Kinematic analysis of the general spatial 7R mechanism

The displacement. velocity and acceleration analysis of the general spatial 7R mechanism is discussed in this paper. Based on the method proposed in Ref. [2], an input-output algebra equation of the 16th degree in the tan-half-angle of the output angular displacement is derived. The derivation process and computation are considerably simple. A program written in AI language is used to derive the coefficients of displacement equations: therefore the amount of manual work is greatly decreased. The results are verified by a numerical example. The researches of this paper and Ref.[5] found a base for establishing an expert system of spatial mechanism analysis in the future.     

On the Application of the Critical Excitation Method to Aseismic Design

ABSTRACT

The problem of critical excitation of linear structures subjected to earthquake support motion is investigated. For a given time duration and peak ground acceleration, the critical time history which maximizes the absolute acceleration response is obtained. Similar considerations are given to the critical ground acceleration which maximizes the relative displacement and velocity responses. Some bounds on the response spectra curves are obtained and discussed.     

任意荷载作用下液体粘滞阻尼器在桥梁工程中减震作用探讨

在桥梁工程中，当需要限制梁端的碰撞或过大的相对位移，经常会在梁端设置液体粘滞阻尼器。由于技术原因，液体粘滞阻尼器在桥梁设计中的参数选取基本上是通过全桥模型的地震非线性时程分析得到的。而在寿命期内，桥梁需要承受各种随机荷载，在具有不同力学特性荷载的激励作用下引起梁端纵向大的响应时，液体粘滞阻尼器是否始终起有利的减震作用，一直困扰着其在桥梁工程中的实践。在液体粘滞阻尼器力学特性研究的基础上，通过矩阵变换得到关于阻尼器的局部动力方程，从变形和受力两个方向对此问题进行探讨，得到液体粘滞阻尼器对于梁端的相对位移、相对速度、相对加速度均有减震作用。但不会得出始终对所有构件的受力有利的结论，并进行了验证。     

Governing equations and numerical solutions of tension leg platform with finite amplitude motion

It is demonstrated that when tension leg platform （TLP） moves with finite amplitude in waves, the inertia force, the drag force and the buoyancy acting on the platform are nonlinear functions of the response of TLP, The tensions of the tethers are also nonlinear functions of the displacement of TLP. Then the displacement, the velocity and the acceleration of TLP should be taken into account when loads are calculated. In addition, equations of motions should be set up on the instantaneous position. A theo- retical model for analyzing the nonlinear behavior of a TLP with finite displacement is developed, in which multifold nonlinearities are taken into account, i.e., finite displace- ment, coupling of the six degrees of freedom, instantaneous position, instantaneous wet surface, free surface effects and viscous drag force, Based on the theoretical model, the comprehensive nonlinear differential equations are deduced. Then the nonlinear dynamic analysis of ISSC TLP in regular waves is performed in the time domain. The degenerative linear solution of the proposed nonlinear model is verified with existing published one. Furthermore, numerical results are presented, which illustrate that nonlinearities exert a significant influence on the dynamic responses of the TLP.     

MR阻尼器的状态跳跃控制参数

对MR阻尼器实施状态跳跃控制可以有效地减少结构的地震响应，状态跳跃控制参数对半主动控制效果有很大的影响。本文对状态跳跃控制的相关参数进行了研究。利用两个数值算例，对采用不同类型的控制参数(位移、速度、加速度)、控制参数的大小、输入地震动的大小等相关因素对结构地震响应的控制效果进行了对比，发现采用速度响应作为状态跳跃控制变量对于减少绝对加速度响应是有利的；建议采用试算法确定合适的速度控制参数，通过和LQG控制相联系的方法给出了该控制参数最优值的估算方法。     

单侧变截面辊弯成型装备动力学建模与分析

机械系统的动力学建模与分析对深入研究和改善系统性能具有理论指导意义。针对四自由度单侧变截面辊弯成型装备,建立了该系统基于拉格朗日方程的动力学模型。通过求解系统微分方程组得到了驱动电机角加速度以及角速度的表达式。计算出在确定载荷下,该系统驱动电机的角加速度以及角速度的变化曲线,为伺服电机的控制以及系统的结构优化奠定了基础。     

