变厚度弹性圆薄板问题

一.引言 变厚度的圆薄板常常在机器零件的设计中遇到,例如蒸汽涡输机和活塞的膜片便是。 用平板小挠度理论求解变厚度平板问题并不是容易的事,因此到目前为止,这类的实际问题已解决的为数并不多。     

Transverse vibrations of thin,elastic plates with concentrated masses and internal elastic supports

The fundamental frequency of vibration of a plate carrying concentrated masses and with internal elastic supports is determined. The case of an orthotropic, rectangular plate elastically restrained against rotation along the four edges is tackled first by using simple polynomial approximations and the Galerkin method. Then, vibrations of clamped and simply supported isotropic plates of regular polygonal shape are studied by using the conformal mapping technique coupled with the variational method. Finally the case of a circular plate elastically restrained against translation and rotation is considered.     

Analysis and computation of the vibration spectrum of the shallow circular cylindrical shell with rectangular domain

An asymptotic method of Bolotin, for the computation of eigenvalues of self-adjoint problems on rectangular domains, is extended to the shallow shell equations for the vibrating circular cylindrical shell. These same eigenfrequencies are then computed using the Legendre-tau spectral method. The asymptotic and numerical results are seen to be in good agreement and, as expected, approach those of the flat plate as the curvature tends to zero.     

计算模拟法改善激光波面

计算模拟方法设计位相元件可将基模高斯光束均匀化,将椭圆波面校正为圆对称波面.本文推导了理论模拟结果和实验参数的关系.计算模拟给出的实验装置较为简单,能量转换效率高.     

Approximate study of the free vibrations of a cantilever anisotropic plate carrying a concentrated mass

This study is concerned with the vibration analysis of a cantilevered rectangular anisotropic plate when a concentrated mass is rigidly attached to its center point. Based on the classical theory of anisotropic plates, the Ritz method is employed to perform the analysis. The deflection of the plate is approximated by a set of beam functions in each principal coordinate direction. The influence of the mass magnitude on the natural frequencies and modal shapes of vibration is studied for a boron-epoxy plate and also in the case of a generic anisotropic material. The classical Ritz method with beam functions as the spatial approximation proved to be a suitable procedure to solve a problem of this analytical complexity.     

A note on a circular panel sound absorber with an elastic boundary condition

Panel sound absorbers are typically used to absorb low-frequency noise in concert halls, auditoriums, recording studios, and other architectural applications. These systems are composed of flexible panels mounted over an air space that can be either partly or completely filled with a porous material. In this paper, a theoretical model is derived for predicting the sound-absorption coefficient of a cylindrical low-frequency absorber made of a circular plate. The theory takes into account the mass, bending stiffness, damping loss and the elastic boundary condition of the circular plate. The effects of the stiffness of an air-back cavity and of partially adding a porous material into the cavity are also considered. It is observed that the low-frequency resonances of such a system are dependent upon the clamping condition, the width of the air-back cavity, and mechanical properties of the plate. There is good agreement between theoretical and experimental results.     

Mass optimization of non-conservative cantilever beams with internal and external damping

An adjoint variational principle has been developed for a non-conservatively loaded cantilever beam with Kelvin-Voigt internal and linear external damping and is applied to a beam with a linearly distributed tangential load acting along the centerline of the beam. Relative mass optimization for beams of both rectangular and circular crosssections is considered from a graphical standpoint and from the viewpoint of a computer optimization routine with data given and discussed in both instances. In going to a Rosenbrock optimization routine for beams of rectangular cross-section with a minimum tip thickness constraint imposed it was quite clear that mass ratio reductions in the range 14·9 % to 38 % are possible and that the values of internal and external damping appear influential in determining just how much of a mass reduction is possible. Similarly, for beams of circular cross-section a Rosenbrock optimization routine with a minimum tip diameter constraint imposed showed that mass ratio reductions of the order of 27 % are possible.     

Energy concentration at the center of large aspect ratio rectangular waveguides at high frequencies

Waveguides in non-destructive evaluation (NDE) applications are commonly of a regular geometry (e.g., circular and ring cross section) for which analytical solutions exist. In this paper, wave propagation in infinitely long strips of large rectangular aspect ratio is discussed. Due to the finite width of strips, a large number of modes exist within the structure. This complicates the analysis and usually discourages the use of strip waveguides in NDE sensors. However, it is shown that among the many modes of a strip, there are some with very desirable properties. This is highlighted by the example of two guided wave modes of a large aspect ratio rectangular strip whose dispersion characteristics approach those of the fundamental modes of an infinitely wide plate at high frequencies. The energy of these modes concentrates in the central region of the strip and decays toward the edges so that the strip waveguide can easily be mechanically attached to other components without influencing the wave propagation. Dispersion curves and mode shapes were derived by using a semianalytical finite element technique and are presented over a range of frequencies. It is shown that selective excitation of both modes is possible in practice and the experimental setup is described.     

