A stabilization procedure for the quadrilateral plate element with one-point quadrature

A stabilization procedure is developed for controlling the kinematic modes of the four-node, bilinear quadrilateral element when single-point quadrature is used. These kinematic modes manifest themselves by spatial oscillations or singularity of the total stiffness. In this stabilization procedure, additional generalized strains are defined which are activated by the kinematic modes; these generalized modes are furthermore not activated by rigid body motions regardless of the shape of the quadrilateral. By using a scaling law developed in an earlier paper, the stabilization parameters are defined so they do not adversely affect the element's performance. Several problems which are subject to kinematic modes are presented to illustrate the performance of this stabilization procedure for linear problems.     

Acoustic wave propagation in piezoelectric fibers of hexagonalcrystal symmetry

An exact analysis is presented for acoustic wave propagation in cladded acoustic fibers having a core and an infinite thick cladding both made of piezoelectric hexagonal crystal of 6 mm point group symmetry. The crystalline Z axes of both the core and cladding coincide with the fiber axis. A general dispersion equation is derived for all the acoustic modes propagating along the fiber axis. Two simpler and independent equations which represent the dispersion relations of torsional and radial-axial modes can be separated from the general dispersion equation. It has been found that the radial-axial and general flexural modes are piezoelectrically active while the torsional modes are not. Approximate dispersion relations for pure guided modes in weakly guiding weakly piezoelectric fibers which are much simpler than the exact ones are also given. Numerical results are only presented for pure guided modes. Exact and approximate dispersion curves of several lower order pure guided flexural, radial-axial and torsional modes in a weakly guiding ZnS fiber are compared and they are in good agreement     

对声辐射模态的讨论

提出利用声辐射模态结合结构模态研究声辐射问题,并且从物理和数学意义上对声辐射模型进行了解释。用声辐射模态研究外部声辐射的主要优点在于消除了结构模态中复杂的耦合项。本文以简支矩形板为例,通过瑞利积分公式计算了其在不同频率下的辐射效率,并比较了在结构模态下和声辐射模态下辐射效率的区别。     

Analytical expressions for optimum alignment modes of highly segmented mirrors

The major sources causing deterioration of optical quality in extremely large optical telescopes are misadjustments of the mirrors, deformations of monolithic mirrors and misalignments of segments in segmented mirrors. For active optics corrections, all three errors, which can partially compensate each other, are measured simultaneously. It is therefore of interest to understand the similarities and differences between the three corresponding types of modes which describe these errors. The first two types are best represented by Zernike polynomials and elastic modes respectively, both of them being continuous and smooth functions. The segment misalignment modes, which are derived by singular value decomposition, are by their nature not smooth and in general discontinuous. However, for mirrors with a large number of segments, the lowest modes become effectively both smooth and continuous. This paper derives analytical expressions for these modes, using differential operators and their adjoints, for the limit case of infinitesimally small segments. For segmented mirrors with approximately 1000 segments, it is shown that these modes agree well with the corresponding lowest singular value decomposition modes. Furthermore, the analytical expressions reveal the nature of the segment misalignment modes and allow for a detailed comparison with the elastic modes of monolithic mirrors. Some mathematical features emerge as identical in the two cases.     

产品全成本集成优化和生产模式的选择

主要对机械产品的材料成本和制造成本进行了集成优化,对面向大批量定制的产品全成本集成优化数学模型进行了研究,为企业选择合适的生产模式提供了一种新的方法.     

Influence of material parameters on acoustic wave propagation modes in ZnO/Si bi-layered structures

The influences of material properties on acoustic wave propagation modes in ZnO/Si bi-layered structures are studied. The transfer matrix method is used to calculate dispersion relations, wave field distributions, and electromechanical coupling coefficients of acoustic wave propagation modes in ZnO/Si bi-layered systems, in which the thickness of the substrate is of the same order of magnitude as the wavelength of the propagating wave modes. The influences of the thin film parameters on the acoustic wave propagation modes and their electromechanical coupling coefficients of the wave modes also are obtained. In addition, some experimental results for characterizing the wave propagation modes and their frequencies have also been obtained, which agree well with the theoretical predictions.     

基于谱峭度的谐波模态检测方法

在旋转机械领域,周期激励的存在使运行模态分析中含有谐波模态。根据结构模态和谐波模态的谱峭度值的不同,该文提出了基于谱峭度的谐波模态辨识方法。首先,给出了谱峭度的定义及其无偏估计算法;其次,从理论上证明应用此方法不需要滤波处理,并提出了简单且易于实现的优化方法;然后,应用频域空间域分解算法分离出谐波模态去除其对结构模态的影响;最后,通过仿真及实验成功检测出了谐波模态并消除其影响,验证了方法的有效性和可靠性。     