Anharmonic 1D actuator model including electrostatic and Casimir forces with fractional damping perturbed by an external force

We modeled a one-dimensional actuator including the Casimir and electrostatic forces perturbed by an external force with fractional damping. The movable electrode was assumed to oscillate by an anharmonic elastic force originated from Murrell–Mottram or Lippincott potential. The nonlinear equations have been solved via the Adomian decomposition method. The behavior of the displacement of the electrode from equilibrium position, its velocity and acceleration were described versus time. Also, the changes of the displacement have been investigated according to the frequency of the external force and the voltage of the electrostatic force. The convergence of the Adomian method and the effect of the orders of expansion on the displacement versus time, frequency, and voltage were discussed. The pull-in parameter was obtained and compared with the other models in the literature. This parameter was described versus the equilibrium position and anharmonicity constant.     

Projected Runge-Kutta methods for constrained Hamiltonian systems

Projected Runge-Kutta (R-K) methods for constrained Hamiltonian systems are proposed. Dynamic equations of the systems, which are index-3 differential-algebraic equations (DAEs) in the Heisenberg form, are established under the framework of Lagrangian multipliers. R-K methods combined with the technique of projections are then used to solve the DAEs. The basic idea of projections is to eliminate the constraint violations at the position, velocity, and acceleration levels, and to preserve the total energy of constrained Hamiltonian systems by correcting variables of the position, velocity, acceleration, and energy. Numerical results confirm the validity and show the high precision of the proposed method in preserving three levels of constraints and total energy compared with results reported in the literature.     

侧向点爆炸作用下地下拱结构的动力响应

首先,利用几何关系与介质中超压、位移衰减公式得出结构表面自由场荷载和位移的分布形式,并对衰减因数、爆距等参数进行讨论;其次,利用MSSI（modified soil-structure interaction）相互作用模型对拱的振动方程进行正交求解,得到任意角度荷载作用下的结构弹性动力响应解析解。基于动力响应解析解,得到了土体的声阻抗对结构位移、速度、加速度时程响应曲线的影响。研究结果表明:侧向爆炸荷载作用下,岩土介质声阻抗越大,埋设其中的地下结构的位移、速度和加速度变化越大。为此,建议地下防护结构应修建在声阻抗小的岩土介质中。     

某港口工程地基处理中的强夯影响范围研究

强夯法是地基处理的一种常用方法,而确定强夯影响范围是强夯法应用的关键。结合某港口工程地基处理的实测资料,分析强夯振动在深度和广度上的影响范围,进而得出振动的位移、速度、加速度随距夯击点距离增大而逐渐衰减的曲线关系式。     

Particle Measurement Sensor for in situ determination of phase structure of fluidized bed

Based on three-dimensional (3D) acceleration sensing, an intelligent particle spy capable of detecting, transferring, and storing data, is proposed under the name of Particle Measurement Sensor (PMS). A prototype 60-mm-dia PMS was tested to track its freefall in terms of velocity and displacement, and served as a particle spy in a fluidized bed delivering the in situ acceleration information it detects. With increasing superficial gas velocity in the fluidized bed, the acceleration felt by PMS was observed to increase. The variance of the signals, which reflect the fluctuation, increased at first, reaching a maximum at the gas velocity (Uc) which marks the transition from bubbling to turbulent fluidization. Through probability density distribution (PDD) analysis, the PDD peak can be divided into the emulsion phase peak and the bubble phase peak. The average acceleration of emulsion and bubble phase increased, while the variance of both phases reached a maximum at Oc, at the same time. However, the difference between the variances of two phases reached the maximum at Oc. Findings of this study indicate that PMS can record independent in situ information. Further, it can provide other in situ measurements when equipped with additional multi-functional sensors.     

