换。针对矩形板分析了声能量辐射和传递,数值计算结果与理论结果一致。结果表明基于声辐射模态讨论声能量辐射与传递是可行的和有效的。     

Vibrations of a polygonal plate having orthogonal straight edges by an extended rayleigh-ritz method

An extended Rayleigh-Ritz method is presented for solving vibration problems of a polygonal plate having orthogonal straight edges. The polygonal plate is considered as an assemblage of several rectangular plates. For each element rectangular plate, the transverse displacement is approximated by interpolation functions corresponding to unknown displacements and slopes at the discrete points which are chosen along the edges, and series of trial functions which satisfy homogeneous artificial boundary conditions. By minimizing the energy functional corresponding to the assumed displacement function, the dynamic stiffness matrix of the element rectangular plate, which is similar to that obtained in the finite element method, is derived. The dynamic stiffness matrix of the whole system is obtained by summing up those of the element rectangular plates. Numerical results are presented for the natural frequencies and mode shapes of cantilever L-shaped and T-shaped plates.     

Analysis of structural - acoustic coupling of elastic rectangular enclosure with arbitrary boundary conditions

The structural acoustic coupling characteristics of a rectangular enclosure con- sisting of two elastic supported flexible plates and four rigid plates are analyzed.A general formulation considering the full coupling between the plates and cavity is developed by using Hamiltonian function and Rayleigh-Ritz method.By means of continuous distributions of ar- tificial springs along boundary of flexible plates,a wide variety of boundary conditions and structure joint conditions are considered.To demonstrate the validity of the analytical model, the responses of sound pressure in the cavity and plate velocity are worked out.The analytical results coincides well with Kim's experimental results.The result is satisfactory.Finally,an- alytical results on the structure vibration and the sound field inside the cavity are presented. These results indicate that the coupling of the combined structure is relatively weak,so the internal cavity sound is controlled by plate directly excited,and the translational stiffness affects the sound more than the rotational stiffness does.     

Transient vibration analysis of a completely free plate using modes obtained by Gorman's superposition method

This paper shows that the transient response of a plate undergoing flexural vibration can be calculated accurately and efficiently using the natural frequencies and modes obtained from the superposition method. The response of a completely free plate is used to demonstrate this. The case considered is one where all supports of a simply supported thin rectangular plate under self weight are suddenly removed. The resulting motion consists of a combination of the natural modes of a completely free plate. The modal superposition method is used for determining the transient response, and the natural frequencies and mode shapes of the plates used are obtained by Gorman's superposition method. These are compared with corresponding results based on the modes using the Rayleigh-Ritz method using the ordinary and degenerated free-free beam functions. There is an excellent agreement between the results from both approaches but the superposition method has shown faster convergence and the results may serve as benchmarks for the transient response of completely free plates.     

Natural frequencies of a pre-twisted blade in a centrifugal force field

In this paper, starting with the thin shell theory, the governing partial differential equation of motion for the transverse deflection of a rotating pre-twisted plate is derived. Strain-displacement relationships include the effect of warping of the cross-section due to twist-bend coupling effect introduced as a result of pre-twist in the plate of non-circular (rectangular) cross-section. Then the equation of motion, thus derived, is used to formulate the free vibration of a typical turbo-machinery cantilevered airfoil blade by considering it as a plate of an equivalent rectangular cross-section subjected to a quasi-static load due to centrifugal force field. The analytical derivation considers both the stress-stiffening as well as stress-softening effects of the centrifugal forces on the spinning airfoil. The partial differential equation governing the flexural motion of the plate is transformed into a matrix-eigenvalue form using a Rayleigh-Ritz technique. The plate deformations are represented by a set of ‘admissible’ sinusoidal trial functions, which fully satisfy all the clamped-end constrains as well as the free-edge boundary conditions. The results of the analytical model exhibit an excellent agreement with the previously published test data both for thin and thick plate geometries and even in highly twisted configurations. The results of the eigenvalue solution are presented in a non-dimensional form for plates of varying aspect ratios and different amounts of pre-twist in the plate. The numerical results are directly applicable in determining the static and running frequencies of typical blades used in turbo-machinery.     