圆盘上的绳张力

讨论绕水平定轴转动的圆盘和跨过圆盘的细绳组成的力学系统,在考虑二者的质量及之间的摩擦的情况下,导出了细绳张力的计算式.     

超声波空气污染物颗粒采样器的新结构及其特性研究*

超声波空气污染物颗粒采样器具有可采集低浓度颗粒污染物、采样速度快、重复性好、结构简单、易分析被采集物以及不破坏污染物成分等优点。为了进一步提高其采样效率,该文提出了一种超声波空气污染物颗粒采样器的新结构。该采样器由超声换能器、被粘接在换能器声辐射面上的圆形声辐射板以及与声辐射板平行的采样板组成。该采样器利用声辐射力和声学流场驱动空气中的污染物颗粒快速聚集到采样板上。样机测试表明,该结构在空气污染物颗粒初始浓度为4 mg/L以及辐射板中心位置的振动速度为0.29 m/s时,对烟雾中PM2.5和PM2.5-10颗粒的采样效率为16.3 mg/m~2·min·W。与不采用高阶弯曲振动圆形声辐射板的结构相比,其采样效率增加了110%。     

Geometrically nonlinear vibrations of rectangular plates carrying a concentrated mass

Nonlinear forced vibrations of rectangular plates carrying a central concentrated mass are studied. The plate is assumed to have immovable edges and rotational springs; numerical results are presented for clamped plates. The Von Kármán nonlinear plate theory is used, but in-plane inertia in both the plate and the mass is retrained. The problem is discretized into a multi-degree-of-freedom (dof) system by using an energy approach and Lagrange equations taking damping into account. A pseudo-arclength continuation method is used in order to obtain numerical solutions. Results are presented as both (i) frequency-amplitude curves and (ii) time domain responses. The effect of gravity and the effect of the consequent initial plate deflection are also investigated.     

高功率过模圆波导到两路矩形波导功分器

基于模式匹配法分析了高功率过模圆波导到两路矩形波导功分器在传输过程中高阶模式的传输和反射问题,分析得到了高传输效率对过模圆波导的要求,并以此仿真设计了中心频率为2.88GHz的功分器,设计结果表明:在中心频率下反射系数为0.05,对应的圆波导TM01模到矩形波导TE10模传输效率大于99%,真空中功率容量为2.83GW;在2.82~2.94GHz的频带范围内反射系数小于0.1,对应的传输效率大于98%。     

Influence of Streamwise Pitch on Local Heat Transfer Distribution for In-Line Arrays of Circular Jets with Spent Air Flow in Two Opposite Directions

Abstract

The effect of streamwise jet-to-jet spacing on local heat transfer distribution due to an in-line rectangular array of confined multiple circular air jets impinging on a surface parallel to the jet plate are experimentally studied. The length-to-diameter ratio of nozzles of the jet plate is 1.0. The flow, after impingement, is constrained to exit in two opposite directions from the confined passage formed between the jet plate and target plate. Mean jet Reynolds numbers based on the nozzle exit diameter (d) covered are 3,000, 5,000, 7,500, and 10,000; jet-to-plate distances studied are d, 2d, and 3d. Streamwise jet-to-jet distances of 3d, 4d, and 5d, and a constant spanwise pitch of 4d, are considered. The jet plates have ten spanwise rows in the streamwise direction and six jets in each spanwise row. The flat heat transfer surface is made of thin stainless-steel metal foil. Local temperature distribution on a target plate is measured using a thermal infrared camera. Wall static pressures in the streamwise direction are measured midway between the spanwise jets to estimate cross-flow velocities and individual jet velocities. The streamwise distribution of the jet flow and the cross flow is found to be least influenced by the streamwise pitch variation for the range of parameters considered during the present study. Heat transfer characteristics are explained partially on the basis of flow distribution. The cooling performance, based on the strip-averaged Nusselt number per unit mass flow rate of coolant per unit area of cooled surface, indicates deterioration for lower streamwise pitch and higher jet-to-plate distance.     

