Natural frequencies of rectangular Mindlin plates coupled with stationary fluid

The present study is concerned with the free vibration analysis of a horizontal rectangular plate, either immersed in fluid or floating on its free surface. The governing equations for a moderately thick rectangular plate are analytically derived based on the Mindlin plate theory (MPT), whereas the velocity potential function and Bernoulli’s equation are employed to obtain the fluid pressure applied on the free surface of the plate. The simplifying hypothesis that the wet and dry mode shapes are the same, is not assumed in this paper. In this work, an exact-closed form characteristics equation is used for the plate subjected to a combination of six different boundary conditions. Two opposite sides are simply supported and any of the other two edges can be free, simply supported or clamped. To demonstrate the accuracy of the present analytical solution, a comparison is made with the published experimental and numerical results in the literature, showing an excellent agreement. Then, natural frequencies of the plate are presented in tabular and graphical forms for different fluid levels, fluid densities, aspect ratios, thickness to length ratios and boundary conditions. Finally, some 3-D mode shapes of the rectangular Mindlin plates in contact with fluid are illustrated.     

Analysis of human-induced vibrations in a lightweight framework

This article analyzes the vibratory behavior of a Material-Composed Sandwich (MCS) framework for residential buildings. It has been observed qualitatively that the use of this kind of framework leads to poor comfort levels. The goal of this study is to find out the sources of this lack of comfort, in order to suggest guidelines that can enhance the performance of the MCS framework, without jeopardizing its advantages with respect to the traditional frameworks.     

电站进水口快速闸门振动特性研究

电站进水口快速闸门是机组和引水系统一旦发生事故后进行快速应对、控制事态扩大的控流设施.论文研究溪洛渡电站快速闸门水力学及流激振动问题.着重对机组甩负荷时的闸门动水压力作用、门体结构的振动状态及待命高度之间的关系、闸门启闭力等进行了深入研究,取得了快速闸门净动水作用力、水流脉动压力、振动加速度等水力结构参数,论证了设计方案的合理性,提出了安全运行建议.     

DYNAMICAL ANALYSIS OF AUTOMOBILE HYSTERESIS NONLINEAR SYSTEM

This paper adopts free interface modal synthesis method to divide the whole automobile model into many sub-structures and establish dynamical equations of automobile nonlinear coupled system. The Monte Carlo method is used to simulate the spectrum of the random excitation of the road and the engine. Based on the automobile dynamical equations, a simulation is carried out within time domain and frequency domain on the characteristic of vibration due to the excitation of automobile wheel and the engine. The results are verified by bench experiment to make the research more practicable. In order to do research of rubber hysteresis’ influence on automobile dynamic property, Poincare diagrams and amplitude frequency characteristic curves were drawn with automobile linear and nonlinear models. The results show that the nonlinear dynamical model concerning rubber hysteresis not only can improve the simulation accuracy, but also is beneficial to find some complex nonlinear dynamical behaviors of vehicles.     

A mathematical approach to study fluid-coupled vibration of eccentric annular plates

A mathematical method is proposed to study fluid-coupled vibration of axisymmetric plate structures with asymmetries due to either imperfection or practical reasons, e.g. the weight reduction of structure, natural frequency shifting, and accessibility. The suggested approach makes use of the separation of variables to determine general solutions of the partial differential equation of the plate transverse displacement, whilst defining multiple polar coordinate systems, each of which offers its own formulation of the plate deformation with respect to its coordinate system. Moreover, closed-form geometric equations and the chain rule for determining derivatives are implemented to move from one coordinate system to the other in order to satisfy boundary conditions. The mode shapes of the vibrating plate in the dry condition are determined and in turn used in the Rayleigh–Ritz method to characterize vibrational properties of the fluid-coupled plate structure. While implementing such an energy method, the fluid motion is formulated employing the velocity potential and solved using the separation of variables. Fluid–structure interaction is also taken into account satisfying the compatibility condition on the fluid–plate​ interface. The developed methodology to predict natural frequencies has been validated by comparison with results obtained by a commercial finite element program. It is also found that the eccentricity tends to reduce natural frequencies of the fluid-coupled system for the lower serial mode, but increases them for the higher serial modes regardless of the presence of liquid.     

Free vibration and stability of tapered Euler–Bernoulli beams made of axially functionally graded materials

The free vibration and stability of axially functionally graded tapered Euler–Bernoulli beams are studied through solving the governing differential equations of motion. Observing the fact that the conventional differential transform method (DTM) does not necessarily converge to satisfactory results, a new approach based on DTM called differential transform element method (DTEM) is introduced which considerably improves the convergence rate of the method. In addition to DTEM, differential quadrature element method of lowest-order (DQEL) is used to solve the governing differential equation, as well. Carrying out several numerical examples, the competency of DQEL and DTEM in determination of free longitudinal and free transverse frequencies and critical buckling load of tapered Euler–Bernoulli beams made of axially functionally graded materials is verified.     

