Vibration of twisted laminated composite conical shells

A methodology for free vibration of a laminated composite conical shell with twist is proposed, in which a strain–displacement relationship of a twisted conical shell is given by considering the Green strain tensor on the general thin shell theory, the principle of virtual work is utilized, and the governing equation is formulated by the Rayleigh–Ritz procedure with algebraic polynomials in two elements as admissible displacement functions. The convergence, the accuracy and the validity of the methodology are verified by comparisons. As a result of the vibration frequencies and mode shapes, the effects of the laminated constructional and the geometric parameters, such as the number of laminae, the fiber orientation angles, the twist angle, the subtended angle and the taper ratio, on the vibration characteristics are studied by the present methodology.     

Free vibration of elastic helicoidal shells

An elastic helicoidal structure modelled as a plate twisted around its axis is studied in this paper. Accurate strain–displacement relationships for the shell are derived by the Green strain tensor in general shell theory and first-order shear deformation theory. An energy equilibrium equation of free vibration is introduced by the principle of virtual work. Applying the Rayleigh–Ritz method, an analytical eigenvalue equation is formulated and solved via an efficient computational approach for vibration characteristics of the helicoidal structure. A set of normalized orthogonal polynomials generated by the Gram–Schmidt procedure is presented to approximate the admissible functions. The first polynomial is taken as a kinematically compliant geometric equation of boundary conditions of the shell. The convergence and the accuracy of the present method, and the effects of geometric parameters and boundary conditions on vibration of the helicoidal structure are investigated.     

Three-dimensional vibration analysis of thick, tapered rods and beams with circular cross-section

A three-dimensional (3-D) method of analysis is presented for determining the free vibration frequencies and mode shapes of thick, tapered rods and beams with circular cross-section. Unlike conventional rod and beam theories, which are mathematically one-dimensional (1-D), the present method is based upon the 3-D dynamic equations of elasticity. Displacement components u_r, u_θ, and u_z in the radial, circumferential, and axial directions, respectively, are taken to be sinusoidal in time, periodic in θ, and algebraic polynomials in the r and z directions. Potential (strain) and kinetic energies of the rods and beams are formulated, the Ritz method is used to solve the eigenvalue problem, thus yielding upper bound values of the frequencies by minimizing the frequencies. As the degree of the polynomials is increased, frequencies converge to the exact values. Convergence to four- digit exactitude is demonstrated for the first five frequencies of the rods and beams. Novel numerical results are tabulated for nine different tapered rods and beams with linear, quadratic, and cubic variations of radial thickness in the axial direction using the 3-D theory. Comparisons are also made with results for linearly tapered beams from 1-D classical Euler–Bernoulli beam theory.     

Method for assessing the similarity and distance between curves/trials and its applications in gait analysis

In clinical assessment or sports exercise.it is common that a subject is required to repeat a specific per-formance so that a stable movement pattern is obtained and analysed.In practice,however,the trials done by a sub-ject vary more or less,depending on the psychological or physical conditions.Some of the trials can be used as rep-resentatives of the stable movement pattern,and some not.Therefore,there is a demand for a new method to identify which trials/curves are similar.The traditional methods used to assess curve similarity are not perfecfly suitable for the case where there are only a few of trials available.This study proposes a similarity-distance coefficient to assess the similarity of curves/trials.A group of designed curves are used to validate the coefficient.The results show that given joint kinematic data during gait as examples,tlle proposed coefficient call be used to quantitatively evaluate the similarity of trials,and thus find which trials would be representative(S)for the gait investigated.The proposed method could be applied in various situations where repeat movements have to be measured and analysed.     

