Coupled bending and torsional vibration of axially loaded thin-walled Timoshenko beams

A dynamic transfer matrix method of determining the natural frequencies and mode shapes of axially loaded thin-walled Timoshenko beams has been presented. In the analysis the effects of axial force, warping stiffness, shear deformation and rotary inertia are taken into account and a continuous model is used. The bending vibration is restricted to one direction. The dynamic transfer matrix is derived by directly solving the governing differential equations of motion for coupled bending and torsional vibration of axially loaded thin-walled Timoshenko beams. Two illustrative examples are worked out to show the effects of axial force, warping stiffness, shear deformation and rotary inertia on the natural frequencies and mode shapes of the thin-walled beams. Numerical results demonstrate the satisfactory accuracy and effectiveness of the presented method.     

基于固有频率的悬臂梁裂缝识别

结构中裂缝的存在使其模态参数发生改变 ,如局部刚度减小、阻尼增大、固有频率降低。把裂缝梁模拟成由扭曲弹簧连接 ,并对其前三阶固有频率的变化与裂缝位置和深度之间的关系进行计算和分析 ;利用特征方程以及前三阶固有频率 ,通过作图法对裂缝参数进行识别。识别结果证明 ,这种方法精度较高、简单可行 ,可用于机械工程实时监测。     

Influence of strain-hardening and strain-rate sensitivity on the permanent deformation of impulsively loaded rigid-plastic beams

A simple method is presented for estimating the combined influence of strain-hardening and strain-rate sensitivity on the permanent deformation of rigid-plastic structures loaded dynamically. A study is made of the particular case of a beam supported at the ends by immovable frictionless pins and loaded with a uniform impulse. The results of this work indicates that considering strain-hardening alone when appropriate or strain-rate sensitivity alone gives permanent deformations which are similar to those predicted by an analysis retaining both effects simultaneously.     

Natural frequencies,modes and critical speeds of axially moving Timoshenko beams with different boundary conditions

In this paper, natural frequencies, modes and critical speeds of axially moving beams on different supports are analyzed based on Timoshenko model. The governing differential equation of motion is derived from Newton's second law. The expressions for various boundary conditions are established based on the balance of forces. The complex mode approach is performed. The transverse vibration modes and the natural frequencies are investigated for the beams on different supports. The effects of some parameters, such as axially moving speed, the moment of inertia, and the shear deformation, are examined, respectively, as other parameters are fixed. Some numerical examples are presented to demonstrate the comparisons of natural frequencies for four beam models, namely, Timoshenko model, Rayleigh model, Shear model and Euler–Bernoulli model. Finally, the critical speeds for different boundary conditions are determined and numerically investigated.     

Lateral-torsional buckling analysis of thin-walled beams including shear and pre-buckling deformation effects

In this paper, lateral-torsional buckling behavior of open-section thin-walled beams is investigated based on a geometrically nonlinear formulation, which considers the effects of shear deformations. A finite element numerical solution along with an incremental-iterative solution procedure is adopted to trace the pre-buckling as well as the post-buckling equilibrium paths. Formulation is applicable to a general type of open-section and load position effects are also included. Numerical results are validated through comparisons with experimental results and those based on other formulations presented in the literature. Comparisons have also been made between the results based on fully nonlinear analysis and linearized buckling analysis in order to illustrate the effects of pre-buckling deformations as well as the shear deformations on the buckling load predictions. Examples illustrate the influence of beam slenderness and moment gradient on the effects of pre-buckling deformations in predicting bucking loads.     

Coupled bending-bending vibrations of pre-twisted cantilever blading allowing for shear deflection and rotary inertia by the Reissner method

The Reissner method and the total potential energy approach are applied to a pre-twisted cantilever blade executing coupled bending-bending vibrations. Shear deflection and rotary intertia are accounted for in the analysis and the natural frequencies and mode shapes of the first four coupled modes are determined. A comparison of the results obtained from this investigation with those available in the literature indicates that the Reissner method gives quicker convergence and better mode shapes than the potential energy method and it is further seen that the inclusion of shear deflection and rotary inertia into the analysis leads to a reduction in the frequency values, thus resulting in a closer agreement with experimental results.     

