FREE-VIBRATION ANALYSIS OF LIQUID-FILLED TANK WITH BAFFLES

The natural frequencies of liquid in a liquid-filled cylindrical rigid tank without and with baffles are evaluated. An annular plate is used as a baffle, which is fitted to the inner periphery of a cylindrical tank. Both rigid and flexible baffles are considered. Finite elements are used to discretize both the liquid and the structural domain. The slosh frequencies of liquid are computed for different dimensions, thicknesses and positions of baffles, both rigid and flexible considering the circumferential wave number as one. The axisymmetric and other asymmetric modes are not studied. The results obtained for rigid baffle case are comparable with the existing results. The coupled vibration frequencies of the tank-flexible-baffle system are computed considering the effect of sloshing of liquid.     

圆柱形通道结构橡胶声障板

本文介绍了具有圆柱通道的橡胶水声反声障板的机理，通过静态近似得到此种橡胶声学参数的计算公式，测试了相关材料的动态力学性能，并对障板的声学特性进行了理论计算和分析，给出了不同频率下的反声性能随材料损耗因子、剪切模量及厚度的变化规律，并对模型进行了试验验证。     

C~0 and C~1 theories and test functions for FEM patch test in microstructures

Among many theories and categories in microstructures,rotation-displacement used as "independent" or "dependent" variables,is a noticeable topic. In FEM,it is called C0 and C1 theory. The convergence criteria of finite elements for microstructures are less mature than those for the conventional thin plate bending problem. In this paper,the patch test functions for assessing convergence of the C0 and C1 finite elements in microstructures is established based on the enhanced patch test theory. The author has further explored the C0 and C1 finite element theories and investigated the difference and correlation between their finite element formulations. Newly proposed finite element theories for microstructures are as follows:(1) the displacement-rotation dependent C1 element that requires the element function satisfying both C0 and C1 continuity;(2) the displacement-rotation independent C0 element which requires new convergence criteria,such as non-zero constant shear stress patch test and zero constant shear stress patch test for approximating C1 element.     

DYNAMIC STABILITY OF CURVED PANELS WITH CUTOUTS

The parametric instability behaviour of curved panels with cutouts subjected to in-plane static and periodic compressive edge loadings are studied using finite element analysis. The first order shear deformation theory is used to model the curved panels, considering the effects of transverse shear deformation and rotary inertia. The theory used is the extension of dynamic, shear deformable theory according to Sanders' first approximation for doubly curved shells, which can be reduced to Love's and Donnell's theories by means of tracers. The effects of static and dynamic load factors, geometry, boundary conditions and the cutout parameters on the principal instability regions of curved panels with cutouts are studied in detail using Bolotin's method. Quantitative results are presented to show the effects of shell geometry and load parameters on the stability boundaries. Results for plates are also presented as special cases and are compared with those available in the literature.     

Analysis and design of pod silencers

Parallel baffle mufflers or split silencers are used extensively in heating, ventilation and air conditioning systems for increased attenuation of noise within a short or given length. Acoustic analysis of rectangular parallel baffle mufflers runs on the same lines as that of a rectangular duct lined on two sides. This simplification would not hold for circular configurations. Often, a cylindrical pod is inserted into a circular lined duct to increase its attenuation (or transmission loss), thereby making the flow passage annular and providing an additional absorptive layer on the inner side of this annular passage. This configuration, called a pod silencer, is analyzed here for the four-pole parameters as well as transmission loss, making use of the bulk reaction model.The effect of thin protective film or a highly perforated metallic plate is duly incorporated by means of a grazing-flow impedance. Use of appropriate boundary conditions leads to a set of linear homogeneous equations which in turn lead to a transcendental frequency equation in the unknown complex axial wave number. This is solved by means of the Newton-Raphson method, and the axial wave number is then used in the expressions for transmission loss as well as the transfer matrix parameters. Finally, results of a parametric study are reported to help the designer in optimization of a pod silencer configuration within a given overall size for minimal cost.     

SENSITIVITY ANALYSIS AS A METHOD OF ABSORBER TUNING FOR REDUCTION OF STEADY STATE RESPONSE OF LINEAR PARAMETRIC SYSTEMS

The aim of this paper is to determine whether one dynamic absorber can reduce the amplitude of the steady state vibration of a parametric system for natural and parametric resonance frequencies simultaneously. The efficiency of both the conventional dynamic absorber and the parametric absorber is analyzed. The first order sensitivity analysis of parametric periodic systems in the time domain is applied to obtain logarithmic sensitivity functions in the frequency domain. The first order sensitivity logarithmic functions are used to tune the conventional absorber and the parametric absorber.     