Vibration analysis of rectangular plates with edge V-notches

A method is presented for accurately determining the natural frequencies of plates having V-notches along their edges. It is based on the Ritz method and utilizes two sets of admissible functions simultaneously, which are (1) algebraic polynomials from a mathematically complete set of functions, and (2) corner functions duplicating the boundary conditions along the edges of the notch, and describing the stress singularities at its sharp vertex exactly. The method is demonstrated for free, square plates with a single V-notch. The effects of corner functions on the convergence of solutions are shown through comprehensive convergence studies. The corner functions accelerate convergence of results significantly. Accurate numerical results for free vibration frequencies and nodal patterns are tabulated for V-notched square plates having notch angle α=5° or 30° at different locations and with various notch depths. These are the first known frequency and nodal pattern results available in the published literature for rectangular plates with V-notches.     

Three-dimensional hydrodynamic analysis of a journal bearing with a two-component surface layer

The article presents a three-dimensional hydrodynamic analysis of a bearing with a two-component surface layer journal. This kind of bearing is characterized by an experimentally proved susceptibility to oil contaminants which is five times lower than that of a typical bearing. The oil flow was described with the Navier–Stokes and energy equations. The equation system was solved by the finite element method. The distributions of pressure, temperature and oil flow velocity were determined. The computation results made it clear that a journal with a two-component surface layer causes a reduction in the bearing load capacity for high eccentricity ratio values (0.7–0.9). Besides, contrary to a typical bearing, considerable velocity changes in oil flow in all directions (circumferential, radial and axial) were observed in the bearing under consideration. Particularly great velocity changes occurred in the radial direction. However, no essential changes were found in the temperature of the oil film and in the attitude angle.     

Vibration analysis of cross-ply laminated beams with general boundary conditions by Ritz method

The present study is concerned with the vibration analysis of cross-ply laminated beams subjected to different sets of boundary conditions. The analysis is based on a three-degree-of-freedom shear deformable beam theory. The continuity conditions between layers of symmetric cross-ply laminated beams are satisfied by the use of the shape function incorporated into the theory which also unifies the 1D shear deformable beam theories developed previously. The governing equations are obtained by means of Hamilton's principle. Six different combinations of free, clamped and simply supported edge boundary conditions are considered. The free vibration frequencies are obtained by applying the Ritz method where the three displacement components are expressed in a series of simple algebraic polynomials. The numerical results obtained for different length-to-thickness ratios and lay-ups are presented and compared with results available in the literature.     

A robust forward-displacement analysis of spherical parallel robots

The forward-displacement analysis of spherical parallel robots (SPRs) is revisited. A robust approach, based on the input–output (I/O) equation of spherical four-bar linkages, is proposed. In this approach, the closed-loop kinematic chain of a SPR is partitioned into two four-bar spherical chains, whose I/O equations are at the core of the analysis reported here. These equations lead to a trigonometric equation in the joint angles, which is solved semigraphically to obtain the joint variables for the determination of the moving plate orientation. Examples are included to demonstrate the application of the method.     

Thermomechanical analysis of elastoplastic medium in sliding contact with fractal surface

The effects of mechanical and thermal surface loadings on deformation of elastic–plastic semi-infinite medium were analyzed simultaneously by using the finite element method. Rigid rough surface of a magnetic head and smooth surface of an elastic–plastic hard disk were chosen to perform a comprehensive thermo-elastic–plastic contact analysis at the head–disk interface (HDI). A two-dimensional finite element model of a rigid rough surface characterized by fractal geometry sliding over an elastic–plastic medium was then developed. The evolution of deformation in the semi-infinite medium due to thermomechanical surface loading is interpreted in terms of temperature, von Mises equivalent stress, and equivalent plastic strain. In addition to this, the effects of friction coefficient, sliding, and interference distance on deformation behavior were also analyzed. It is shown that frictional heating increases not only the contact area but also the contact pressure and stresses.     