结构声辐射有源控制中主导辐射模态的抵消及次级力的最优布放

在基于声辐射模态理论的结构声有源控制中，主导辐射模态的确定及抵消策略是至关重要的，它直接决定次级力源的优化布放及有源控制的效果。以往研究中对于主导辐射模态的认识是模糊而片面的，现对该问题进行了深入分析。首先基于辐射模态理论和振动模态的叠加性，结合辐射模态幅度和辐射效率，确定了结构在不同的激励频率（振动模态）下对应的主导辐射模态，然后在此基础上对次级力源进行了优化布放，最后用一系列的计算机仿真实例验证了理论结果的正确性。     

简支矩形板声辐射的有源控制

文章以简支平板为例 ,通过声辐射模态研究结构声辐射的有源控制。首先分析了声辐射模态的数学和物理意义。由于在中、低频时 ,声辐射模态对应的辐射效率随着模态阶数的增加而迅速降低。在此基础上 ,文中提出了一种新的控制策略 ,即抵消前k阶声辐射模态的伴随系数 ,使得前k阶声辐射模态的声功率为零。文中以压电陶瓷作动器作为控制力源进行了数值计算研究。并与传统的控制策略———声功率最小化策略进行了比较。     

Collective modes and spin waves in superfluid3He-B

Making use of a model Hamiltonian, which includes, besides the kinetic energy and the BCS-like pairing energy, the spin exchange energy as well as the dipolar interaction energy, we study theoretically the collective modes of the Balian - Werthamer state in the collisionless limit. In the absence of the dipolar interaction energy, the collective modes are classified according to their total angular momentumJ. Among 18 distinct modes, one mode withJ=0 and three modes withJ=1 are gapless. The latter modes couple with the spin fluctuation and are identified with spin wave modes. The effect of the dipolar interaction on these modes is discussed.Supported by the National Science Foundation.     

Nanoscale vibration characterization of multi-layered graphene sheets embedded in an elastic medium

Detailed studies on the nanoscale vibration characteristics of multi-layered graphene sheets (MLGSs) that are embedded in an elastic medium are carried out using continuum-based modelling and Generalized Differential Quadrature (GDQ) method. Natural frequencies and their associated vibration modes of practical interest of single-layered and triple-layered graphene sheets, as well as general MLGSs that are embedded in an elastic medium are established. Numerical simulations are conducted to examine the effects of van der Waals (vdW) interactions, which are present as bonding forces between the layers, on nanoscale vibration natural frequencies and their mode shapes. The results show that for a general MLGSs embedded in an elastic medium, vibration modes can in general be classified into three families - lower classical synchronized modes which are independent of van der Waals forces and are somewhat sensitive to the surrounding elastic medium, middle van der Waals enhanced modes which are largely determined by the presence of van der Waals interactions and are hence less sensitive to the changes of the surrounding elastic medium, and higher mixed modes which are combinations of classical synchronized modes and van der Waals enhanced modes. Detailed characterizations of these modes from their derived mode shapes have been achieved for the typical case of an embedded triple-layered GSs, as well as general embedded MLGSs. Effects of Winkler modulus K_W, the shear layer modulus G_b, different boundary conditions, aspect ratio β and the number L of graphene layers on nanoscale vibration properties have been examined in detail. The results presented in this paper, for the first time, provide accurate and wholesome studies and characterizations on the interesting nanoscale vibration properties of multi-layered graphene sheets embedded in an elastic medium and the results obtained will certainly be useful to those who are concerned with the dynamics of embedded graphene sheets which are increasingly being deployed for various innovative engineering applications such as nano-electro-mechanical systems (NEMS).     

行星传动系统的固有特性及模态跃迁研究

建立了单级2K-H直齿行星传动的纯扭转集中参数动力学模型。研究了行星传动的固有特性,归纳出两种振动模式:行星轮振动模式和扭转振动模式,并研究了两种振动模式下行星传动的振动特征。通过求解子特征值问题得到了解析形式的固有频率表达式,并推导了固有频率对构件的支承刚度、质量、转动惯量以及齿轮啮合刚度等参数的敏感度解析式。从模态能量角度深入分析了模态跃迁现象对传动特性的影响,并给出了此现象发生的判别准则。仿真算例证明了所得结论的正确性。     

Nonlinear torsional vibration of a circular cylindrical piezoelectric rod with relatively large shear deformation

We show that, in a circular cylindrical rod, torsional modes are coupling to extension when the shear deformation associated with the torsional modes is no longer infinitesimal. A set of a couple equations is derived with which the effect of extension on the torsional frequency is examined. The results are useful to the understanding and design of devices operating with torsional modes.     

Ion Concentration Effect on Nanoscale Electrospray Modes

The phenomena and mechanism of electrospray modes in nanoscale are investigated from experiments and molecular dynamics simulations. It is found that the ionic concentration plays a crucial role in determining the dripping or the jetting modes in a nanoscale electrospray system. Molecular dynamics simulations uncover that the two modes are caused by the competition between the electric field stress and surface tension, which is similar to the mechanism in a macroscale electrospray system. However, in a nanoscale electrospray system, the two competing forces of the electric field stress and surface tension are more sensitive to the ion distributions than that in a macroscale electrospray system, in which the applied voltage and pressure dominate. With the decrease of the nozzle diameter to nanoscale, the ions not only affect the local electric field stress, but also destroy the hydrogen bonds among water molecules, which lead to that the ion concentration becomes a dominant factor in determining the electrospray modes in nanoscale. The discovery provides a novel method to control nanoscale electrospray modes, which may find potential applications for mass spectrometry, film deposition, and electrohydrodynamic printing.     

