Transverse vibration of a quarter of an elliptic plate with variable thickness

Rayleigh-Ritz method has been used to find the first three frequencies and mode shapes for free flexural vibration of a plate in the form of a quadrant of an ellipse with linear and quadratic thickness variations. The results for a quarter of a circular plate with uniform thickness have been obtained as a special case and comparison has been made with results already available. By taking various combinations of clamped, simply-supported and completely-free edges we get twenty-seven different cases. Tables are given for the first three frequencies for different values of parameters. Mode shapes have also been plotted in some cases. The convergence of results is indicated by working out approximations of various orders.     

Transverse vibrations of elliptical plate of linearly varying thickness with half of the boundary clamped and the rest simply supported

The Rayleigh–Ritz method has been applied to study the problem of transverse vibrations of elliptical plate with half of the boundary clamped and the rest simply supported. The thickness of the plate is varying linearly in the space coordinates. For the same thickness variation, the tabulated results in case of mixed boundary conditions lies between those reported for the two extreme cases when the entire boundary is either clamped or simply supported. Convergence of the results is indicated by increasing the order of approximation. Some results for a circular plate of linearly varying thickness with half of the boundary clamped and the rest simply supported have been obtained as special case. Comparisons have been made with the known results. Three-dimensional mode shapes have been drawn for some selected cases.     

Numerical solution for frequencies and mode shapes of elliptical plate half of whose boundary is simply supported and the rest free

Free transverse vibrations of elliptical and circular plates of variable thickness with half of the boundary is simply supported and the rest is completely free have been computed till the first four frequencies converge to at least four significant digits. The thickness of the plate is taken varying linearly with space coordinates. Computations have been carried out by using the famous Rayleigh–Ritz method. Results are reported for various values of the taper parameters. Almost all the results reported here are entirely new. A table has been prepared to indicate the trend of convergence of the results with increasing the order of approximation. Comparison has been made with known results in special cases. For the sake of completeness, results for the cases when the entire boundary is simply supported or completely free are also reported. Three-dimensional mode shapes and the associated contour lines have been plotted in some selected cases using tools of Computer Graphics and Turbo C++.     

Bright-field scanning confocal electron microscopy using a double aberration-corrected transmission electron microscope

Scanning confocal electron microscopy (SCEM) offers a mechanism for three-dimensional imaging of materials, which makes use of the reduced depth of field in an aberration-corrected transmission electron microscope. The simplest configuration of SCEM is the bright-field mode. In this paper we present experimental data and simulations showing the form of bright-field SCEM images. We show that the depth dependence of the three-dimensional image can be explained in terms of two-dimensional images formed in the detector plane. For a crystalline sample, this so-called probe image is shown to be similar to a conventional diffraction pattern. Experimental results and simulations show how the diffracted probes in this image are elongated in thicker crystals and the use of this elongation to estimate sample thickness is explored.     

Free transverse vibration of elliptical plates of variable thickness with half of the boundary clamped and the rest free

First four frequencies have been computed for an elliptical plate half of whose boundary (y0) is clamped and the other half is free. The thickness of the plate is taken varying linearly with space coordinates. The Rayleigh–Ritz method has been used to obtain successive approximations utill convergence is achieved up to at least four significant figures. Results are tabulated for various values of the taper parameters. Three-dimensional mode shapes and the associated contour lines have been plotted in some selected cases. A table showing the rate of convergence with increasing order of approximation is given. Comparison has been made with known results in special cases. For the sake of completeness, results for the cases when the entire boundary is clamped or completely free are also reported.     

Transverse vibration of a circular plate with unidirectional quadratic thickness variation

Free transverse vibration of a circular plate with thickness varying as (1 + α× + βx²) has been studied when the edge of the plate is clamped or simply-supported. The Rayleigh—Ritz method with suitable choice of basis functions satisfying the essential boundry conditions, has been employed to find the fundamental frequency and the associated mode shapes for various values of α and β with different boundary conditions. The convergence of results is ensured by working out several approximations till the results converge to the desired accuracy. The results for uniform thickness, linear and parabolic variation of thickness have been obtained as special cases. Tables and graphs are given for frequency, mode shapes and for depicting the effect of parameters α and β on the frequency.     

Three-dimensional free vibration analysis of perforated super elliptical plates via the p-Ritz method

A three-dimensional free vibration analysis of a perforated plate with rounded corners is presented. A solution method based on the linear, small strain, three-dimensional elasticity theory and the p-Ritz algorithm is employed. This analysis method uses sets of uniquely defined one- and two-dimensional polynomial functions as the trial displacements in the thickness and surface directions to arrive the eigenvalue equation which yields the natural frequencies and mode shapes for the perforated super elliptical plates. The accuracy of these results, if possible, is validated through comparison with the available literature. Parametric investigations on the vibration behaviours of the perforated super-elliptical plates with respect to different thickness ratios, cutout sizes and boundary constraints are examined.     

