Experimental analysis and modeling of biaxial mechanical behavior of woven composite reinforcements

This paper presents experimental studies on the mechanical behavior of fiber fabrics using a biaxial tensile device based on two deformable parallelograms. The cross-shaped specimens are well adapted to fabrics because of their lack of shear stiffness. Tension versus deformation curves, for different strain ratios, are obtained in the case of composite woven reinforcements used in aeronautic applications. It is shown that the tensile behavior of the fabric is strongly nonlinear due to the weaving undulations and the yarn contraction, and that the phenomenon is clearly biaxial. A constitutive model is described and identified from the experimental data. The essential role played by the yarn crushing will be pointed out.     

Nonlinear Stiffness of a Magneto-Rheological Damper

The last decade has witnessed an important role of magneto-rheological dampers in the semi-active vibration control on the basis of empirical models. Those models established by fitting experimental data, however, do not offer any explicit expressions for the stiffness and the damping of magneto-rheological dampers. Hence, it is not easy for engineers to get any intuitive information about the effects of stiffness and damping of a magneto-rheological damper on the dynamic performance of a controlled system. To manifest the nonlinear properties of a magneto-rheological damper, this paper presents the hysteretic phenomena and the additional nonlinear stiffness of a typical magneto-rheological damper in terms of equivalent linear stiffness and equivalent linear damping. Then, it gives a brief discussion about the effect of nonlinear stiffness on the vibration control through the numerical simulations and an experiment for the semi-active suspension of a quarter car model with a magneto-rheological damper installed. Both numerical simulations and experimental results show that the additional nonlinear stiffness in the magneto-rheological damper is remarkable, and should be taken into consideration in the design of vibration control.     

基于实验的心肌被动力本构模型

在狗心脏外科手术和心肌力学性能试验的基础上,对心肌力学性能实验数据进行处理和拟合,并应用有限元方法对心肌的单拉实验、松弛实验进行数值模拟和计算. 得到不同心肌位点的本构模型的非线性弹性和黏性参数,从而发展了心肌被动力的非线性黏弹性本构模型,体现了心脏力学行为的非均匀性和黏弹性. 在理论模型和试验数据的基础上,开发了有限元软件ABAQUS的VUMAT材料子程序,应用于数值心脏的仿真研究.      

鲫鱼皮肤和肌肉的力学性能研究

鱼在水中游动时,参与鱼体弯曲变形的组织和器官与水媒介相互作用,形成了不同的游动模式和变形方式。为了更好地理解鱼体变形机制并为今后的流固耦合计算提供基础实验数据,本文采用万能试验机进行单轴拉伸试验,对鲫鱼皮肤和肌肉等生物材料的力学性能进行研究。通过破坏实验的方式确定其杨氏模量,通过松弛实验的方式确定其归一化松弛函数。针对皮肤和肌肉的生物材料粘弹性性质,给出本构方程。通过简化为标准线性固体模型进行讨论,得到的结论是:鲫鱼游动过程中以很小的能量损耗为代价,增加了其有效刚度。     

Tuning methods for tuned inerter dampers coupled to nonlinear primary systems

This study develops displacement- and kinetic energy-based tuning methods for the design of the tuned inerter dampers (TIDs) coupled to both linear and nonlinear primary systems. For the linear primary system, the design of the TID is obtained analytically. The steady-state frequency–response relationship of the nonlinear primary system with a softening or hardening stiffness nonlinearity is obtained using the harmonic balance (HB) method. Analytical and numerical tuning approaches based on HB results are proposed for optimal designs of the TID to achieve equal peaks in the response curves of the displacement and the kinetic energy of the primary system. Via the developed approaches, the optimal stiffness of the TID can be obtained according to the stiffness nonlinearity of the primary system and the inertance of the absorber. Unlike the linear primary oscillator case, for a nonlinear primary oscillator the shape of its resonant peaks is mainly affected by the damping ratio of the TID, while the peak values depend more on the stiffness ratio. The proposed designs are shown to be effective in a wide range of stiffness nonlinearities and inertances. This study demonstrates the benefits of using inerters in vibration suppression devices, and the adopted methods are directly applicable for nonlinear systems with different types of nonlinearities.