Thermoelastic damping in rectangular and circular microplate resonators

Predicting thermoelastic damping (TED) is crucial in the design of high Q micro-electro-mechanical systems (MEMS) resonators. In the past, some analytical models have been developed for TED in microbeam resonators. Rectangular and circular microplates are also common elements in many micro-resonators. Two analytical models have been developed for TED in the contour-mode vibration and the out-of-plane vibration of circular microplates, respectively. However, there is lack of works that model the TED in the out-of-plane vibration of rectangular microplates. This paper presents an analytical model for the TED in the fully clamped and simply supported rectangular microplates. The quality factor is found by calculating the energy dissipated per cycle of vibration over the volume of the microplate. The derivation in this paper shows that the model for the TED in the fully clamped and simply supported rectangular plates is the same as the model for the TED in the fully clamped and simply supported circular plates. For the rectangular microplates with other boundary conditions, based on Rayleigh's method, this paper presents a set of analytical approximate models to estimate the TED in the rectangular microplates vibrating in the fundamental mode. The present model is validated by comparison with previously reported model and the FEM model.     

Free vibration analysis of cantilever plates by the method of superposition

The method of superposition is employed to analyze the first five symmetric and antisymmetric free vibration modes of a cantilever plate for a wide range of aspect ratios. It is shown that this method provides a simple, straightforward and highly accurate means of solution for this family of problems. Convergence to exact values is shown to be remarkably rapid. The first two symmetric and antisymmetric modal shapes for a square plate are accurately described by means of contour line drawings. The numerous advantages of this method over previously used methods are discussed. It is shown that it lends itself readily to the entire family of rectangular plates with classical edge conditions: i.e., clamped, simply supported, and free. Its applicability to a wide family of rectangular plates with boundary conditions other than the classical type is also discussed.     

圆波导TE01模激励器设计及实验研究

对比分析了几种可输出圆波导TE₀₁模激励器的仿真设计结果。结果表明,利用行波功分结构实现矩形波导TE₁₀模到4路矩形波导TE₁₀模的等幅同相功分,进而合成转换成圆波导TE₀₁模的转换过程,可在较宽的频带范围内,实现圆波导TE₀₁模的高效激励。以中心频率9.40 GHz仿真设计的圆波导TE₀₁模激励器,在中心频率上的传输效率超过99.9%;在9.08~9.61 GHz的频率范围内,传输效率大于99%。实验测量结果表明,所加工激励器在较宽的频带范围内,传输损耗优于-0.2 dB,与仿真结果的差异主要来自于波导壁面的欧姆损耗和波同转换结构;器件工作频带内平坦特性良好,有利于开展测量工作。     

A note on vibrating polar orthotropic circular plates carrying concentrated masses

The fundamental frequency of vibration of a circular plate of polar orthotropy carrying concentrated masses is determined by using (a) an extension of the Rayleigh-Schmidt technique and (b) a Ritz-Lagrange multipliers method. Numerical results are presented for clamped and simply supported plates for several combinations of orthotropic parameters and values of the concentrated mass to plate mass ratio.     

Transverse vibrations of plates with stepped thickness over a concentric circular region

This paper deals with the determination of the fundamental frequency of vibration of: (a) rectangular, (b) regular polygonal and (c) circular plates with stepped thickness over a concentric, circular subdomain of the plates. The problems are solved in a unified fashion by adopting simple polynomial co-ordinate functions and making use of the Ritz method to generate the frequency determinant.     

Higher-dimensional chaotic dynamics of a composite laminated piezoelectric rectangular plate

The analysis on the chaotic dynamics of a six-dimensional nonlinear system which represents the averaged equation of a composite laminated piezoelectric rectangular plate is given for the first time. The theory of normal form and the energy-phase method are combined to investigate the higher-dimensional chaotic dynamics of the composite laminated piezoelectric rectangular plate. Firstly, the theory of normal form is used to reduce the six-dimensional averaged equation to the simpler normal form. Then, the energy-phase method is extended to analyze the global bifurcations and chaotic dynamics of a six-dimensional nonlinear system. The analysis results indicate that there exist the homoclinic bifurcation and Shilnikov type multi-pulse chaos for the composite laminated piezoelectric rectangular plate. Finally, numerical simulations are also used to investigate the nonlinear dynamic characteristics of the composite laminated piezoelectric rectangular plate. The results of numerical simulations also demonstrate that there exist the chaotic motions and the multi-pulse jumping orbits of the composite laminated piezoelectric rectangular plate.     

Computation of the gas mass and heat fluxes in a rectangular channel in the free molecular regime

The problem of heat- and mass transfer in a long rectangular channel of a constant cross section is solved in the free molecular regime. The distributions of the mass flow rate and the heat flux vector over the channel cross section are calculated. The specific gas mass flux and heat flux are calculated. The results are compared with those obtained for nearly free molecular flows.