功能梯度旋转圆板的热弹性固有振动

在考虑热因素及旋转运动条件下，针对金属－陶瓷功能梯度圆板的固有振动问题进行研究．给出随温度变化且材料组分沿厚度方向按幂律分布的材料物性参数，依据热弹性理论得到圆板的能量关系式．基于哈密顿原理建立旋转金属－陶瓷功能梯度圆板热弹性动力学方程．采用伽辽金法得到边界约束下圆板的自由振动方程，确定了静挠度及固有振动频率．基于数值计算，得到系统固有频率值随体积分数指数、转速和温度等参量的变化曲线，讨论了静挠度变化规律及动力系统的奇点稳定性问题．结果表明，固有频率随体积分数指数、材料表面温度以及转速的增加而减小．     

Simultaneous Measurement of Plate Natural Frequencies and Vibration Mode Shapes Using ESPI

The natural frequencies and vibration mode shapes of flat plates are simultaneously measured using ESPI. The method involves measuring the surface shape of a vibrating plate at high frame rate using a modified Michelson interferometer and high-speed camera. The vibration is excited here by impact; white (random) noise could alternatively be used. Fourier analysis of the acquired data gives the natural frequencies and associated mode shapes. The analytical procedure used has the advantage that it simultaneously identifies full-field quantitative images of all vibration modes with frequencies up to half the sampling frequency. In comparison, the ESPI time-averaging and the traditional Chladni methods both require that the plate be excited at each natural frequency to allow separate qualitative measurements of the associated mode shapes. The Instrumented Hammer method and Laser Doppler Vibrometry give quantitative measurements but require sequential sampling of individual points on the test surface to provide full-field results. Example ESPI measurements are presented to illustrate the use and capabilities of the proposed plate natural frequency and mode shape measurement method.     

Vibration-based construction and extraction of structural damage feature index

The finite element dynamic model of a honeycomb sandwich plate is presented using different mesh division for the surface plates and the sandwich plate to accurately express the crack damage status of the plate. The experimental measurements of plate natural frequency and dynamic responses are carried out for dynamic model verification. The feasibility of detecting small crack damage according to structural natural frequency and dynamic responses is evaluated. The results show that the energy spectrum of the decomposed wavelet signals of dynamic responses has a higher sensitivity to small crack damage, and more high order modes should be included in the dynamic model for structural damage detection.     

COUPLING BETWEEN LAMINAR FILM CONDENSATION AND NATURAL CONVECTION ON OPPOSITE SIDES OF A VERTICAL PLATE

Theoretical analyses which incorporate one-dimensional heat conduction along a plate and transverse heat conduction approximations are presented to predict the net heat transfer between laminar film condensation of a saturated vapour on one side of a vertical plate and boundary layer natural convection on the other side. It is assumed that countercurrent boundary layer flows are formed on the two sides. The governing boundary layer equations of this problem and their corresponding boundary conditions are all cast into dimensionless forms by using a non-similarity transformation. Thus the resulting system of equations can be solved by using the local non-similarity method for the boundary layer equations and a finite difference method for the heat conduction equation of the plate. The plate temperature and the heat flux through the plate are repetitively determined until the solutions for each side of the plate match. The predicted results show that the effect of Pr_c is not negligible for larger values of A* (thermal resistance ratio between natural convecti on side and condensing film side) and the approximation of transverse heat conduction overpredicts the plate temperature for lower values of R_t (thermal resistance ratio between plate and condensing film). However, no significant differences are observed between the two different approximations for higher values of R_t. © by 1997 John Wiley & Sons, Ltd.     

Natural frequencies of composite plates with tailored thermal residual-stresses

Thermal residual-stresses introduced during manufacture and their effect on the natural frequencies and vibration modes of stringer stiffened composite plates is investigated. The principal idea in the work is to include stiffeners on the perimeter of a composite plate in which the laminate design of the stiffeners and plate are different. Such an arrangement yields manufacturing induced thermal residual-stresses; these stresses result from the difference in manufacturing and operating temperatures as well as the difference in thermal expansion coefficients and elastic properties of the plate and the stiffeners. The analysis is based on an enhanced Reissner–Mindlin plate theory and involves two separate calculations. In the first, the thermal residual-stress state is determined for an unconstrained plate. In the second, the free vibration problem is solved; thermal effects from the first calculation are included by way of nonlinear membrane-bending coupling which in turn defines the free vibration reference state. The problem is solved using a 16-node bi-cubic Lagrange element in a finite element formulation. Three different plate-stiffener geometries are used to illustrate the effects of stringer size, stringer placement and temperature difference. Two principal results are obtained: first, it is shown that thermal residual-stresses can have a significant effect on the natural frequencies; secondly, thermal residual-stresses can be tailored to increase natural frequencies. Therefore it is concluded that an evaluation of these stresses and a judicious analysis of their effects must be included in the design of this class of composite structures.     

