The elastic spring behavior of a rhombus frame constructed from non-prismatic beams under large deflection

The spring behavior due to large deflection of a flexible rhombus frame with rigid joints is studied in this paper. The system consists of two equal and opposite diagonal forces that act on two opposite corners of a rhombus frame with a given apex angle γ. The frame sides have a rectangular cross-section and are non-prismatic due to tapering in the section's dimensions. The relations between the large displacement at the corners and the applied forces are obtained using a new robust numerical technique. The technique is based on representing the angular deflection of the side beam by a polynomial on the position variable along the deflected beam axis. The polynomial coefficients are obtained through a numerical optimization procedure based on minimizing the residual error and satisfying the boundary conditions. A classical numerical integration technique is used to verify some of the results obtained by the proposed technique. The frame spring behavior is investigated for different taper ratios and apex angles. The results are transformed into regression relations to utilize its implementation in design and analysis.     

非局域非线性介质中厄米高斯光束的变分解

非局域非线性介质中的薛定谔方程很难用传统的方法得出精确解析解,利用变分法系统研究了强非局域非线性介质中厄米高斯光束的传输问题。通过对非线性介质中响应函数的展开,使得非线性薛定谔方程得以简化,求解出高阶高斯光束孤子解。利用数值模拟研究了厄米高斯光束在介质中传输时束宽不变的问题,结果显示当非局域程度非常大时,解析解非常接近数值解。     

Shakedown analysis of beams using nonlinear kinematic hardening materials coupled with continuum damage mechanics

The nonlinear kinematic hardening theory of plasticity based on the Armstrong-Fredrick model and isotropic damage was used to evaluate the cyclic loading behavior of a beam under the axial, bending, and thermal loads. Damage and inelastic deformation were incorporated and they were used for the beam shakedown and ratcheting analysis. The beam material was assumed to follow the nonlinear strain hardening property coupled with isotropic damage. The effect of the damage phenomenon coupled with the elastoplastic nonlinear kinematic hardening was studied for deformation and load control loadings. The Bree's diagram was obtained for two different types of loading, and all numerical results confirmed the reduction of the safe loading domain due to material damage.     

高阻尼多层U形波纹管轴向等效刚度的有限元分析

运用ADINA有限元软件对高阻尼多层u形波纹管的轴向等效刚度进行了分析。考虑几何非线性、材料非线性、层间接触非线性以及夹层阻尼材料特性对波纹管轴向等效刚度的影响,其分析结果对含夹层阻尼波纹管的设计与研究有一定的参考意义。     

水轮发电机转子非线性电磁振动的幅频特性

分析了非线性电磁力和机械不平衡力对水轮发电机转子动态特性的影响。采用解析方法得到了偏心转子的非线性电磁力,建立了动态偏心条件下转子的机电耦联动力学方程。采用复变函数将系统的动力学方程简化,利用谐波平衡法分析了系统的稳态解,得到了系统的幅频响应。结果表明,动态偏心条件下水轮发电机转子的电磁振动呈现非线性特征,幅频曲线在一定条件下将出现跳跃现象,系统呈现明显的软特性。     

Nonlinear saturation controller for vibration supersession of a nonlinear composite beam

In this paper, a study for nonlinear saturation controller (NSC) is presented that used to suppress the vibration amplitude of a structural dynamic model simulating nonlinear composite beam at simultaneous sub-harmonic and internal resonance excitation. The absorber exploits the saturation phenomenon that is known to occur in dynamical systems with quadratic non-linearities of the feedback gain and a two-to-one internal resonance. The analytical solution for the system and the nonlinear saturation controller are obtained using method of multiple time scales perturbation up to the second order approximation. All possible resonance cases were extracted at this approximation order and studied numerically. The stability of the system at the worst resonance case (Ω = 2ω _s and ω _s = 2ω _c ) is investigated using both frequency response equations and phase-plane trajectories. The effects of different parameters on the system and the controller are studied numerically. The effect of some types of controller on the system is investigated numerically. The simulation results are achieved using Matlab and Maple programs.     