离轴三反光学遥感器遮光罩的设计与试验验证

遮光罩是空间光学遥感器的重要组成部分,是抑制空间光学遥感器杂散光的首要措施。遮光罩削弱杂散光效果的好坏直接影响到光学遥感器光学系统的成像品质。本文设计了一种满足离轴三反空间光学遥感器要求的大尺寸碳纤维/环氧复合材料遮光罩,并结合有限元分析、杂散光分析及力学试验、光学系统传递函数检测手段来验证该遮光罩是否满足航天使用要求。结果显示,各视场光学系统传递函数检测结果基本一致,均在0.2以上。表明该大尺寸遮光罩具备良好的结构的稳定性、可靠性,能够满足空间应用要求。     

A numerical study of the effects of the vertical baffle on liquid sloshing in two-dimensional rectangular tank

The liquid sloshing in a moving partially filled rectangular tank with a vertical baffle is investigated. A numerical algorithm based on the volume of fluid (VOF) technique is used to study the nonlinear behavior of liquid sloshing. The numerical model solves the complete Navier–Stokes equations in primitive variables by using of finite difference approximations with the moving coordinate system. The ratio of baffle height to the initial liquid depth has been changed in the range of 0≤h_B/h≤1.2. The critical baffle height to reach the roof of the tank and the baffle height beyond the liquid does not get over the baffle anymore have been investigated. The vortex originated by the flow separation from the baffle tip became weaker with increasing the baffle height. In order to assess the accuracy of the method used, some results with baffle height are compared with the experimental results. Comparisons show good agreement for slosh loads in the cases investigated. The free surface elevation and the time variations of pressures have been also presented.     

Estimation of dynamic parameters of overthreshold parametric phase conjugation of ultrasound in magnetostrictive ferrites according to data of quasi-static measurements

A simple method for testing ferrite samples intended to be active elements of parametric phase conjugator of ultrasound was proposed and experimentally approved. The method allows one to estimate such dynamic parameters of parametric phase conjugator of ultrasound as the parametric amplification increment, threshold of absolute parametric instability, and optimum operating point position for a particular sample using results of measurements in a dc magnetic field. Results for two ferrite samples of different compositions and properties were compared to direct measurement data; their satisfactory agreement was obtained.     

COMBINATION OF FINITE AND BOUNDARY ELEMENT METHODS IN INVESTIGATION AND PREDICTION OF LOAD-CONTROLLED NOISE OF POWER TRANSFORMERS

A recently developed calculation scheme for the computer modelling of the load-controlled noise of oil-insulated three-phase power transformers is presented. This modelling scheme allows the precise and efficient computation of the coupled electromagnetic, mechanical and acoustic fields. The equations are solved using the finite element method (FEM) as well as the boundary element method (BEM), resulting in a separation of the calculation of the winding and tank surface vibrations (using FEM) and the computation of the acoustic free-field radiation (using BEM). The complex dynamic behaviour of the loaded transformer can then be studied and, furthermore, an appropriate computer-aided design including an investigation and optimization of design parameters can be established.The validity of the computer simulations has been verified by means of appropriate measurements. Simulated and measured values for winding and tank surface vibrations as well as sound power levels of the loaded transformer are found to be in good agreement. The applicability of the calculation scheme with respect to the computer-aided design of power transformers is demonstrated by reporting two practical applications: the influence of the stiffness of winding supports and the influence of the tap changer positions.     

Correlation of finite element models of multi-physics systems

The modal assurance criterion (MAC) and normalized cross-orthogonality (NCO) check are widely used to assess the correlation between the experimentally determined modes and the finite element model (FEM) predictions of mechanical systems. Here, their effectiveness in the correlation of FEM of two types of multi-physics systems, namely, viscoelastic damped systems and a shunted piezoelectric system are investigated using the dynamic characteristics obtained from a nominal FEM, that are considered as the ‘true’ or experimental characteristics and those obtained from the inaccurate FEMs. The usefulness of the MAC and NCO check in the prediction of the overall loss factor of the viscoelastic damped system, which is an important design tool for such systems, is assessed and it is observed that these correlation methods fail to properly predict the damping characteristics, along with the responses under base excitation. Hence, base force assurance criterion (BFAC) is applied by comparing the ‘true’ dynamic force at the base and inaccurate FEM predicted force such that the criterion can indicate the possible error in the acceleration and loss factor. The effect of temperature as an uncertainty on the MAC and NCO check is also studied using two viscoelastic systems. The usefulness of MAC for the correlation of a second multi-physics FEM that consists of a shunted piezoelectric damped system is also analyzed under harmonic excitation. It has been observed that MAC has limited use in the correlation and hence, a new correlation method – current assurance criterion – based on the electric current is introduced and it is demonstrated that this criterion correlates the dynamic characteristics of the piezoelectric system better than the MAC.     