Numerical and experimental study of free convection above a sinusoidal horizontal plate

A numerical and experimental analysis is performed to study the laminar free convection above a horizontal plate facing upward subjected to an uniform heat flux. The surface of the plate, in contact with the fluid, is described by a sinusoidal profile. The natural convection equations are discretized, using an implicit finite difference technique, based on the finite volume approach. The SIMPLE algorithm assumes the linkage between velocities and pressure fields. The top and the lateral boundaries of the space, where free convection is developing, are determined by using an iterative procedure. The temperature fields of the fluid, over the plate, are visualized by an experimental device, which can realize a simultaneous measurement of the temperature and the position. Qualitative information about the natural convection flow above the plate is obtained by using a laser tomography technique. The numerical results show that the flow and the heat transfer are strongly affected by the amplitude, the period of the sinusoidal profile and the type of fluid. Comparisons between numerical and experimental results show a good qualitative agreement.     

加热压电纤维复合材料圆板的横向自由振动

基于经典薄板理论和极正交各向异性材料的本构理论,建立了加热压电纤维复合材料圆板的线性振动控制微分方程。采用打靶法分别获得了加热压电纤维复合材料圆板在周边固支和简支情况下,无量纲固有频率随温度和电场强度变化的关系曲线,并分析了压电纤维体积分数、刚度参数、电场强度和温度变化对压电纤维复合材料圆板无量纲固有频率的影响。结果表明,一定体积分数或者电场强度下,压电纤维复合材料圆板的无量纲固有频率都随温度的升高而单调下降;同一温度下,刚度参数越小,无量纲固有频率越低;电场强度越大,无量纲固有频率越高。     

Radial Vibrations and Heating of a Ring Piezoplate under Electric Excitation Applied to Nonuniformly Electroded Surfaces

Radial vibrations and dissipative heating of a polarized piezoceramic ring plate are studied. The plate is excited by a harmonic electric field applied to nonuniformly electroded surfaces of the plate. The viscoelastic behavior of piezoceramics is described in terms of complex quantities. An analytical solution is found in the case of quasistatic harmonic loading. The dynamic nonlinear problem of coupled thermoviscoelasticity is solved with regard for the temperature dependence of the properties of piezoceramics by step-by-step integration in time, using the numerical methods of discrete orthogonalization and finite differences. A numerical analysis is conducted for TsTStBS-2 piezoceramics to study the influence of partial electroding on the stress–strain distribution, natural frequency, and amplitude–frequency and temperature–frequency characteristics     

曲壁蜂窝夹层板的振动特性研究

曲壁蜂窝具有负刚度特性,可以在大变形过程中吸收能量、抗冲击,并且在冲击过后可以自我恢复而不像传统蜂窝被压溃。本文将曲梁构成的负刚度蜂窝作为芯层,建立夹层板的动力学模型;推导出了曲壁负刚度蜂窝胞元的等效弹性参数,将其周期性排列为蜂窝芯,应用Reddy高阶剪切变形理论、Von-Karman大变形关系和Hamilton原理推导了负刚度蜂窝夹层板的非线性动力学方程;应用Navier法计算了四边简支边界条件下的固有频率。并利用有限元软件ABAQUS建立模型,计算固有频率,与理论计算结果进行比较,结果显示二者的计算结果具有较好的一致性,验证了芯层等效弹性参数及模型的有效性。探讨了在蜂窝胞元具有较高吸能情形下,夹层板在不同芯层厚度、不同芯厚比以及不同胞元曲壁厚度时的固有频率的变化特性。     

Numerical study of the natural convective cooling of a vertical plate

We study numerically in this paper the natural convective cooling of a vertical plate. The full transient heat conduction equation for the plate, coupled with the natural convection boundary layer equations are solved numerically for a wide range of the parametric space. Assuming a large Rayleigh number for the natural convection flow, the balance equations are reduced to a system of three differential equations with three parameters: the Prandtl number of the fluid, Pr, a non-dimensional plate thermal conductivity α and the aspect ratio of the plate ?. The nondimensional cooling time depends mainly on α/?², obtaining a minimum of this time for values of 1?α??².     

