滞回摩擦型调谐惯质阻尼器结构隔震研究

本文研究一种新型非线性阻尼器——滞回摩擦型调谐惯质阻尼器(HFTID)在工程结构抗震控制中的应用。HFTID由调谐惯质阻尼器(TID)和滞回弹簧摩擦元件并联组成。首先通过谐波平衡方法推导了HFTID单自由度系统力与位移的传递率。然后对HFTID进行了最佳调谐参数优化,得到HFTID最优参数的近似表达式,比较了HFTID和TID振动控制系统的减振效果。结果表明,HFTID相比TID可以进一步降低振动控制系统的传递率。最后,以一栋多层隔震结构为例,将HFTID与TID的隔震效果进行了对比,结果表明,HFTID相比TID在降低地震响应峰值和均方根值方面具有更大优势,验证了HFTID在降低地震响应方面的有效性和实用性。HFTID在建筑和桥梁结构抗震、车辆悬挂系统和其他机械隔震问题上具有潜在的应用前景。     

Stick-slip chaos detection in coupled oscillators with friction

We consider two coupled oscillators with negative Duffing type stiffness which are self (due to friction) and externally (harmonically) excited. The fundamental solutions of the homoclinic orbit are constructed. Then, the Melnikov–Gruendler approach is used to define the Melnikov’s function including smooth and stick-slip chaotic behaviour. Theoretical considerations are supported by numerical examples.     

A design concept with a displacement dependent semi-active hydraulic damper for energy dissipation

Experimental Techniques -     

Study of oscillators with a non-negative real-power restoring force and quadratic damping

Oscillators with a non-negative real-power restoring force and quadratic damping are considered in this paper. The equation of motion is transformed into a linear first-order differential equation for the kinetic energy. The expressions for the energy-displacement function are derived as well as the closed form exact solutions for the relationship between subsequent amplitudes. They are expressed in terms of incomplete Gamma functions. On the basis of these results, expressions for the phase trajectories and the loci of maximal velocities are obtained. It is also demonstrated that the time difference between two consecutive relative maxima and minima of the displacement can both increase and decrease with time.     

Noise-induced chaos in the elastic forced oscillators with real-power damping force

The chaotic behavior of the elastic forced oscillators with real-power exponents of damping and restoring force terms under bounded noise is investigated. By using random Melnikov method, a mean square criterion is used to detect the necessary conditions for chaotic motion of this stochastic system. The results show that the threshold of bounded noise amplitude for the onset of chaos in the system increases as the intensity of the random frequency increases, and decrease as the real-power exponent of damping term increase. The threshold of bounded noise amplitude for the onset of chaos is determined by the numerical calculation via the largest Lyapunov exponents. The effects of bounded noise and real-power exponent of damping term on bifurcation and Poincaré map are also investigated. Our results may provide a valuable guidance for understanding the effect of bounded noise on a class of generalized double well system.     

Clamping force of a multilayered cylindrical clamper with internal friction

Holding an object by clamping force is a fundamental phenomena. Layered or laminated architectures with internal sliding features are essential mechanism in natural and man-made structural system. In this paper, we combine the layered architecture and clamping mechanism to form a multilayered clamper and study the clamping force with internal friction. Our investigations show that the clamping force and energy dissipation are very much depend on the number of layers, its geometry and elasticity, as well as internal friction. The central goal of studying the multilayered clamp is not only to predict the clamping force, but also as a representative case to help finding some clue on the universal behaviours of multilayered architectures with internal friction.     

Bifurcation of a shaft with hysteretic-type internal friction force of material

IntroductionItwasfoundlongtimeagothattheinternalfrictionofmaterialcancauseinstabilityofrotatingshaft.Soitisalwaysoneoftheimportantsubjectsinrotordynamics[1].Earlyinvestigationswerefocusedonthedynamicalstabilityproblemofrotorinfluencedbythelinearinternalfrictionofmaterial,aimingtoobtainthecriterionofstability[2～4 ].Asthedevelopmentofnonlineardynamics,moreandmoreattentionswerepaidtothestudyoftheself_excitedmotionofrotatingshaft,thatisthebifurcation .Thestabilityregionsandbifurcationsofbothanau…     

摩擦力判别函数的引入及应用

在涉及摩擦力的力学问题中,首次提出了摩擦力判别函数的概念.该函数的引入完善了库仑摩擦定律的表达式形式.为含有摩擦力、特别是对具有多处摩擦力的问题的清晰分析及解决提供了方便.应用该函数求解摩擦力问题时,无论研究对象处于何种状态、摩擦力的方向均可根据约束的性质作出任意假设,假设正确与否由摩擦力判别函数来确定.举例说明了该函数的适用性.     