     

基于非线性吸能机理的涡激振动减振理论与实验研究

流致振动现象广泛存在于机械、航空、土木和石油等重要工程领域, 为防止工程结构因流致振动行为而造成疲劳破坏, 有必要对稳定性、动力学响应及其振动控制做深入研究. 本文提出了一种由弹簧和质量块构成的非线性吸能器(nonlinear targeted energy transfer, NTET), 研究了该非线性吸能器对弹性支承圆柱体涡激振动的被动控制影响机制. 基于能量法推导了圆柱体涡激振动非线性被动控制的耦合动力学方程, 通过设计非线性弹簧?质量块构型的NTET, 进一步开展了涡激振动控制的实验研究, 并与理论预测结果进行了较好的对比, 获得提升涡激振动控制效果的最佳参数值. 研究发现, NTET的质量、弹簧刚度以及弹簧预应力等参数会对涡激振动控制效果产生显著的影响. 本文研究结果表明, 该耦合系统中圆柱体和NTET均表现出周期性的稳态振动响应, NTET质量的改变会显著影响系统的耦合频率. 在无预应力状态下, NTET质量越大、刚度越小时, 有更好的减振效果. 当弹簧预应力逐渐增大时, NTET的非线性刚度逐渐变弱, 会降低涡激振动控制性能. 参数分析表明: 随着涡激振动控制性能的提升, 圆柱体的振幅逐渐较小, NTET的振幅逐渐增大, 能量传递效率逐渐提高. 研究结果可为工程中涡激振动控制策略的高效设计提供有用的理论支撑和实验数据.      

Hysteretic linear and nonlinear acoustic responses from pressed interfaces

An analysis of the linear and nonlinear acoustic responses from an interface between rough surfaces in elastoplastic contact is presented as a model of the ultrasonic wave interactions with imperfect interfaces and closed cracks. A micromechanical elastoplastic contact model predicts the linear and second order interfacial stiffness from the topographic and mechanical properties of the contacting surfaces during a loading–unloading cycle. The effects of those surface properties on the linear and nonlinear reflection/transmission of elastic longitudinal waves are shown. The second order harmonic amplitudes of reflected/transmitted waves decrease by more than an order of magnitude during the transition from the elastic contact mode to the elastoplastic contact mode. It is observed that under specific loading histories the interface between smooth surfaces generates higher elastoplastic hysteresis in the interfacial stiffness and the acoustic nonlinearity than interfaces between rough surfaces. The results show that when plastic flow in the contacting asperities is significant, the acoustic nonlinearity is insensitive to the asperity peak distribution. A comparison with existing experimental data for the acoustic nonlinearity in the transmitted waves is also given with a discussion on its contact mechanical implication.     

层板复合材料的疲劳剩余刚度统计分布模型

在分析现有关于层板复合材料疲劳剩余刚度衰退模型的基础上，根据层板复合材料在疲劳载荷作用下刚度衰退变化的现象，研究了疲劳载荷对层板复合材料刚度衰退的影响，建立了一个新的、更为合理的用于描述层板复合材料在常幅疲劳载荷作用下的刚度衰退模型，导出了剩余刚度统计分布的表达式，给出了确定模型参数的方法。为验证该模型，设计了几组测试实验，并利用试验结果对模型参数进行了估计。利用该统计分布模型，可以预报层板复合材料在给定应力水平的疲劳载荷作用下循环指定周次时剩余刚度的统计分布。实验数据表明，理论预报和实验结果符合得是很好的。     

Dramatically stiffer elastic composite materials due to a negative stiffness phase?