Aeolian tones of a plate cascade

A model for the aeroacoustic resonance effects (aeolian tones) excited around a plate cascade in a gas flow is suggested. Methods of calculating the frequencies of natural acoustic oscillations near the cascade are developed. The effect of the cascade geometry and the Mach number of the main flow on the frequencies, abundance, and modes of the natural oscillations is investigated. Anomalous acoustic oscillations near a cyclic plate cascade are shown to exist and are studied. It is shown that there always exist no less than two natural oscillation frequencies in the gas flow near any nontrivial cyclic plate cascade. It has been found that the natural oscillation frequencies can be combined in bundles such that in the case where the number of plates in a period is large the frequencies pertaining to each bundle occupy a certain interval with arbitrary density. The natural oscillations are classified with respect to the form of the eigenfunctions; the classification is based on the theory of representations of groups of locally plane symmetries of the cyclic plate cascade in the solution space. The correctness of the proposed model of the aeroacoustic resonance effects (aeolian tones) excited near a plate cascade in a gas flow is supported by a comparison with the available experimental and theoretical data. On the basis of the investigation performed, some previously unknown physical phenomena are predicted. Thus, the existence of frequency zones or main-flow Mach number ranges on which aeroacoustic resonance phenomena exist near a cyclic cascade with a large number of plates in a period is proved; it is shown that for certain frequencies of the natural oscillations near the cyclic plate cascade the resonance oscillations may be localized in the vicinity of the source; and the existence of narrow-band wave packets slowly propagating along the cascade is demonstrated. Novosibirsk, e-mail: sukhinin@hydro.nsc.ru. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 171–186, March–April, 2000.     

波纹板结构动力学建模及其自由振动特性分析

波纹板结构是高速列车中较为常见的型材结构,因其具有轻质、高强度和高稳定性等一系列优点,所以广泛应用于车体结构轻量化设计。首先,基于一阶剪切变形理论和中厚壳(圆弧壳)理论,采用微分求积有限元法(DQFEM)建立一般边界条件下五自由度波纹板结构的通用动力学分析模型;紧接着对五自由度波纹板结构动力学模型进行收敛性验证,确定最佳微分节点数和惩罚因子的取值;然后,采用有限软件(ABAQUS)验证了建立模型的准确性;最后根据已建立模型,研究波纹板结构参数对其振动特性的影响。结果表明,波纹板结构厚度和固支边界条件会增加其固有频率,提高波纹板结构的稳定性,使得共振频率向高频移动;增加波纹板结构长度、参与耦合圆弧壳半径和参与耦合圆弧壳弧度会降低其固有频率,使得共振频率向低频移动。     

热环境中旋转运动功能梯度圆板的强非线性固有振动

研究热环境中旋转运动功能梯度圆板的非线性固有振动问题．针对金属－陶瓷功能梯度圆板，考虑几何非线性、材料物理属性参数随温度变化以及材料组分沿厚度方向按幂律分布的情况，应用哈密顿原理推得热环境中旋转运动功能梯度圆板的非线性振动微分方程．考虑周边夹支边界条件，利用伽辽金法得到了横向非线性固有振动方程，并确定了静载荷引起的静挠度．用改进的多尺度法求解强非线性方程，得出非线性固有频率表达式．通过算例，分析了旋转运动功能梯度圆板固有频率随转速、温度等参量的变化情况．结果表明，非线性固有频率随金属含量的增加而降低；随转速和圆板厚度的增大而升高；随功能梯度圆板表面温度的升高而降低．     

Numerical and experimental analysis of natural vibrations of rectangular plates with variable thickness

It is proposed to solve problems on natural vibrations of rectangular plates of variable thickness under complex boundary conditions using the numerical-analytical spline-collocation method in combination with the discrete-orthogonalization method and the experimental method of holographic interferometry. As a mathematical model, the problem on natural vibrations of a square plate with constant thickness and fixed ends is solved. The approximate solutions obtained are compared with experimental data. Translated from Prikladnaya Mekhanika, Vol. 36, No. 2, pp. 131–134, February 2000.     

Vibrations of polygonal plates with various boundary conditions

The bending vibrations of polygonal (L-shaped) plates with different shapes and boundary conditions are studied. The natural frequencies are calculated using the inverse-iteration and Kantorovich-Vlasov methods. To take the configuration of the domain into account, the fictitious domain method and an analog of the force method of structural mechanics are used. Different trends in the dependence of the lowest natural frequency of an L-shaped plate on its geometry are illustrated for different boundary conditions.Acorrelation between the extreme values of the bending frequency and some relations for the energy characteristics of the plate is established __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 5, pp. 63–72, May 2007.     