基于MC的差分式低温泵人字形挡板结构分析

差分式低温冷凝泵主要用来维持EAST-NBI内的真空环境,以满足中性束生成与传输过程对真空压力分布的要求。人字形辐射挡板吸收高温壁面的辐射热,冷却到达低温冷凝板的气体。传输几率是影响人字形辐射挡板的一个重要的参数。为了寻求最佳的人字形辐射挡板的结构参数,文中主要利用蒙特卡罗方法,模拟气体分子的运动过程,计算不同参数下人字形辐射挡板的传输几率。根据中性束注入装置的尺寸要求,确定了人字形辐射挡板的具体尺寸。这为进一步优化人字形辐射挡板提供了理论基础。     

Added mass matrix estimation of beams partially immersed in water using measured dynamic responses

An added mass matrix estimation method for beams partially immersed in water is proposed that employs dynamic responses, which are measured when the structure is in water and in air. Discrepancies such as mass and stiffness matrices between the finite element model (FEM) and real structure could be separated from the added mass of water by a series of correction factors, which means that the mass and stiffness of the FEM and the added mass of water could be estimated simultaneously. Compared with traditional methods, the estimated added mass correction factors of our approach will not be limited to be constant when FEM or the environment of the structure changed, meaning that the proposed method could reflect the influence of changes such as water depth, current, and so on. The greatest improvement is that the proposed method could estimate added mass of water without involving any water-related assumptions because all water influences are reflected in measured dynamic responses of the structure in water. A five degrees-of-freedom (dofs) mass-spring system is used to study the performance of the proposed scheme. The numerical results indicate that mass, stiffness, and added mass correction factors could be estimated accurately when noise-free measurements are used. Even when the first two modes are measured under the 5 percent corruption level, the added mass could be estimated properly. A steel cantilever beam with a rectangular section in a water tank at Ocean University of China was also employed to study the added mass influence on modal parameter identification and to investigate the performance of the proposed method. The experimental results demonstrated that the first two modal frequencies and mode shapes of the updated model match well with the measured values by combining the estimated added mass in the initial FEM.     

Dynamic stability in parametric resonance of axially accelerating viscoelastic Timoshenko beams

This paper investigates dynamic stability of an axially accelerating viscoelastic beam undergoing parametric resonance. The effects of shear deformation and rotary inertia are taken into account by the Timoshenko thick beam theory. The beam material obeys the Kelvin model in which the material time derivative is used. The axial speed is characterized as a simple harmonic variation about the constant mean speed. The governing partial-differential equations are derived from Newton's second law, Euler's angular momentum principle, and the constitutive relation. The method of multiple scales is applied to the equations to establish the solvability conditions in summation and principal parametric resonances. The sufficient and necessary condition of the stability is derived from the Routh-Hurvitz criterion. Some numerical examples are presented to demonstrate the effects of related parameters on the stability boundaries.     

Transient sloshing in half-full horizontal elliptical tanks under lateral excitation

A semi-analytical mathematical model is developed to study the transient liquid sloshing characteristics in half-full horizontal cylindrical containers of elliptical cross section subjected to arbitrary lateral external acceleration. The problem solution is achieved by employing the linear potential theory in conjunction with conformal mapping, resulting in linear systems of ordinary differential equations which are truncated and then solved numerically by implementing Laplace transform technique followed by Durbin's numerical inversion scheme. A ramp-step function is used to simulate the lateral acceleration excitation during an idealized turning maneuver. The effects of tank aspect ratio, excitation input time, and baffle configuration on the resultant sloshing characteristics are examined. Limiting cases are considered and good agreements with available analytic and numerical solutions as well as experimental data are obtained.     