On the frequency behaviour,stability and isolation properties of dry friction oscillators

This paper proposes a new approach to the frequency responses of one-degree-of-freedom oscillators subject to periodic excitations in presence of mixed dry-viscous friction. The idea is to get free from the analysis of one fixed system by letting the physical parameters cover their own whole ranges and investigating the various behavioural aspects of wide classes of oscillators. The existence, uniqueness and stability of the steady-state solutions are analysed in detail, assuming different coefficients of static and sliding friction. The possible arising of motions characterized by anti-periodic asymmetry or multi-stick oscillations is enlightened and maps of the system behaviour are presented. A study on transmissibility shows the favourable features of dry friction isolators in the high-frequency range.     

摩擦力对两个恢复系数公式等价性条件的影响

文章讨论两个作一般运动的刚体在考虑摩擦力的情况下碰撞(不受外力作用)．首先由欧勒动力学方程和质心运动定理导出在碰撞的压缩阶段和恢复阶段二碰撞点沿公法线的相对速度的变化量, 然后给出两个恢复系数公式的等价性条件与刚体之间摩擦力的关系．     

Stress and displacement of ring shells under centrifugal force

Using the results of refs. [1] and [2] about the general axial symmetrical problem, this paper calculates the stress and displacement of ring shells under centrifugal force. The solution is given in Fourier series form.In the paper the examples of open ring shells and close ring shells are given respectively.     

Observations of shear adhesive force and friction of Blatta orientalis on different surfaces

The shear adhesive force of four non-climbing cockroaches (Blatta orientalis Linnaeus, 1758) was investigated by the use of a centrifugal machine, evaluating the shear safety factor (adhesion force divided by body weight) on six surfaces (steel, aluminium, copper, two sandpapers and a common paper sheet) having different roughness. The adhesive system of Blatta orientalis was characterized by means of a field emission scanning electron microscope and the surface roughness was determined by an atomic force microscope. The cockroach maximum shear safety factor, or apparent friction coefficient, is determined to be 12.1 on the less rough of the two sandpapers, while its minimum value is equal to 1.9 on the steel surface. A two-sample Student t analysis has been conducted in order to evaluate the significance of the differences among the obtained shear safety factors due to both roughness and chemistry. An interesting correlation between cockroach shear adhesion and surface roughness emerges with a threshold mechanism dictated by the competition between claw tip radius and roughness, indicating that the best adhesion is obtained for roughness larger than the claw tip radius.     

Analytical parametric study of bi-linear hysteretic model of dry friction under harmonic,impulse and random excitations

Hysteretic behavior due to some nonlinear sources is a common phenomenon in many dynamical systems. One of the sources of this behavior in mechanical systems is dry friction. Dry friction in bolted or riveted joints of mechanical structures makes their dynamic behavior hysteretic. Bi-linear hysteresis is one of the models that can be used to study these systems which is used in this paper. A SDOF system containing a bi-linear hysteretic element called Jenkins element under harmonic, impulse and random excitations is considered. For all three types of excitations, the effects of system and excitation parameters on the defined equivalent system parameters and the response specifications are studied. Harmonic balance method is employed for harmonic excitation studies, and optimum friction threshold for minimizing response amplitude is obtained versus other system parameters and response amplitude. Energy balance method is used for impulse excitation through which the desired decaying ratio can be achieved by tuning the friction threshold, depending on stiffness ratio. System under random excitation is investigated by equivalent linearization technique in two steps. At the first step, equivalent properties are obtained versus instantaneous amplitude of response. In this step, the paper contains the parametric study of system in which the variations of equivalent parameters are described when physical parameters of system or input intensity vary. Overall variance of system response is determined in the second step, and optimum sliding threshold is obtained to have minimum overall variance of system response.     

Prediction of transient displacement, velocity, and force on projectiles penetrating cohesive soils

A closed-form solution is developed for predicting transient displacement, velocity, and force as well as residual displacement and duration for both flat and pointed projectiles penetrating cohesive soils. Because transient response can be represented as a 3 parameter space of nondimensional numbers, displacement, velocity, and force are each presented in a single graph. Experimental test data for different soils and penetrator contours are used to demonstrate the validity of both transient and residual responses. Of great importance in this solution and soil dynamics in general is the advancement of a hypothesis for the dynamic interaction of intergranular stress, pore water pressure, and pore air pressure in the resisting force that retards penetration. Because fundamental dynamic pore pressure theory is used to develop this analysis, basic soil properties (cohesive yield strength, density, and degree of saturation) are used to characterize the cohesive soil.     