A unified approach for predicting sound radiation from baffled rectangular plates with arbitrary boundary conditions

This paper discusses sound radiation from a baffled rectangular plate with each of its edges arbitrarily supported in the form of elastic restraints. The plate displacement function is universally expressed as a 2-D Fourier cosine series supplemented by several 1-D series. The unknown Fourier expansion coefficients are then determined by using the Rayleigh-Ritz procedure. Once the vibration field is solved, the displacement function is further simplified to a single standard 2-D Fourier cosine series in the subsequent acoustic analysis. Thus, the sound radiation from a rectangular plate can always be obtained from the radiation resistance matrix for an invariant set of cosine functions, regardless of its actual dimensions and boundary conditions. Further, this radiation resistance matrix, unlike the traditional ones for modal functions, only needs to be calculated once for all plates with the same aspect ratio. In order to determine the radiation resistance matrix effectively, an analytical formula is derived in the form of a power series of the non-dimensional acoustic wavenumber; the formula is mathematically valid and accurate for any wavenumber. Several numerical examples are presented to validate the formulations and show the effect of the boundary conditions on the radiation behavior of planar sources.     

Minimum stiffness location of point support for control of fundamental natural frequency of rectangular plate by Rayleigh-Ritz method

The Rayleigh-Ritz method is employed to determine the minimum stiffness location of the elastic point support for raising the fundamental natural frequency of a rectangular plate to the second frequency of the unsupported plate, which usually is the upper limit of the first frequency for a single support. Based on the optimal design of the support position, the minimum stiffness can be obtained numerically by solving a characteristic eigenvalue sub-problem. In the Rayleigh-Ritz procedure the boundary characteristic orthogonal polynomials are used for the admissible functions. Several typical examples of plate structures with the additional point supports are analyzed in detail, and the results prove that the proposed method is very effective in the solution to the optimal design of the supports. It will be shown that elastic supports can be designed like rigid ones for the purpose of increasing the fundamental natural frequency of a rectangular plate.     

Rayleigh-Ritz vibration analysis of rectangular Mindlin plates subjected to membrane stresses

A previously developed analysis of the flexural vibration of isotropic rectangular plates is extended to include the presence of a membrane stress system. The method of analysis is the Rayleigh-Ritz method and Mindlin plate theory is used which takes into account effects which are disregarded in the classical plate theory. As in the aforementioned earlier analysis the spatial variations of the deflection and two rotations over the plate middle surface are based on the use of Timoshenko beam functions. The membrane stress system comprises biaxial direct stress plus in-plane shearing stress and is uniform throughout the plate. Numerical results are presented for a number of types of plate and of applied stress which show the manner of variation of the frequencies of vibration as the intensity of stress changes. This manner of variation is similar in form to that demonstrated elsewhere by analyses based on the use of the classical plate theory but the magnitudes of the present calculated frequencies are considerably reduced for moderately thick plates.     

Sound transmission loss of metamaterial-based thin plates with multiple subwavelength arrays of attached resonators

This paper is concerned with sound transmission loss of metamaterial-based thin plates consisting of multiple subwavelength arrays of spring–mass resonators attached to an unbounded homogenous thin plate. Two analytical wave approaches are developed for the calculation of diffuse field sound transmission loss of such metamaterial-based thin plates. Numerical results show that a metamaterial-based plate can result in much higher sound transmission loss than a bare plate (with the same surface mass density) at frequencies within the mass-law region and the coincidence region. It is also demonstrated that by using an extremely thin plate to form a metanaterial-based plate, the construction can be implemented as a potential sound insulation material with good performance at low frequencies.     

传递矩阵法预报时空随机激励下任意薄壳腔体内部噪声

利用结构有限元结合声有限元及边界元方法,建立了任意薄壳腔体弹性壳板振动与内外声场的耦合模型,并计算了激励力与壳板振动和内部声场之间的传递矩阵;湍流边界层脉动压力具有时空随机面激励特性,引入整体形状函数矩阵,进一步推导弹性壳板广义节点力功率谱密度函数矩阵与随机面分布激励力功率谱密度函数的关系,再利用声振耦合传递矩阵,得到弹性壳板振动和内部声场功率谱密度函数与广义节点力功率谱密度函数矩阵的关系,形成随机分布激励下任意薄壳腔体结构振动及内部声场的计算方法。以典型的内外均有声介质且一面为弹性矩形板的矩形腔声振耦合模型为例,计算了弹性壳板振动和内部声场功率谱密度函数,并与解析方法进行了比较,两者基本吻合,偏差分别为1 dB和2 dB左右。传递矩阵法不受腔体结构及其内部区域形状的制约,具有良好的适用性。