On the use of the asymptotic scaled modal analysis for time-harmonic structural analysis and for the prediction of coupling loss factors for similar systems

The paper presents the results of an ongoing research on a scaling procedure aimed at the reduction of the computational cost associated, in a deterministic approach, to the wavelength simulation. The adoption of the energy distribution approach allowed to completely define the way in which a scaled model can represent the mean response of a given original model. This goal is achieved through a reduction in the dimensions not involved in the energy propagation and accordingly in an increase of the original damping loss factors. Here, the coupled systems under observation are those in which the same wave is allowed to travel, exchange and reflect. Specifically the results coming from the classical modal response and the statistical energy analysis are compared with those in output from the scaling procedure. Some highlights with experimental test-case results and comparisons for a plate assembly are also given. The work presents also an investigation about the possibility of estimating the energy influence coefficients through scaled finite element models.     

Development of the meshless Hermite–Cloud method for structural mechanics applications

In this work, a novel true meshless numerical technique is proposed. It is termed the Hermite–Cloud method and is based on the classical reproducing kernel particle method except that a fixed reproducing kernel approximation is used instead. Another distinction is that the point collocation technique is used for the discretization of the governing partial differential equations. In this method, the Hermite theorem is employed for the construction of the interpolation functions. Through the constructed Hermite-type interpolation functions, we are able to generate the expressions of approximate solutions of both the unknown functions and the first-order derivatives, in a direct manner. A set of auxiliary conditions have also been developed so as to construct a complete set of PDEs with mixed Dirichlet and Neumann boundary conditions. Through several structural analysis examples, it is shown that the numerical results at the scattered discrete points generated by the Hermite–Cloud method are distinctly improved, for both the approximate solutions as well as the first-order derivatives.     

Scaling of pulse loaded mild steel plates with different edge restraint

This paper reports the results of scaled tests on mild steel square plates with different edge restraint subjected to uniformly distributed triangular pulse pressure loading producing large inelastic deformations without tearing or rupture. The loading is representative of overpressure loading arising from a confined hydrocarbon explosion. A scale factor of 0.5 was examined in this series of tests on 16 plates, eight 1 m by 1 m × 2 mm thick and eight 0.5 m × 0.5 m × 1 mm thick. Both static and dynamic test results are presented. A quasi-static rigid–plastic and elastic–plastic analysis of a fully restrained square plate is also presented and compared with the test results. The transient response of the plates under dynamic loading show some divergence from the laws of geometrically similar scaling while the permanent deformations in both the static and dynamic tests show good compliance with the laws of similitude, within the accuracy expected in such tests.     

松散物料在水平圆振动干燥机中的运动分析

依据流体力学和振动学的基本原理,建立物料在水平圆振动干燥机中的运行方程,得出物料在单层孔板上运行周期及时间表达式.并通过该方程的电算方法得到物料运行任意位置所需时间,经实际验证模拟值与实测值吻合较好.     

Time–frequency analysis of tribological systems—part I: implementation and interpretation

A novel technique adapting the time–frequency analysis has been utilized to characterize stationary and non-stationary signals from tribological interactions. This representation displays time, frequency, and signal magnitude to decipher signals emanating from such interactions. Short-time Fourier transform, Wigner, Coi–Williams, and Zhao–Atlas–Marks distributions are suited to represent stationary and non-stationary signals. Some of the most complex tribological phenomena involve head–disk interactions in magnetic recording systems. Examples drawn from practical head–disk interface tests are analyzed by using the fast Fourier transform algorithm to illustrate the dynamic features of various distributions. Time–frequency representation of output spectrums of laser doppler vibrometer (LDV), strain gage sensor, and acoustic emission (AE) sensor obtained from head–disk experiments giving evidence of stationary and non-stationary behavior are investigated.     

Thermoelastohydrodynamic analysis of the static performance of tilting-pad journal bearings with the Newton–Raphson method

Thermoelastohydrodynamic lubrication (TEHD) analysis is presented to investigate the static performance of tilting-pad journal bearings. A completely numerical solution is obtained. The Newton–Raphson method is employed to predict the bearing characteristics of the hydrodynamic pressure, the eccentricity and the pad attitude angles simultaneously. For the temperature calculation, three-dimensional (3D) energy equations for the fluid under each pad and 3D heat transfer equations for the pads are solved using a sequential sweeping method. The elastic deformation and thermal expansion of each pad are calculated with the 20-node isoparametric finite element method. It is found that the Newton–Raphson method is a smart and efficient method. The results show that the elastic deformation due to the hydrodynamic pressure and the influence of the temperature elevation play an important role in the calculated bearing system.     