基于矩阵变换的空间刚架内力图和位移图绘制

利用三维图形的矩阵变换原理,将单元内力和位移绘图数据进行伸缩、旋转和平移变换,在Matlab中实现了空间刚架内力图和位移图的绘制.本文提出的绘图方法可用于杆系结构有限元计算结果的图形显示.     

Effect of electric displacement saturation on the hysteretic behavior of ferroelectric ceramics and the initiation and propagation of cracks in piezoelectric ceramics

This paper presents a computational investigation of a proposed simplified account for electric displacement saturation on the hysteretic behavior of initially unpoled ferroelectric ceramics as well as on the initiation and propagation of cracks in poled ferroelectric ceramics within the linear regime of piezoelectricity. For the latter case, experimental observations suggest an odd dependency of the onset of crack initiation in these brittle materials on the orientation of the applied electric field with respect to their poling direction which contradicts theoretical results which propose an even dependency of the energy release rate on the applied electric field within the framework of anisotropic linear piezoelectricity. Electric non-linearities arising at regions of inhomogeneities such as inclusions or at the crack tip are proposed in the literature to avoid this discrepancy. Electric displacement saturation is one such non-linear effect which is investigated in this work. A simplified account of this effect is proposed based on an exponential saturation model of the identified material parameters which can be related to this non-linearity. Its advantage over the superposition of a complex function onto the singular solution of a crack within the framework of linear piezoelectricity lies in the straightforward extension of the proposed approach to problems where no analytical solutions exist. This is outlined based on its incorporation into a rate-dependent ferroelectric model accounting for polarization switching as well as based on its incorporation into a finite element framework capable of simulating the initiation and propagation of cracks in piezoelectric ceramics through strong discontinuities in the displacement field and the electric potential. It is shown that besides the determination of the crack initiation onset also the crack propagation direction is influenced by the appearance of saturation zones arising at the crack tip normal to the polarization direction. The numerically obtained crack paths are found to be close to the experimentally reported results.     

Friction force model and rolling dynamics for a ball on a rough surface with presliding displacement taken into account

A model of sliding and spinning friction forces for a ball in the form of finite relations obtained by integrating the tangential stresses over the contact area whose parameters are determined by Hertz’s theory for the “ball-rough horizontal surface” tribological conjunction pair is supplemented with a model of rolling friction torques. The combined model is peculiar in that the presliding displacement effect in rolling and spinning friction torques is taken into account. It is shown that the ball motions in the presliding displacement zone are of quasilinear character and, under shock perturbations, have the form of damping vibrations in the three orientation angles. The numerical parameters of the rolling and spinning friction model are experimentally determined for the presliding displacement zones, while the sliding friction parameters and partly the spinning friction parameters are calculated. Mathematical modeling permits one to discover new properties of the ball, namely, its deceleration in rolling, the onset of damping vibrations at the beginning and end of motion, and the transient process parameters.     

Green function on two-phase saturated medium by concentrated force in two-dimensional displacement field

The Green function on two-phase saturated medium by concentrated force has a broad and important use in seismology, seismic engineering, soil mechanics, geophysics, dynamic foundation theory and so on. According to the Green function on two-phase saturated medium by concentrated force in three-dimentional displacement field obtained by Ding Bo-yang et al. , it gives out the Green function in two-dimensional displacement field by infinite integral method along x3 -direction derived by De Hoop and Manolis. The method adopted in the thesis is simpler. The result will be simplified to the boundary element method of dynamic problem.     

纯滚动圆轮静摩擦力方向的确定

给出了匀质圆轮受力偶或水平力作用在水平地面上作纯滚动时, 其静摩擦力方向的确定方法. 只受力偶作用作纯滚动的圆轮, 其摩擦力的方向仅取决于外力偶矩的转向, 判断依据为摩擦力在该圆轮的平面运动中起阻碍圆轮的转动和为圆轮的平移提供主动力两相对的作用.当圆轮只受水平力作用作纯滚动时, 用刚体平面运动微分方程和动能定理两种方法对摩擦力方向进行了推导判定, 摩擦力的方向不仅与水平力的作用位置相关, 还与圆轮的大小和相对质心的惯性半径等因素相关.