机械零件三维形貌的光栅投影测量系统

建立了一种基于虚拟复合光栅的三维形貌测量系统 ,利用两种频率光栅的合成投影 ,实现物体表面突变部分的测量。测量系统适用于机械零件的三维形貌检测 ,并且得到令人满意的测量结果。     

测量信息对飞行器工作模态辨识精度影响分析

针对模态辨识结果对输入的敏感性,研究了测量信息对飞行器工作模态辨识精度的影响。介绍了自回归 滑动平均(auto-regressive and moving average,简称ARMA)模型环境激励模态辨识方法的理论、试验测点和激励情况,并给出了试验研究方案情况。通过选择不同测点布置组合,研究了测点布置对辨识结果的影响。对各测点数据人为增加噪声,研究了数据品质对辨识结果的影响。研究发现,测点数目较多,且测点布置在振型数值较大位置,辨识结果较好。     

Frequency response function shape-based methods for structural damage localisation

The ultilisation of structural shape signals for damage localisation has shown some promise, especially in the applications where an accurate finite element model of the structure is not available. For this purpose, traditional shape signals, like mode shapes, flexibility matrices, uniform load surface (ULS) and operational deflection shapes (ODS) have been widely used. Using frequency response function (FRF) shapes for structural damage localisation is however, a relatively new but promising technique. Unlike mode shapes, ULS and ODS, FRF shapes are defined on broadband data and so have potential to reveal damage location more clearly. Another advantage of using FRF shapes is that the test data can be directly used without the necessity of conducting modal identification. Nevertheless, some problems associated with this approach still remain to be solved. No solid foundation or deduction about the use of FRF shapes for damage localisation has been given in any literature so far. In addition, it has been observed that this method only works for a low-frequency range. This limitation of FRF shapes has not been explained or well treated so far. In this study, a scheme of using FRF shapes for structural damage localisation is proposed. Methods within this scheme include some important modifications like using the imaginary parts of FRF shapes and normalising FRF shapes before comparison. The theoretical explanation of using FRF shapes for damage localisation is presented and the limitations of the previous FRF shape methods have been overcome. The proposed methods have shown great potential in structural damage localisation.     

MEASUREMENT OF FOIL AND CABLE THICKNESSES BY A TRANSMISSION METHOD

X-ray fluorescence analysis techniques can be applied to determine sample thickness by either absolute or relative methods. An absolute method for thickness determination by x-ray fluorescence analysis has been devised, based on two types of independent measurements of the fluorescence intensity of the constituents of the sample and performance of transmission and reflection irradiation setups.

In the present work, a method for determination of the average thickness of material between a gamma-ray source and a detector is presented. The thicknesses of Au, Ag, and Cu foils, and Cu cables have been calculated by a transmission method. An Am-241 radioisotope source and a Si(Li) detector have been used.

The method has high accuracy and is easy to use, it is non-destructive towards the sample, and it allows one to the control the sample thickness. To assess the reliability of the method, the results obtained are compared with the results obtained with a micrometer. The results are in good agreement with each other, within the estimated experimental error     

Synergetic representation of stick-slip mode of boundary friction

The melting of an ultrathin lubricating film clamped between two atomically smooth solid surfaces that are in relative motion is studied based on the Lorentz model for the approximation of a viscoelastic medium. An equation of motion for the stresses has been derived in the form of a three-order differential equation and analyzed at various friction surface temperatures. In all cases, the phase portraits and the time dependences of the stresses have been plotted. It has been found that, depending on the temperature and the lubricant parameters, either the damped oscillation mode or the stochastic oscillation mode may occur. The stochastic oscillation mode is presented in the phase plane as a strange attractor. It has been shown that initial conditions have a critical effect on the system behavior. Based on the model, the behavior of two types of tribosystems, i.e., with the unidirectional shear of the surfaces and under an alternating external effect, has been described.     

Non-axisymmetric buckling behaviour of elastic-plastic circular tubes subjected to a nosing operation

Theoretical investigations have been carried out to predict the non-axisymmetric buckling seen in the throat of circular elastic-plastic tubes subjected to a nosing operation along a frictionless conically shaped die. The buckling points and associated modes are determined by Hill's bifurcation theory in conjunction with a non-axisymmetric buckling mode. The results show that increasing the die semi-angle and the tube thickness or decreasing the material work-hardening rate are always beneficial to improve the buckling limit. The associated critical buckling mode number generally decreases as the tube thickness increases and does not depend drastically on the die semiangle nor on the hardening rate. The effect of the average r value is substantial and the buckling limit is improved when the r value reduces. Part of the present results predict well the results observed in existing experimental work.     

Scaling-factor estimation using an optimized mass-change strategy

In operational modal analysis, only unscaled mode shapes can be obtained. The mass-change method is in many cases the simplest way to estimate the scaling factors, which involves repeated modal testing after changing the mass at different points of the structure where the mode shapes are known. With this method, the scaling factors are determined using the natural frequencies and mode shapes of both the modified and the unmodified structure. However, the uncertainty on the scaling-factor estimation depends on the modal-analysis accuracy and the mass-change strategy (number, magnitude, and location of the masses) used to modify the dynamic behavior of the structure. In this paper, a procedure to optimize the mass-change strategy is proposed, which uses the modal parameters (natural frequencies and mode shapes) of the original structure as the basic information.     