The envelope order spectrum based on generalized demodulation time–frequency analysis and its application to gear fault diagnosis

The generalized demodulation time–frequency analysis is a novel signal processing method, which is particularly suitable for the processing of multi-component amplitude-modulated and frequency-modulated (AM–FM) signals as it can decompose a multi-component signal into a set of single-component signals whose instantaneous frequencies own physical meaning. While fault occurs in gear, the vibration signals measured from gearbox would exactly display AM–FM characteristics. Therefore, targeting the modulation feature of gear vibration signal in run-ups and run-downs, a fault diagnosis method in which generalized demodulation time–frequency analysis and envelope order spectrum technique are combined is put forward and applied to the transient analysis of gear vibration signal. Firstly the multi-component vibration signal of gear is decomposed into some mono-component signals using the generalized demodulation time–frequency analysis approach; secondly the envelope analysis is performed to each single-component signal; thirdly each envelope signal is re-sampled in angle domain; finally the spectrum analysis is applied to each re-sampled signal and the corresponding envelope order spectrum can be obtained. Furthermore, the gear working condition can be identified according to the envelope order spectrum. The analysis results from the simulation and experimental signals show that the proposed algorithm was effective in gear fault diagnosis.     

Elastic analysis of unbounded solids using volume integral equation method

A volume integral equation method (VIEM) is used to calculate the plane elastostatic field in an unbounded isotropic elastic medium containing isotropic or anisotropic inclusions subject to remote loading. It should be noted that this newly developed numerical method does not require the Green’s function for anisotropic inclusions to solve this class of problems, since only the Green’s function for the unbounded isotropic matrix is involved in their formulation for the analysis. A detailed analysis of displacement and stress fields is carried out for isotropic or anisotropic inclusions. The method is shown to be very accurate and effective for investigating the local stresses in composites containing isotropic or anisotropic fibers.     

含间隙弹性连杆机构的KED分析

将传统的ＫＥＤ分析方法与以牛顿法为基础的含间隙刚性机构二阶段模型相结合,建立了较为简洁的含间隙弹性连杆机构动力学模型,采用了ＫＥＤ求解思路,分析了运行副间隙和结构阻尼对弹性连杆机构动态响应的影响,算例表明,该方法是正确可行的。     

双稳态膜片的有限元分析与实验研究

双稳态结构是降低微流体器件功耗的有效手段,使膜片获得双稳态结构往往需要对材料进行热处理。文中提出了一种不需要进行材料热处理,通过将圆形膜嵌入半径相对较小的圆形槽从而使膜片达到双稳态效果的方法。基于聚丙烯材料,对设计和制作的双稳态结构的初始挠度、开关压强及密封能力进行了有限元分析。结果显示,当槽半径为19.75 mm,膜片半径较槽半径大100μm时,膜片能够在其中心半径为0.5 mm的区域密封600 kPa以上的入口压力,而膜片的开关压强约为5.2 kPa。通过实验测量了膜片中心变形随压强的变化及实际开关压强的大小,实验结果与仿真结果吻合较好。最后就结构制造精度对初始挠度、开关压强及密封压强的影响进行了分析。     

A deposition technique for the imaging and analysis of protein interactions with metal and semiconductor surfaces

A new technique for placing biological molecules on metal, insulator, and semiconductor surfaces is described. The procedure requires only 10 μl of solution containing molecules at a concentration of 0.1—10 μg/ml. The use of a buffer that does not affect metal substrates, the possibility of fixing the molecules in solution prior to deposition, and the ability to minimize surface tension forces during air drying are other features of the new protocol. Simultaneous deposition on TEM grids and highly curved substrates permits biomolecular adsorption on technologically interesting materials to be visualized in the transmission electron microscope.