Two-dimensional analysis of spurious modes in aluminum nitride film resonators

In this paper, a hybrid method, which combines the traditional concept of guided waves and the finite element method (FEM), is proposed to analyze the spurious modes of aluminum nitride (AIN) film with electrodes. First, the guided wave modes in the plated area are obtained by 1-D FEM. Second, a mode-match method is used to satisfy the boundary conditions. The vibration of the film resonator is a superposition of all of the guided modes. With respect to an A1N film resonator, which is a thickness-stretch mode resonator, we have identified three families of spurious modes: extension, thickness-stretch, and thickness-shear. The spectrum of spurious modes is calculated and the influence of the spurious modes is discussed.     

A uniform strain hexahedron and quadrilateral with orthogonal hourglass control

The treatment of zero energy modes which arise due to one-point integration of first-order isoparametric finite elements is addressed. A method for precisely isolating these modes for arbitrary geometry is developed. Two hourglass control schemes, viscous and elastic, are presented and examined. In addition, a convenient one-point integration scheme which analytically integrates the element volume and uniform strain modes is presented.     

Failure mode and effects analysis using function–motion–action decomposition method and integrated risk priority number for mechatronic products

Failure mode and effects analysis is a widely applied risk assessment method in various engineering and management domains. However, the identification of failure modes is difficult and uncountable. Therefore, a function–motion–action (FMA) decomposition method is developed to identify failure modes from the perspective of motion and extraordinarily suitable for mechatronic products. In the typical risk assessment, the ranking orders of failure modes are determined by risk priority number (RPN), which has been criticized for several drawbacks and improved by some alternative RPNs, but some drawbacks still exist, such as duplicate values, narrow admissible value range, and missing failure modes’ and risk factors’ weights. This study formulates several alternative weighted RPNs to overcome the above drawbacks, and the final ranking orders of failure modes are garnered through the integrated RPN (IRPN). First, failure modes are identified via the proposed FMA decomposition method and evaluated with crisp values, whose weights are aggregated from the basic failure modes’ weights. Second, the weights of the basic failure modes, risk factors and different RPN methods are derived from analytic hierarchy process. Third, the conditional weights of risk factors are determined by incorporating risk factors’ weights and failure modes’ conditional weights deduced from Shannon entropy. Next, several alternative weighted RPNs and IRPN are formulated to rank failure modes’ risk levels. Finally, an illustrative example about computer numerical control machine center is presented to demonstrate the application and effectiveness of the proposed method.     

A restricted hybrid stress formulation based on a direct finite element method

A direct method, which uses stress and displacement modes obtained from the governing equations of a problem, is adopted for finite element formulation. It is shown that this method actually leads to a restricted hybrid stress formulation if the displacement modes are changed to ensure symmetry of the stiffness matrix. Through this direct method, however, the problem of selecting the appropriate number of stress modes in the regular hybrid stress model is bypassed. Only the minimum number of modes that are compatible with the number of nodal degrees-of-freedom of an element is needed in the formulation. Using more modes only leads to a combination of stress modes, and will not improve the order of performance of the element. It is shown through numerical examples that the restricted hybrid stress formulation leads to well-balanced elements.     

某地铁站厅不同送回风方式的气流组织数值模拟和分析

地铁站厅公共区现今的空调设计,送回风方式主要有单送单回和两侧送中间回两种。根据不同的土建结构采用不同的方式。但由于空间比较大,送回风方式不合适可能会导致气流组织不良。本文以某地铁站厅为例,利用CFD方法,模拟和对比同一站厅不同送回风方式,并从各方面评价两种方式的效果,为地铁站气流组织的进一步研究和工程设计提供参考。     

Excitation Mechanism of Flexural-Guided Wave Modes F(1, 2) and F(1, 3) in Pipes

The L(0, 2) and T(0, 1) modes are the two most commonly used modes in a pipe inspection; however, they are insensitive to axial cracks in the pipe. Therefore, it is meaningful to explore the excitation and utilization of the guided wave modes, which are different from the L(0, 2) and T(0, 1) modes. In this study, the excitation mechanism of two kinds of flexural-guided wave modes, F(1, 2) and F(1, 3), in a pipe is discussed in detail. The discussion is based on the dynamic response solution, which is obtained by the eigenfunction expansion method. Either mode can be excited by employing two transducer arrays. Each array is composed of sixteen elements. Moreover, the position, vibration direction, and phase of each element should be appropriately chosen. The validity of the excitation method is demonstrated by the numerical results obtained using the finite element method.