Elastoplastic response and recoil of lattice structures under hyperbolic hardening

Elastoplastic response and recoil analyses for hexagonal honeycomb lattice structures are presented when hardening is described by a hyperbolic law. By exploiting the translational symmetry of the problem, the analysis is reduced to that of a thin beam under combined bending and axial loading coupled with the kinematics of lattice deformation and its relationship with cell wall deformation. A closed-form solution for the load-curvature relationship of a beam with rectangular cross-section is obtained. A systematic study of beam response, as the stress-strain curve of the constituent material approaches an ideal elastic-perfectly plastic law, is presented. The analysis is then applied to an infinite honeycomb sheet under remote tensile load to obtain the apparent non-linear structural response. Apparent recoil of such a lattice material upon unloading is also calculated in closed form, when unloading is assumed to take place along a linear stress-strain curve. The analytical results are in excellent agreement with the numerical calculations.

     

管内可控铰接柔性结构双层接触非线性力学分析

管内可控万向铰接柔性细长结构是超短半径侧钻水平井的特有结构。考虑可控万向铰结构中的机构问题、结构不连续和开槽不完整结构的三体两层接触问题,将空间梁单元、万向铰单元、刚性梁单元和梁梁接触单元相结合,建立了管内可控万向铰接柔性结构双重接触非线性有限元模型及数值计算方法。与有解析解的算例进行比对,计算结果吻合较好。通过对超短半径水平井造斜钻进时的柔性钻具进行力学分析,得到了柔性钻具受力变形状态、载荷传递规律及其与井壁之间的接触力分布规律。     

200MW机组转子-轴承系统非线性动力学特性分析

利用大型有限元计算软件ADiNA对某国产200MW汽轮发电机组转子-轴承系统的非线性动力学特性进行了初步分析。通过ADINA程序提供的用户接口将滑动轴承的非线性油膜力进行了考虑,计算中只计入了电机转子两端轴承的非线性影响。为了验证方法的有效性,以单盘柔性转子-轴承系统为对象,将计算结果与数值积分方法的结果进行了对比,表明该处理方法有很高的计算精度。最后,将对200MW机组转子-轴承系统的非线性动力学特性分析结果与线性分析结果也进行了比较,证明利用ADINA程序对大型机组转子-轴承系统的菲线性动力学特性进行分析是可行的。     

Nonlinear model identification of a frictional contact support

Accurate predictions of a structure dynamics require precise modeling of its boundary conditions including any nonlinear effects. This paper investigates the behavior of frictional supports that are examples of boundary conditions exhibiting nonlinear effects, such as stiction and slip phenomena, depending on the structure vibration amplitudes. The dependency of restoring forces in a frictional contact to the vibration amplitude level is identified in this study using experimental observations. In an experimental case study measured responses of a beam fixed at one end and frictionally supported at the other end were expanded using corresponding nonlinear normal modes of the structure and a reduced order model of the continuous system containing dominant nonlinear effects of the contact was obtained. The obtained discrete model constitutes bases for identification of restoring forces in the contact interface using force state mapping. The identified nonlinear restoring forces are then employed to specify parameters of a predictive contact model for the boundary support. The obtained contact model is capable of predicting damping and softening effects due to micro/macro-slippage and accurately regenerates the experimental results at various response levels.     

Cold drawing of regular polygonal tubular sections from round tubes

An analytical solution is obtained for the problem of cold drawing through flat idle rolls of regular polygonal metal tubular sections from round tube. The solution is based on obtaining a compatible velocity field that satisfies kinematic conditions to yield the strain-rate components. The stresses are obtained by combining the material constitutive law with Levy–Mises flow rule and integrating the equations of equilibrium. The solution is applied to the case of a low-carbon steel standard round pipe to investigate the effects of drawn section shape, friction at the roll interface, roll radius and wall thickness on the roll load and drawing force. The results obtained have shown that for different section shapes the roll load and drawing force decrease with the increase of the number of sides and increase with the decrease of corners radius. Surface friction has no appreciable effect on the loads which allows dry drawing. An increase in the roll radius increases the roll load but the drawing force remains unchanged. Increasing the wall thickness does not proportionally increase the roll load and drawing force; the tube wall behaves as a thin shell subjected to biaxial combined membrane and bending stresses.     