Composite materials of extremely high stiffness can be produced by employing one phase of negative stiffness. Negative stiffness entails a reversal of the usual codirectional relationship between force and displacement in deformed objects. Negative stiffness structures and materials are possible, but unstable by themselves. We argue here that composites made with a small volume fraction of negative stiffness inclusions can be stable and can have overall stiffness far higher than that of either constituent. This high composite stiffness is demonstrated via several exact solutions within linearized and also fully nonlinear elasticity, and via the overall modulus tensor estimate of a variational principle valid in this case. We provide an initial discussion of stability, and adduce experimental results which show extreme composite behavior in selected viscoelastic systems under sub-resonant sinusoidal load. Viscoelasticity is known to expand the space of stability in some cases. We have not yet proved that purely elastic composite materials of the types proposed and analyzed in this paper will be stable under static load. The concept of negative stiffness inclusions is buttressed by recent experimental studies illustrating related phenomena within the elasticity and viscoelasticity contexts.     

Time-dependent behavior of passive skeletal muscle

An isotropic three-dimensional nonlinear viscoelastic model is developed to simulate the time-dependent behavior of passive skeletal muscle. The development of the model is stimulated by experimental data that characterize the response during simple uniaxial stress cyclic loading and unloading. Of particular interest is the rate-dependent response, the recovery of muscle properties from the preconditioned to the unconditioned state and stress relaxation at constant stretch during loading and unloading. The model considers the material to be a composite of a nonlinear hyperelastic component in parallel with a nonlinear dissipative component. The strain energy and the corresponding stress measures are separated additively into hyperelastic and dissipative parts. In contrast to standard nonlinear inelastic models, here the dissipative component is modeled using an evolution equation that combines rate-independent and rate-dependent responses smoothly with no finite elastic range. Large deformation evolution equations for the distortional deformations in the elastic and in the dissipative component are presented. A robust, strongly objective numerical integration algorithm is used to model rate-dependent and rate-independent inelastic responses. The constitutive formulation is specialized to simulate the experimental data. The nonlinear viscoelastic model accurately represents the time-dependent passive response of skeletal muscle.     

On the Need for Control of Nonlinear Oscillations in Machine Systems

Oscillations in machines are invariably nonlinear. This is either because of inertial coupling effects between different motions of the moving components, material and constitutive phenomena giving rise to stiffness modifications, nonlinear dissipation mechanisms, large deflections, or, as is most likely, some sort of combination of all of these. The net effect of nonlinear vibrations is that at best the machine may well behave a little differently from the way the designer intended, or at worst, in a manner which renders it completely unsuitable for the job. The extent of such problems depends on the nature and the scale of the nonlinearities that are present but it is safe to say that nonlinear oscillations can rarely be completely overlooked in precision machinery analysis and design. The unifying theme in this paper is pendulum motion, firstly in the case of a mobile gantry crane for container stacking where we wish to minimise such motion and converge on a target, and then secondly in the case of a vibration absorber in which we choose to initiate pendulum motion within a special absorber, for the purposes of vibration minimisation. The third example involves the potential for pendulum motion at a very much larger scale and summarises the main control problem that is likely to be encountered in a fully deployed momentum exchange propulsion tether operating in space. The paper discusses the general mathematical issues that pertain to pendulum motion in each of the three cases. This motion is investigated initially in the context of the mobile gantry crane, in the form of a basic three dimensional dynamical model. A feedback linearised controller is shown to offer some advantages for the control of such a system and then a simulation based on data from a practical implementation of this within a real-time control system on a 1/10 laboratory scale model is discussed. It is recalled that the real-time effectiveness of the controller can be compromised by relatively slow sensing and data logging hardware but that despite this some useful performance gains can still be obtainable using this sort of control strategy. The second example comprises an autoparametric vibration absorber and here it is shown how even a simple hunting controller can exploit the mode-locking and wide detuning region effects inherent in autoparametric systems. Further experimental results are discussed in the case of a hunting controller for detuning a vertically oriented parametrically excited pendulum in order to exploit and enhance the powerful and persistent absorption available during autoparametric interaction. The paper concludes with a summary review of the third problem in which the theoretical attitude dynamics of a motorised momentum exchange space propulsion tether are summarised and it is shown that they need to be controlled for reliable and optimal payload velocity boost from both circular parking orbits and elliptical transfer orbits about the Earth.     