Vibration response of stepped FGM beams with elastically end constraints using differential transformation method

In this paper, free vibration response of stepped beams made from functionally graded materials (FGMs) is investigated. The beams are supported by various types of elastically end constraints. The differential transformation method (DTM) is employed to solve the governing differential equations of such beams in order to obtain natural frequencies and mode shapes. The power law distribution is used and modified to describe material compositions across the thickness of the beams made of FGMs. Two main types of the stepped FGM beams in which their material compositions can be described by using the modified power law distribution are selected to investigate their vibration behaviour. The significant parametric studies such as step ratio, step location, boundary conditions, spring constants and material volume fraction are taken into investigation.     

金属管线高温环境下的断裂失效分析

超燃冲压发动机燃烧室试验台配置了大量金属管线,煤油作为燃料和冷却介质在其中输运,在实验过程中发生管线早期断裂失效,对此开展了分析。首先利用三维体视显微镜与扫描电镜进行了断口观察与分析,表明管线的开裂起源于焊缝根部,具有典型的多源起源特征;裂纹源区具有蓝色半圆形特征,表明存在焊接裂纹。同时,断口呈现明显的疲劳辉纹,间距为亚微米量级。根据辉纹间距与管材壁厚以及使用寿命分析,确定了疲劳载荷的频率范围;根据理论公式与有限元模态分析对管线的自振频率进行了估算,其结果与断口分析的结果吻合良好。以上研究结果表明管线断裂是典型的振动疲劳失效导致的。为此,建议在管线中部增加固定点约束,改变管线的自振频率以降低振幅,并改进焊接工艺,提高管线焊接质量。基于以上措施,有效解决了管线的早期断裂失效问题。     

Interference of vortex-induced vibration and transverse galloping for a rectangular cylinder

The phenomenon of interference between vortex-induced vibration (VIV) and galloping in the transverse degree of freedom was studied in the wind tunnel in the case of a spring-mounted slender rectangular cylinder with a side ratio of 1.5 having the short side perpendicular to the flow. The tests were carried out in a wide Scruton number range, starting from low values and increasing it in small steps by using eddy-current viscous dampers. This study helped understanding the dynamics of the interaction between the two excitation mechanisms and clearly highlighted the transition through four regimes of VIV-galloping interference. It was found that a high value of the mass-damping parameter is required to decouple the ranges of excitation of vortex-induced vibration and galloping completely, and for the quasi-steady theory to predict the galloping critical wind speed correctly. This conclusion is also relevant from the engineering point of view, as it means that structures and structural elements with ordinary mass-damping properties can exhibit sustained vibrations in flow speed ranges where no excitation is predicted by classical theories of vortex-induced vibration and galloping. Although most of the experimental tests were conducted in smooth flow at zero angle of attack, the paper also discusses the sensitivity of the results to a small variation of the mean flow incidence and to the presence of a low-intensity free-stream turbulence.     

ANLYTICAL SOLUTION OF THERMOELASTIC DAMPING IN RECTANGULAR MINDLIN MICRO PLATES 1)

首次给出了四边简支的 Mindlin 矩形微板热弹性阻尼的解析解. 基于考虑一阶剪切变形的 Mindlin 板理论和单向耦合热传导理论建立了微板热弹性耦合自由振动控制微分方程. 忽略温度梯度在面内的变化,在上下表面绝热边界条件下求得了用变形几何量表示的温度场的解析解. 进一步将包含热弯曲内力的结构振动方程转化为只包含挠度振幅的四阶偏微分方程. 利用特征值问题之间在数学上的相似性,在四边简支条件下给出了用无阻尼 Kirchhoff 微板的固有频率表示的 Mindlin 矩形微板的复频率解析解,从而利用复频率法求得了反映热弹性阻尼水平的逆品质因子. 最后,通过数值结果定量地分析了剪切变形、材料以及几何参数对热弹性阻尼的影响 规律. 结果表明,Mindlin 板理论预测的热弹性阻尼小于 Kirchhoff 板理论预测的热弹性阻尼. 两种理论预测的热弹性阻尼之间的差值在临界厚度附近十分显著. 另外,随着微板的边/厚比增大,Mindlin 微板的热弹性阻尼最大值单调增大,而 Kirchhoff 微板的热弹性阻尼最大值却保持不变.