电磁振动给料器给料速度的研究

针对电磁振动给料器在输送不同性质物料时存在调整困难的问题,将物料滑移和抛掷理论应用到电磁振动给料器的设计与调整中,开展了电磁振动给料器力学模型分析,提出了根据振幅选择合适工作点的方法,在对物料受力情况进行分析的基础上,着重研究了振幅与物料运动方式之间的关系,并建立了物料的运动方程,通过求解方程得到了物料在正向滑移、正反向滑移和抛掷等3种供料方式下的平均速度与振幅之间的关系。研究结果表明,电磁振动给料器的振幅不仅决定物料的运动方式,而且对送料速度也有很大影响。     

电动汽车车身的回传射线矩阵刚度链分析方法

基于LifeDrive纯电动汽车模块化结构形式,通过拓扑优化得到一款纯电动汽车车架结构;建立了基于梁单元的车架结构回传射线矩阵计算模型;由模型得到车架梁单元尺寸以及车身与车架之间的多个耦合力,以更合理的刚度链方法优化了车身简化模型的主断面参数;利用有限元方法计算了车身与车架的承载度。结果证明设计的车架与车身结构满足目标承载度和刚度性能的要求,该方法为非承载式电动汽车车身及车架的概念设计提供了参考。     

Analytical studies for buckling and vibration of weld-bonded beam shells of rectangular cross-section

An approach to analytical solution is presented for vibration and buckling of thin-walled tubular beam shells typical of automotive structures, which are fabricated by joining sheet metal stampings along the two longitudinal edges with periodic spot welds, adhesive bonding, or combination of spot welds and bonding, known as weld bonding. Solutions are obtained for such beam shells of rectangular cross-section with two opposite ends simply supported. The beam shell is modeled as an assembly of the constituent walls and Levy-type formulation is used to obtain a series solution for the transverse displacement of each of the walls. The challenge of expressing the discrete point support conditions at the spot welds by a continuous function is addressed using the flexibility function approach used in literature. The flexibility function, used earlier to represent the flexibility distribution along weld-bonded edges of rectangular plates with periodic spot welds, is used here. The characteristic equations are obtained by satisfying the displacement, slope, shear, and moment equilibrium at the mating edges of the walls including the two weld-bonded edges and the compatibility conditions at the spot-weld locations. This approach to analytical solution, described here for thin-walled beam shells of rectangular cross-section, can be suitably adopted for more general cross-sections and joints along non-symmetric edges. A parametric study is undertaken to show the effect of aspect ratio of the beam shell, adhesive joint parameters, and the number of spot welds on the elastic buckling loads and the natural frequencies. Such parametric studies can be of use to designers in arriving at an optimal joint configuration of weld-bonded beam shells from buckling and vibration considerations.     

Simulation of Spindle Units Running on Rolling Bearings

This paper presents a general approach to solution of the complex simulation problem of spindle units (SUs) running on rolling bearings (ball bearings and roller bearings) and proves the necessity of making a complex analysis of their nonlinear tribo-mechanical properties at the development stage. For doing this, we apply SU beam analytical diagrams and develop a complex mathematical model of SUs, which incorporates theparticular models, e.g. elastic-deformation, dynamic and heat models, and the model of the bearing fatigue life. To facilitate practical analysis in design, we develop software and demonstrate its application by examples of the comparative analysis the typical structures of SUs.     

Mathematical modeling of the thermal relaxation of nominally flat surfaces in contact using fractal geometry: Maxwell type medium

This work aims at studying the stress relaxation behavior of a nominally flat (rough) surface of a viscoelastic material in contact with a rigid half space. The effect of temperature will be included through the concept of activation energy using Arrhenius's equation. A synthesized Cantor-Borodich (C_B) profile is used to construct the rough surface. C_B profile has two scaling parameters, a and b, and different heights h_i for each generation of asperities. This simple model is applicable for fractal surfaces in which a single exponent (the fractal dimension) is enough to describe their quality.The surfaces in contact are viscoelastic, and they are assumed to behave according to the linear Maxwell model. An asymptotic power law is obtained, which relates the force and the bulk temperature acted on the punch to its approach. This model is valid only when the approach between the punch and the half space is in the range of the roughness size. The proposed model admits an analytical solution for the case when the deformation is linear thermo-viscoelastic. The obtained model shows a good agreement when compared with the experimental results obtained by Handzel-Powierza et al. [Handzel-Powierza Z, Klimczak T, Polijaniuk A. On the experimental verification of the Greenwood-Williamson model for the contact of rough surfaces. Wear 1992;154:115-24].     