Analysis and improvement of sound radiation performance of spherical cap radiator

A spherical cap radiator is one of the important parts of an underwater wide-beam imaging system. The back radiation of a traditional spherical cap radiator, which is composed of a vibrating cap and a rigid baffle, is strong and its far-field directivity function may fluctuate in big amplitude in the vicinity of the polar axis. These shortcomings complicate the processing of the reflective waves received for imaging the targets. In this study, the back radiation is weakened by adding an acoustic soft material belt between the vibrating cap and the rigid baffle. And the fluctuation mentioned above is lowered remarkably by dividing the spherical cap radiator into many annuluses and a relatively smaller spherical cap, and by controlling the phase retardations of all elements appropriately. Furthermore, the numerical experiments are carried out by the finite element method (FEM) to prove the validity of the above methods.     

某稳瞄转塔结构的有限元模态分析与试验验证

结构动态效应是影响稳瞄系统稳定精度的关键因素。目前有限元模态分析与试验模态分析结合的方法是分析结构动力学特性的最有效途径之一。以某型稳瞄具两轴四框架结构为研究对象,首先利用有限元方法进行了模态预分析。根据仿真结果获取的振型特征,对两轴四框架的外环进行模态测试,给出了前8阶模态的固有频率、振型和模态阻尼比。模态仿真与测试的结果相互验证表明:有限元仿真可实现两轴四框架结构固有频率相对误差小于15%的精度要求,在测点密度足够的条件下振型相关性良好。     

高分辨率空间相机遮光罩结构参数的有限元分析

根据经典薄壳振动理论,利用有限元法对高分辨率空间相机遮光罩的结构参数进行了分析。将正交试验法与有限元法相结合,定量地分析了加强筋的数量和形状对遮光罩动力学特性的影响程度;根据模态分析的结果,考察了单个加强筋的参数对其动力学特性的影响。结果表明,加强筋的高度对结构刚度的影响最大,遮光罩的固有频率随着加强筋的数量和高度以及周向加强筋厚度的增加而增加,随着轴向加强筋的厚度的增加而减小。分析结果为高分辨率空间相机遮光罩的结构设计提供了必要的指导。     

Experimental study of different modes of block sliding along interface. Part 2. Field experiments and phenomenological model of the phenomenon

The paper reports the results of field experiments on studying different modes of gravitational sliding of a block on the natural fault surface. Various materials were used as interface filler to model the whole range of deformation events that can be arbitrarily divided into three groups: accelerated creep, slow slip, and dynamic slip. The experiments show that the type of modeled deformation events is defined by both structural parameters of contact between blocks and material composition of the contact filler.Foundations for a new geomechanical model of occurrence of different-type dynamic events were developed. The model is based on the idea that “contact spots” form subnormally to the crack edges during shear deformation; the “spots” are clusters of force mesostructures whose evolution governs the deformation mode. The spatial configuration of “contact spots” remains unchanged during the entire “loading-slip” cycle but changes after the dynamic event occurrence. The destroyed force mesostructures can be replaced by similar structures under intergranular interaction forces when the external influence is fully compensated. Unless “contact spots” are incompletely destroyed, the deformation process dynamics is defined by their rheology. The migration of “contact spots” during deformation of a crack filled with heterogeneous material causes changes in deformation parameters and transformation of the mode itself due to changing rheology of local contact areas between blocks.It is found by fractal analysis that in order for dynamic slip to occur, spatially structured “contact spots” characterized by low fractal dimension must be formed; slow slip events can exist only in a certain parametric domain called the “dome of slow events”. It is found that the probability of slow slip occurrence is higher on fault regions characterized by maximum fractal dimension values: fault tips, fault branching and fault intersection zones.     

Parametrically excited helicopter ground resonance dynamics with high blade asymmetries

The present work is aimed at verifying the influence of high asymmetries in the variation of in-plane lead-lag stiffness of one blade on the ground resonance phenomenon in helicopters. The periodical equations of motions are analyzed by using Floquet's Theory (FM) and the boundaries of instabilities predicted. The stability chart obtained as a function of asymmetry parameters and rotor speed reveals a complex evolution of critical zones and the existence of bifurcation points at low rotor speed values. Additionally, it is known that when treated as parametric excitations; periodic terms may cause parametric resonances in dynamic systems, some of which can become unstable. Therefore, the helicopter is later considered as a parametrically excited system and the equations are treated analytically by applying the Method of Multiple Scales (MMS). A stability analysis is used to verify the existence of unstable parametric resonances with first and second-order sets of equations. The results are compared and validated with those obtained by Floquet's Theory. Moreover, an explanation is given for the presence of unstable motion at low rotor speeds due to parametric instabilities of the second order.