DYNAMICAL ANALYSIS ON A KIND OF SEMI-ACTIVE VIBRATION ISOLATION SYSTEMS WITH DAMPING CONTROL 1)

研究了一类基于相对速度反馈的含立方刚度的单自由度非线性半主动隔振系统.通过平均法得到了系统分别在基于加速度-相对速度反馈的加速度驱动阻尼控制策略、速度-相对速度反馈的天棚阻尼控制策略和位移-相对速度反馈的地棚阻尼控制策略下主共振响应的近似解析解,并利用数值解验证了近似解析解的准确性.通过 Lyapunov 理论对不同控制策略下系统的稳定性进行了分析,讨论了系统参数对控制效果的影响.分析结果表明,对 3 种基于相对速度反馈的控制策略进行解析研究时,切换条件中的控制参数具有相同的表达式;在抑制共振响应振幅方面,基于速度-相对速度反馈的天棚阻尼控制策略在低频时的减振效果最好,而基于加速度-相对速度反馈的加速度驱动阻尼控制策略在高频时的减振效果最优;在抑制瞬态响应振幅方面,基于速度-相对速度反馈的天棚阻尼控制策略的减振效果最好.此类解析研究方法可应用到其他半主动开关控制策略中,为半主动隔振系统的控制策略研究提供了有效的方法和手段.     

一类阻尼控制半主动隔振系统的解析研究

研究了一类基于相对速度反馈的含立方刚度的单自由度非线性半主动隔振系统.通过平均法得到了系统分别在基于加速度-相对速度反馈的加速度驱动阻尼控制策略、速度-相对速度反馈的天棚阻尼控制策略和位移-相对速度反馈的地棚阻尼控制策略下主共振响应的近似解析解,并利用数值解验证了近似解析解的准确性.通过 Lyapunov 理论对不同控制策略下系统的稳定性进行了分析,讨论了系统参数对控制效果的影响.分析结果表明,对 3 种基于相对速度反馈的控制策略进行解析研究时,切换条件中的控制参数具有相同的表达式;在抑制共振响应振幅方面,基于速度-相对速度反馈的天棚阻尼控制策略在低频时的减振效果最好,而基于加速度-相对速度反馈的加速度驱动阻尼控制策略在高频时的减振效果最优;在抑制瞬态响应振幅方面,基于速度-相对速度反馈的天棚阻尼控制策略的减振效果最好.此类解析研究方法可应用到其他半主动开关控制策略中,为半主动隔振系统的控制策略研究提供了有效的方法和手段.      

修正荷载的Wilson-θ法的稳定性与精度分析

Wilson-θ法求得的位移、速度与加速度不满足t时刻的动力平衡方程。提出修正荷载的Wilson-θ法:增加一个荷载δF(t),使得t时刻的动力平衡方程得以满足;将-θ′δF(t)作为荷载加入t+Δt时刻的计算中,当θ′=0时,修正荷载的Wilson-θ法退化为Wilson-θ法。对应于不同的θ′值,在无条件稳定的前提下,θ的取值范围也不同。定义了逐步积分法中的计算误差。计算结果表明:计算误差与θ值成正相关,当θ′=0.6,无条件稳定的θ为最小值1.24,因而θ′=0.6,θ=1.24时,计算误差最小,建议在计算中采用。保持Wilson-θ法无条件稳定、几乎不增加计算量的条件下,修正荷载的Wilson-θ法可以提高计算精度。     

Methods of Identification of Nonlinear Mechanical Vibrating Systems

Methods for determination of the dynamic characteristics and parameters of mechanical vibrating systems by processing experimental data on controlled vibrations are presented. These methods are intended for construction of mathematical models of objects to be identified and classed as parametric and nonparametric methods. The quadrature formulas of the nonparametric-identification method are derived by inverting the integral parameters of approximate analytical solutions of nonlinear differential equations. The parametric-identification method involves setting up and solving systems of linear algebraic equations in the sought-for inertia, stiffness, and dissipation parameters by integrating experimental processes using special weighting functions. Depending on the type of the nonlinearity of the vibrating system and the method of representing experimental processes, the weighting functions can be oriented toward displacement, velocity, or acceleration gauges. The results of studies made mainly at the Institute of Mechanics of the National Academy of Sciences of Ukraine are presented     