Dynamic response analysis of a cantilevered beam due to an elastic impact

The beam structure models with impact or contact parts under impact forces have been applied to the design of mechanical and electronic accessories. Switches, pick-ups and sensors are the typical examples of the structure to be designed to colliding with other parts. The damping characteristics and stiffness of an impacter have a great effect on dynamic responses of structures subjected to impact forces. Since the response characteristics of structures have an effect on the generation of impact forces, both theoretical and experimental investigations for the dynamic relationships between the impacter and impact mechanism are required for the structural design to reduce impact forces or eliminate unwanted vibration modes. In this paper, in order to examine the relationship between the changes of the stiffness and damping of an impacter and the variations of the dynamic characteristics of the impact model of a cantilevered beam with an impacter, the impact force of the impacter and response characteristics of the cantilevered beam were analyzed by both numerical simulation and experiments. Since the stiffness and damping of the impacter are highly nonlinear, the contact model using revised Hertz-model was established by experiments. Also, the results of numerical analyses for the dynamic response and impact force of a cantilevered beam with an impacter have a good agreement with experimental results. It is believed that the mathematical model and the analytical method presented here can be used for the design analysis and the improvement of performances of the beam-shape switches and pickup devices.     

Investigation for dimension effect on mechanical behavior of a metallic curved micro-cantilever beam

This paper is aimed at studying the mechanical behaviors such as maximum stress, contact force, and fatigue life of a special designed metallic curved micro-cantilever beam, using analytical, numerical (FEM), and experimental methods. This micro-beam is an applicable specimen generally used in MEMS devices. The focus is at determining the dimensions which are very important in functional conditions, reliability evaluation, and durability of this specimen and at finding a guideline for optimum design. Various types of samples that have different dimensions have been simulated and some specific specimens requested to be fabricated by a manufacturing company. In our research work, the material of the specimen is assumed to be of metallic alloys, which have good mechanical and electrical properties. Also, the structure of the specimen has a special shape and includes some fingers which have effect on mechanical behavior and electrical conductivity. In experimental method, with specified boundary conditions, mechanical loading is applied to the beam by simple but accurate methods. In analytical approach, after some mathematical calculations, for a curved cantilever beam, the equations related to the mechanical behaviors are obtained. Finally, the results obtained from the foregoing methods are compared with each other and the most fundamental effective dimension parameter on mechanical behavior of this special designed metallic curved micro-cantilever beam is determined.     

Dynamic plastic behavior of a free–free beam striking the mid-span of a clamped beam with shear and membrane effects considered

Recently Yu et al. (Int. J. Solids Struct. 38 (2001) 261) made a study on the dynamic behavior of a flying free–free beam striking the tip of a cantilever beam using the rigid, perfectly plastic (r-p-p) material model. Later, also based on the r-p-p material model Yang and Yu (Mech. Struct. Mach. 29 (2001) 391) analyzed another impact problem of a free rotating hinge beam striking a cantilever beam. Both of these studies ignored the finite deflection effects on the plastic behavior of the colliding beams. However if the free–free beam strikes a clamped beam, the influence of finite-deflections, or, geometric changes, must be retained in the governing equation if the maximum permanent transverse displacement of the clamped beam exceeds the corresponding beam thickness. The problem becomes more interesting since the deformation mechanisms of the beam system and the partitioning of energy dissipation in the beams are significantly different from those predicted by ignoring the influence of membrane forces. Accordingly the failure modes of the structure are different.In the present paper, a theoretical model based on the r-p-p material idealization is proposed to simulate the dynamic behavior when the mid-point of a translating free–free beam impinging on the mid-span of a clamped beam with the beam axes perpendicular to each other. The plastic behavior of the beam system is explored with shear sliding and finite deflection effects taken into account. The final deflection, the dissipation of energy within the two beams after impact and the influence of the structural and material parameters are discussed. It is shown that membrane force plays an important role during the response process, especially when the deflection is of the same order as the thickness of the clamped beam.