Stochastic bending–torsion coupled response of axially loaded slender composite-thin-walled beams with closed cross-sections

The stochastic bending–torsion coupled response of axially loaded slender composite beams with solid or thin-walled closed cross-sections are investigated by using normal mode method in conjunction with receptance method. The classical composite beam theory with shear deformation and rotary inertia ignored is employed and the effects of bending–torsion coupling and axial force are included in the present formulations. The theoretical expressions for the displacement response of axially loaded slender composite beams subjected to concentrated or distributed stochastic excitations with stationary and ergodic properties are derived. The proposed method is illustrated by its application to two particular examples to study the effects of bending–torsion coupling and axial force on the stochastic response of the composite beams.     

Transverse shear and rotary inertia effects on the stability analysis of functionally graded shells under combined static and periodic axial loadings

The effect of transverse shear and rotary inertias on the dynamic stability of functionally graded cylindrical shells subjected to combined static and periodic axial forces is investigated in this paper. Material properties of functionally graded cylindrical shells are considered temperature-dependent and are graded in the thickness direction according to a power-law distribution in terms of the volume fractions of the constituents. Numerical results for silicon nitride-nickel cylindrical shells are presented based on two different methods: the first-order shear deformation theory (FSDT) which considers the transverse shear strains and the rotary inertias, and the classical shell theory (CST). The results obtained show that the effect of transverse shear and rotary inertias on the dynamic stability of functionally graded cylindrical shells subjected to combined static and periodic axial forces is dependent on the shell’s material composition, environmental temperature, amplitude of static load, deformation mode, and the shell’s geometry parameters.     

Predictions of permanent deformation of impulsively loaded simply supported square tube steel beams

The paper describes experimental and theoretical work on model scale simply supported hollow steel beams of square tube section. In the experimental work, the beams were loaded impulsively by detonating a strip of sheet explosive along the top surface, using a fairly thick layer of styrofoam to spread the effect of the explosive strip. Impulses were measured by means of a ballistic pendulum. Local deformations of the order of the cross-section dimensions took place; however, these were uniform along the beam, indicating that the local and global beam deformations were sequential. In the analysis it is assumed that the local and global deflections are uncoupled. The local deformation is predicted approximately by treating the cross-section as a rigid-viscous portal frame, and the global deformation by treating the simply supported beam by an approximate elastic-plastic approach. Given the simplicity of the analysis, acceptable estimates of the deformation are obtained.     

Bending of axially constrained beams on elastic foundation

Approximate analysis of bending of a pin-pointed beam under distributed load resting on elastic foundation is considered. The supports are assumed to be immovable, thereby giving rise to the axial stretching of the neutral surface under lateral loads. The resulting problem is nonlinear since the axial force of constraint is dependent on the lateral displacements. Quantitative results of axial force, benidng moment and deflections are given in terms of two dimensionless parameters which depend on the load intensity, foundation modulus and properties of the beam.     

Natural frequencies of composite plates with random material properties using higher-order shear deformation theory

Composites are known to display a considerable amount of scatter in their material properties due to large number of parameters associated with the manufacturing and fabrication processes. In the present work, the material properties have been taken as random variables for accurate prediction of the system behavior. Higher order shear theory including rotatory inertia effects has been accounted for in the system dynamic equations. A first order perturbation technique has been employed to obtain the solution of the governing equations. An approach has been outlined for obtaining closed form expressions for the variances of eigen solutions. The effects of side to thickness ratio and variation in standard deviation of the material properties have been investigated for cross-ply symmetric and anti-symmetric laminates. The mean and standard deviations of the first five natural frequencies have been worked out for laminated rectangular plates with all edges simply supported. The higher order shear deformation theory results have been validated with Monte Carlo simulation results and compared with the results based on classical laminate and first order shear deformation theories.     

Explicit lower bounds for the buckling of axially loaded cylinders

Previously postulated, lower bound estimates of the buckling loads for axially loaded unstiffened cylinders are simplified by means of a Donnell-type approximation to provide compact, explicit, analytical expressions which could prove particularly suited to design. For a wide range of practical geometric parameters these simplified expressions are shown to provide close approximations of the exact lower bound loads and associated modes. In addition they allow the independent and significant influence of length to radius, radius to thickness, and Poisson's ratio to be isolated, and suggest a convenient means of summarising buckling loads in terms of a single composite geometric parameter.     