Erratum to “Scaling-factor estimation using an optimized mass-change strategy” [Mech. Syst. Signal Process. 24(5) (2010) 1260–1273]

In operational modal analysis, only unscaled mode shapes can be obtained. The mass-change method is in many cases the simplest way to estimate the scaling factors, which involves repeated modal testing after changing the mass at different points of the structure where the mode shapes are known. With this method, the scaling factors are determined using the natural frequencies and mode shapes of both the modified and the unmodified structure. However, the uncertainty on the scaling-factor estimation depends on the modal-analysis accuracy and the mass-change strategy (number, magnitude, and location of the masses) used to modify the dynamic behavior of the structure. In this paper, a procedure to optimize the mass-change strategy is proposed, which uses the modal parameters (natural frequencies and mode shapes) of the original structure as the basic information.     

Effect of lateral morphology formation of polymer blend towards patterning silane-based SAMs using selective dissolution method

A number of strategies have been developed including soft lithography and photolithography for patterning various surfaces. Here we have discussed a customized strategy for surface patterning of nanosized, silane-based SAMs and monolayer thickness measurement investigated using atomic force microscope (AFM). We have utilized the versatile morphology of a binary polymer blend to generate patterned SAMs over silicon substrate by employing a selective dissolution procedure. This method was confirmed with different organosilanes with varying number of C-atoms and to other polymer blend. The samples were imaged both in tapping mode and pulsed force mode AFM.     

考虑黏压效应的风电齿轮热弹流分析

在线接触热弹流润滑的基础上,考虑黏压效应,对风电行星轮系齿轮副进行热弹流润滑数值分析,并采用热弹流润滑数值方法和ISO/TS 6336-22计算了齿轮副的最小油膜厚度、安全系数和闪温温度,并比较各主要啮合点的压力和油膜厚度分布。结果表明：与使用ISO/TS 6336-22计算的结果对比,采用热弹流润滑理论计算的油膜更厚,但安全系数更小;在风电齿轮副热弹流润滑分析时应考虑压力对黏度的影响;风电主齿轮箱齿面因啮合产生油膜厚度随温度增加会迅速降低,最小油膜厚度会随载荷增加迅速减小,因此风电齿轮箱要保证足够的润滑,并尽量避免在高于额定载荷下长时间持续运行     

Transverse vibration of completely-free elliptic and circular plates using orthogonal polynomials in the Rayleigh-Ritz method

The Rayleigh-Ritz method using characteristic orthogonal polynomials has been applied to study the problem of transverse vibration of completely-free elliptic and circular plates of uniform thickness. A sequence of successive approximations has been generated to work out the frequencies and mode shapes. The process is continued until at least the first four frequencies converge to five significant digits. It has been found that the results agree completely with the known results for a circular plate. A comparison has also been made with some known experimental and theoretical results for an elliptic plate.     

Exact solutions for the free in-plane vibrations of rectangular plates

All classical boundary conditions including two distinct types of simple support boundary conditions are formulated by using the Rayleigh quotient variational principle for rectangular plates undergoing in-plane free vibrations. The direct separation of variables is employed to obtain the exact solutions for all possible cases. It is shown that the exact solutions of natural frequencies and mode shapes can be obtained when at least two opposite plate edges have either type of the simply-supported conditions, and some of the exact solutions were not available before. The present results agree well with FEM results, which show that the present solutions are correct and the direct separation of variables is practical. The exact solutions can be taken as the benchmarks for the validation of approximate methods.     

Collapse mode transitions of thin tubes with wall thickness, end condition and shape eccentricity

Transition of deformation mode shapes of round aluminum tubes from axisymmetric concertina to non-axisymmetric diamond mode have been studied with varying tube wall thickness, boundary conditions and tube shape eccentricities. Quasi-static axial compression experiments were carried out on as received aluminum tubes and tubes with wall thickness eccentricity, incorporated by off center machining. Tubes were of D/t=29 and L/D=1.4. The numerical simulation of the collapse phenomenon has been undertaken using a static non-linear finite element analysis in ANSYS with a fine mesh discretization of the tube domain and small incremental displacements as load steps. Convergence studies for the finite element model with respect to load step size and mesh density have also been established. The numerical results are found to compare well with the experimental load compression and energy absorption responses both for the axisymmetric concertina and non-axisymmetric diamond collapse modes. Having validated the numerical model with experiments, it has been used to undertake a systematic study of the load–deformation characteristics, energy absorption response and collapse mode transition of the tubes in varying configurations of wall thickness, shape and inplane boundary condition eccentricities. Dependence of tube collapse characteristics and collapse mode transitions on such eccentricities have been discussed.