地基水平运动时高桥墩的动力屈曲

考虑大变形的影响,建立了高桥墩在地震波冲击下引起的地基水平运动时的非线性动力学基本方程式;通过位移形函数假设,采用伽辽金积分方法得到了时间变率的动力学控制方程;对时间变率的非线性微分方程进行数值求解,给出了同一地震波不同强度下高桥墩的位移响应曲线以及从产生横向振动到失稳的全过程;得到了地震波冲击时高桥墩失稳的临界地震加速度acr和失稳时刻。通过数值算例比较了地震波幅值、高桥墩柔度、桥面质量大小对位移幅值响应、临界地震加速度、失稳时刻等参数的影响。算例表明当发生7.5级以上地震时,桥墩会有较大程度的破坏。     

Time-response functions of mechanical networks with inerters and causality

This paper derives the causal time-response functions of three-parameter mechanical networks that have been reported in the literature and involve the inerter—a two-node element in which the force-output is proportional to the relative acceleration of its end-nodes. This two-terminal device is the mechanical analogue of the capacitor in a force–current/velocity–voltage analogy. The paper employs a methodology that was recently presented for simpler, two-parameter mechanical networks (Makris in J Eng Mech 143:04017123-1–04017123-13, 2017) with which the real and imaginary parts of the enhanced frequency response functions are Hilbert pairs within the context of generalized functions; therefore, yielding causal time-response functions in the time domain. The integral representation of the output signals presented in this paper offers an attractive computational alternative given that the constitutive equations of the three-parameter networks examined herein involve the third derivative of the nodal displacement which may challenge the numerical accuracy of a state-space formulation when the input signal is only available in digital form as in the case of recorded seismic accelerograms.     

Spectral element modelling and analysis of a pipeline conveying internal unsteady fluid

In this paper, a spectral element model is developed for the uniform straight pipelines conveying internal unsteady fluid. Four coupled pipe-dynamics equations are derived first by using the Hamilton's principle and the principles of fluid mechanics. The transverse displacement, the axial displacement, the fluid pressure and the fluid velocity are all considered as the dependent variables. The coupled pipe-dynamics equations are then linearized about the steady-state values of the fluid pressure and velocity. As the final step, the spectral element model represented by the exact dynamic stiffness matrix, which is often called spectral element matrix, is formulated by using the frequency-domain solutions of the linearized pipe-dynamics equations. The fast Fourier transform (FFT)-based spectral dynamic analyses are conducted to evaluate the accuracy of the present spectral element model and also to investigate the structural dynamic characteristics and the internal fluid transients of an example pipeline system.     

Water entry of spinning hydrophobic and hydrophilic spheres

An experimental investigation of the trajectories, forces and cavity formation behind spinning hydrophobic and hydrophilic spheres is presented. Several cases are also presented for non-spinning spheres which are half hydrophobic and half hydrophilic. Data from high speed imaging are processed using advanced data techniques to gain accurate position, velocity and acceleration trends for the spheres as they descend and curve along their trajectories. The data show that an increase in lateral (sideways) force corresponds with the asymmetric cavity formation around the spinning or half-and-half coated spheres. Despite the lack of cavity formation, the slower translating and rotating hydrophilic spheres still move along a curved trajectory, but with less lateral displacement, velocity and acceleration, thus indicating that spin induces less lateral force compared to asymmetrical cavity formation.     

有氧化剂(AP)含铝炸药的爆轰性能

对有氧化剂含铝炸药(RDX/AP/Al/粘合剂=20/43/25/12,下称含铝炸药)爆轰反应的点火增长模型进行研究。用VLW状态方程方法计算了含铝炸药爆轰产物JWL状态方程;用激光速度干涉仪（VISAR）测量炸药/窗口界面粒子速度和炸药驱动金属平板自由表面速度,对试验进行了数值模拟计算,拟合了含铝炸药的反应速率方程。研究结果表明,用VLW状态方程方法和炸药/窗口界面粒子速度确定JWL状态方程和反应速率方程可行,金属平板驱动试验的计算结果与试验结果吻合。