钢筋混凝土空间杆件精细非线性分析模型

针对现有钢筋混凝土空间杆件非线性分祈模型进行了评还,应用结构力学方法推导得到了沿秆长配筋分布均匀的钢筋混凝土空间杆件的非线性单元刚度矩阵,建立了应用高斯积分点所在截面的非线性性质描述钢筋混凝土空间杆件非线性的计算过程。对于沿杆长配筋分布不均匀的杆件,根据其实际情况,将其细分为两段或三段沿杆长配筋分布均匀的杆段,以沿杆长配筋分布均匀的钢筋混凝土空间杆件非线性分析模型为基础,建立了沿杆长配筋分布不均匀的空间杆件的非线性分析模型。最后,给出了两个算例。就本文方法及程序的计算结果与模型结构振动台试验结果、常规非线性杆件模型的计算结果进行了比较。     

Modeling the dispersion effects of contractile fibers in smooth muscles

Micro-structurally based models for smooth muscle contraction are crucial for a better understanding of pathological conditions such as atherosclerosis, incontinence and asthma. It is meaningful that models consider the underlying mechanical structure and the biochemical activation. Hence, a simple mechanochemical model is proposed that includes the dispersion of the orientation of smooth muscle myofilaments and that is capable to capture available experimental data on smooth muscle contraction. This allows a refined study of the effects of myofilament dispersion on the smooth muscle contraction. A classical biochemical model is used to describe the cross-bridge interactions with the thin filament in smooth muscles in which calcium-dependent myosin phosphorylation is the only regulatory mechanism. A novel mechanical model considers the dispersion of the contractile fiber orientations in smooth muscle cells by means of a strain-energy function in terms of one dispersion parameter. All model parameters have a biophysical meaning and may be estimated through comparisons with experimental data. The contraction of the middle layer of a carotid artery is studied numerically. Using a tube the relationships between the internal pressure and the stretches are investigated as functions of the dispersion parameter, which implies a strong influence of the orientation of smooth muscle myofilaments on the contraction response. It is straightforward to implement this model in a finite element code to better analyze more complex boundary-value problems.     

Simulation of metal-forming processes by the finite element method

An algorithm to model the contact, with friction, between a deformable body and rigid surfaces is presented. The method shown is to integrate the equation of motion in the actual reference frame, taking into account the proper constraint set induced by the contact conditions; moreover, the various terms of the 3D stiffness tangent matrix are calculated. The model has been implemented in an FEM code suitable for dealing with finite deformation problems, and the results obtained in the simulation of a bulge-test case and a deep-drawing test are presented and compared with experimental data.     

LOW-FREQUENCY RESPONSES OF NONLINEARLY MOORED VESSELS IN RANDOM WAVES: COUPLED SURGE,PITCH AND HEAVE MOTIONS

The responses of a multi-degree-of-freedom model of a moored vessel are analysed, accounting for the hydroelastic interaction between the nonlinear wave hydrodynamics and the nonlinear mooring stiffness. A two-scale perturbation method developed by Sarkar & Eatock Taylor to determine low-frequency hydrodynamic forces on a single-degree-of-freedom model of a nonlinearly moored vessel has been extended to analyse the nonlinear multi-degree-of-freedom dynamics of the system. Surge, heave and pitch motions are considered. The perturbation equations of successive orders are derived. To illustrate the approach, semi-analytical expressions for the higher-order hydrodynamic force components have been obtained for a truncated circular cylinder in finite water depth. In addition to conventional quadratic force transfer functions, a new type of higher-order force transfer function is introduced. This is used to characterize the hydrodynamic forces on the vessel which arise due to nonlinearity of the mooring stiffness. These are a type of radiation force, generated by the nonlinear interaction of the fluid–structure coupled system. Based on a Volterra series model, the power spectral densities of the new higher-order forces are then derived for the case of Gaussian random seas. It is shown that the additional response arising due to nonlinear dynamics of the mooring system can significantly contribute to low-frequency drift forces and responses of the vessel. Unlike conventional non-Gaussian second-order forces which are quadratic transformations of a Gaussian random process, the new higher-order forces arising due to the nonlinear mooring stiffness are polynomials of a Gaussian random process (up to fourth order for a Duffing oscillator model). This may significantly influence the extreme responses.     