Analysis of lateral vibrations of rotating cantilever blades allowing for shear deflection and rotary inertia by reissner and potential energy methods

The lateral vibrations of a uniform rotating blade have been analysed applying the Reissner and the potential energy methods. Shear deflection and rotary inertia are taken into account. A convergence study of the two methods is made and the effects of shear deflection, rotary inertia, rotation and stagger angle on the blade vibration characteristics are discussed. Comparison of the results indicates a quicker convergence and better mode shapes by the Reissner method than the classical potential energy method.     

2#回转剪的设计

介绍了2#回转剪的设计过程、产品用途、主要技术性能参数、结构改进等,论述了2#回转剪的市场前景。     

带钢切边圆盘剪的使用及维护

圆盘剪是连续酸洗生产线中的重要设备,剪切质量的好坏直接影响到后续轧制工艺。重点分析了影响圆盘剪剪切质量的几个重要因素,总结了提高设备作业率的维护方法,并根据实际使用情况给出了一套最优参数值。     

A unified graphical approach to the static analysis of axially loaded structures

The paper presents a unified approach to graphical methods for the static force analysis of axially loaded plane structures. This approach consists of a unified diagram which incorporates both the frame and stress diagrams. This unified representation is applied to a simple Maxwell frame and the authors include a rigorous investigation of the equivalence between the unified diagram and traditional diagrams. The paper shows that traditional diagrams can, in fact, be regarded as particular cases of the unified diagram. The concept of self-reciprocity is introduced and a dual kinematic interpretation of the unified diagram is obtained from a sequence of equivalent diagrams. These diagrams can be obtained in a straightforward manner by changing the force scale factor.     

On the frictional behaviour of thermally loaded beams resting on a plane

The problem of an elastic beam resting on a frictional surface and loaded by a uniform temperature moment is treated analytically and numerically. The introduction of proper non-dimensional parameters identifies the deformation pattern which varies with monotonically increasing temperature load in a self-similar manner. This fact reduces the complexity of the mathematical system considerably and offers the derivation of the solution on an analytical basis. Several approaches are described, discussed and compared against each other. This problem is typical for a broader class of problems involving Coulomb friction in beam deformation. In addition to the fact that it is interesting from the structural as well as from the mathematical points of view, it is of practical importance, for example in the simulation of the cooling processes of hot rolled railway rails.     

The influences of shear deformation on the evolutions of the extrusion shear for magnesium alloy

A new type of magnesium alloy extrusion-shear (short for ES) composite extrusion technology which combines the characteristics of direct extrusion and two pass equal channel extrusion has been put forward. The experiments of ES process and direct extrusion have been performed, and direct extrusion and ES dies suitable for industrial horizontal extruder have been designed and manufactured. Three-dimensional thermomechanical finite element models and conditions of the ES process and direct extrusion have been established. Extrusion forces and accumulated strains and stresses and temperatures evolution of the ES process have been obtained. The loads of the ES process increase obviously compared with those of direct extrusion. Maximum temperatures during the ES process are higher than those of direct extrusion. The computer simulation analyses of stress state for the billets reveal that part of the billet is exerted in four directions of compressive stress. The ES process could cause cumulative strains and shear stress in magnesium alloy billets than direct extrusion. Therefore, more grain refinements could be achieved. Based on the microstructure observations of center positions for the ES process and direct extrusion rods, grains have been effectively refined with extrusion temperature. It is found that there are many similarities between finite element simulation results and experimental results.     

Influence factors on natural frequencies of composite materials

Frontiers of Mechanical Engineering - Compared with traditional materials, composite materials have lower specific gravity, larger specific strength, larger specific modulus, and better...     

滚切式双边剪剪刃间隙调整的研究

滚切式双边剪剪刃间隙是影响剪切质量的的最重要因素之一.为了对剪刃间隙进行有效调整,在分析了滚切式双边剪剪刃间隙调整原理的基础上,重点研究了剪刃间隙调整过程中出现的剪刃间隙平行问题、剪刃间隙调整范围问题、剪刃间隙调整装置编码器故障及剪刃间隙与钢板厚度的关系,提出了这些问题所产生的故障机理及处理方法.