Dynamic modelling and active vibration control of a submerged rectangular plate equipped with piezoelectric sensors and actuators

The active vibration control of a rectangular plate either partially or fully submerged in a fluid was investigated. Piezoelectric sensors and actuators were bonded to the plate, and the assumed mode method was used to derive a dynamic model for the submerged plate. The properties of the piezoelectric actuators and sensors, as well as their coupling to the structure, were used to derive the corresponding equations of their behaviour. The fluid effect was modelled according to the added virtual mass obtained by solving the Laplace equation. The natural vibration characteristics of the plate both in air and in water were obtained theoretically and were found to be consistent with the experimental results, and the changes in the natural frequencies resulting from submersion in fluid can be accurately predicted. A multi-input, multi-output positive position feedback controller was designed by taking the natural vibration characteristics into account and was then implemented by using a digital controller. The experimental results show that piezoelectric sensors and actuators along with the control algorithm can effectively suppress the vibration of a rectangular plate both in air and submerged in a fluid.     

Dynamic modelling of thin plate made of certain functionally graded materials

The aim of the contribution is to formulate a macroscopic mathematical model describing the dynamic behaviour of a certain composite thin plates. The plates are made of two-phase stratified composites with a smooth and a slow gradation of macroscopic properties along the stratification. The formulation of mathematical model of these plates is based on a tolerance averaging approach (Woźniak, Michalak, Jędrysiak in Thermomechanics of microheterogeneous solids and structures, 2008). The presented general results are illustrated by analysis of the natural frequencies for two cases of plates: a plate band and an annular plate. The spatial volume fractions of the two different isotropic homogeneous components are optimized so as to maximize or minimize the first natural frequency of the plate under consideration.     

碳纳米管增强型复合材料功能梯度板的自由振动模型与尺度效应

基于一种新的各向异性修正偶应力理论,建立了碳纳米管增强复合材料功能梯度板的自由振动模型。该模型能够描述尺度效应,且仅包含一个尺度参数。基于一阶剪切变形理论和哈密顿原理推演了板的运动微分方程,并以四边简支板为例给出了自振频率的解析解。讨论了板的几何尺寸、碳纳米管体分比含量和分布方式等因素对板的自振频率的影响。结果表明,本文模型所预测的板的自振基频总是高于经典弹性理论的Mindlin板模型的预测结果,两者间的差异在板的几何尺寸接近尺度参数的值时非常明显,且会随着板的几何尺寸的增大而逐渐消失。     

Characteristic orthogonal polynomials in the study of transverse vibrations of nonhomogeneous rectangular orthotropic plates of bilinearly varying thickness

Effect of nonhomogeneity on the vibrational characteristics of thin orthotropic rectangular plates of bilinearly varying thickness has been studied using boundary characteristic orthogonal polynomials in the Rayleigh-Ritz method. The thickness variation is taken as the Cartesian product of linear variations along two concurrent edges of the plate. The orthogonal polynomials in two variables are generated using the Gram-Schmidt process. The nonhomogeneity of the plate material is assumed to arise due to linear variations in Young’s moduli, shear modulus and density of the plate with the in-plane coordinates. Numerical results have been computed for four different combinations of clamped, simply supported and free edges. Effect of thickness variation together with varying values of aspect ratio and nonhomogeneity on the natural frequencies is illustrated for the first three modes of vibration. Three dimensional mode shapes have been presented. Comparison has been made with the known results.     

基于各向异性修正偶应力理论的Reddy型层合板的自由振动

本文基于各向异性修正偶应力理论建立了只含一个尺度参数的Reddy型复合材料层合板的自由振动模型。同见诸于文献的细观尺度Kirchhoff薄板偶应力模型相比,本文提出的新模型能够更精确的预测细观尺度下的中、厚层合板的自振频率。基于Hamilton原理推导了细观尺度下Reddy型复合材料层合板的运动微分方程以及边界条件,并以正交铺设的四边简支复合材料层合方板为例进行了解析求解,分析了尺度参数对自振频率的影响并对比了Kirchhoff、Mindlin和Reddy等三种板模型计算结果的异同。算例结果表明本文所给出的模型能够捕捉到复合材料层合板自由振动问题的尺度效应。另外,在细观尺度下Kirchhoff板模型所预测的自振频率相对于Mindlin板模型和Reddy板模型总是过高,且越接近厚板三者的差别就越大,这与经典理论中三种板模型的对比情况是一致的。