Nonlinear and viscous effects on wave propagation in an elastic axisymmetric vessel

In this paper, a power series and Fourier series approach is used to solve the governing equations of motion in an elastic axisymmetric vessel with the assumption that the fluid is incompressible and Newtonian in a laminar flow. We obtain solutions for the wave speed and attenuation coefficient, analytically where possible, and show how these differ under a number of different conditions. Viscosity is found to reduce the wave speed from that predicted by linear wave theory and the nonlinear terms to increase the wave speed in comparison to the linear solution. For vessels with a wall stiffness in the arterial range, the reduction in the wave speed due to the viscous terms is approximately 10% and the increase due to the nonlinear terms is approximately 5%. This difference between the linear and nonlinear wave speeds was found to be largely constant irrespective of the number of terms considered in the power series for the velocity profile. The linear wave speed was found to vary weakly with stiffness, whilst the nonlinear wave speed was found to vary significantly with the stiffness, especially at low values of stiffness. The 10% variation in the wave speed due to the viscous terms was found to be constant with wall stiffness whilst the 5% variation due to the nonlinear terms was found to vary with wall stiffness. The importance of the number of terms considered in the power series is discussed showing that only a relatively small number is required in the viscous case to obtain accurate results.     

两种典型螺栓连接结构的刚度特性比较研究

针对法兰对接和径向套接两种典型舱段螺栓连接形式,基于有限元静刚度计算、动力学简化建模、冲击响应特性分析及结构冲击试验,系统研究了两种连接形式的轴向刚度特性及其对动力学冲击响应的影响.有限元静刚度分析揭示了法兰对接与径向套接的轴向拉压刚度分别是非对称的和对称的,而法兰对接的平均刚度更大.之后,为两种连接形式建立了统一的动力学模型,证明非对称的轴向拉压刚度导致结构在受到横向载荷作用时会产生附加的耦合轴向振动,并且利用高精度幂函数拟合刚度跳变,得到耦合轴向振动频率是弯曲振动频率的二倍的结论.最后,通过冲击动力学试验证明了法兰对接存在二倍频的耦合轴向振动,而径向套接则不存在该耦合振动.径向套接虽然一阶频率较低,但阻尼效果更好.     

复合材料层板基于剩余刚度比的剩余强度模型

本文从唯裂 学的观点提出了一个复合材料疲劳剩余刚度衰退模型,根据该模型导出了基于疲劳乘余刚度比的复合材料层合板疲劳剩余强度概率分布模型,给出了确定该模型中各参数的计算方法,根据该模型可预报复合材料层合板在某一应力水平的疲劳载荷作用下疲劳剩余刚度比为某一确定值时的疲劳剩余强度概率分布。为验证该模型的合理性,用典型复合材料层合板做了几组疲劳实验,并用实验数据对模型中的参数进行了估计,计算结果证明,该模型预报的疲劳剩余强度概率理论分布与实验结果符合较好。     

Magnetoelastic interactions in a soft ferromagnetic body with a nonlinear law of magnetization: Some applications

Linearized equations and boundary conditions of a magnetoelastic ferromagnetic body are obtained with the nonlinear law of magnetization. Magnetoelastic interactions in a multi-domain ferromagnetic materials are considered for magneto soft materials, i.e. the case when the magnetic field intensity vector and magnetization vector are parallel. As a special case, the following two problems are considered: (1) the magnetoelastic stability of a ferromagnetic plate-strip in a homogeneous transverse magnetic field; (2) the stress–strain state of a ferromagnetic plane with a moving crack in a transverse magnetic field. It is shown that the modeling of magnetoelastic equations with a nonlinear law of magnetization provides qualitative and quantitative predictions on physical quantities including critical loads and stresses. In particular, it is shown that the critical magnetic field in plate stability problems found with the nonlinear law of magnetization is in better agreement with the experimental finding than the one found with a linear law. Furthermore, it is also shown that the stress concentration factor around a crack predicted with the nonlinear law of magnetization is more accurate than the one obtained with a linear counterpart. Numerical results are presented for above mentioned two problems and for various forms of nonlinear laws of magnetization.