Nonlinear vibration analysis of viscoelastic cable with small sag

Both the inplane and out-of-plane transverse vibrations of a viscoelastic cable subjected to an initial stress distributing uniform on the cross section are studied. The constitution of the cable material is assumed to be of the hereditary integral type. The partial differential-integral equations of motion are derived first. Then by applying Galerkin's method, the governing equations are reduced to a set of second-order nonlinear differential-integral equations which are solved by finite difference numerical integration procedures. Finally, the effects of the viscosity parameter and the elastic parameter on the transient amplitudes of the first mode are investigated by numerical simulation. Project supported by the National Natural Science Foundation of China (No. 59635140) and the National Postdoctoral Foundation of China.     

ELASTIC PERFECTLY-PLASTIC FIELDS AT A RAPIDLY PROPAGATING CRACK-TIP

All the stress components at a rapidly propagating crack-tipin an elastic perfectly-plastic material are the functions of θ only.Making use of this condition and theequations of steady-state motion.stress-strain relations and yield conditions,we obtain thegeneral solutions in both the cases of anti-plane and in-plane strain.Applying these twogeneral solutions to propagating Mode III and Mode I cracks.respectively,the elasticperfectly-plastic and the perfectly-plastic fields at the rapidly propagating tips of Mode IIIand Mode I crocks are derived.     

Nonlinear random stability of viscoelastic cable with small curvature

The nonlinear planar mean square response and the random stability of a viscoelastic cable that has a small curvature and subjects to planar narrow band random excitation is studied. The Kelvin viscoelastic constitutive model is chosen to describe the viscoelastic property of the cable material. A mathematical model that describes the nonlinear planar response of a viscoelastic cable with small equilibrium curvature is presented first. And then a method of investigating the mean square response and the almost sure asymptotic stability of the response solution is presented and regions of instability are charted. Finally , the almost sure asymptotic stability condition of a viscoelastic cable with small curvature under narrow band excitation is obtained.     

斜拉桥拉索-阻尼器系统非线性响应分析

考虑索的抗弯刚度、垂度及几何非线性的影响,得出了索一阻尼器系统的空间非线性振动偏微分方程,用中心差分法将微分方程在空间内离散,导出了系统的非线性振动常微分方程组。结合Newmark法及虚拟力法提出了一种用于求解非线性振动瞬态响应的杂交分析算法。并以典型的斜拉桥拉索为研究对象,给出了数值算例,并与Runge—Kutta直接积分法进行了比较,说明了杂交算法的准确性及有效性。     

Nonlinear transient response of stay cable with viscoelasticity damper in cable-stayed bridge

Taking the bending stiffness, static sag, and geometric non-linearity into consideration, the space nonlinear vibration partial differential equations were derived. The partical differential equations were discretized in space by finite center difference approximation, then the nonlinear ordinal differential equations were obtained. A hybrid method involving the combination of the Newmark method and the pseudo-force strategy was proposed to analyze the nonlinear transient response of the inclined cable-dampers system subjected to arbitrary dynamic loading. As an example, two typical stay cables were calculated by the present method. The results reveal both the validity and the deficiency of the viscoelasticity damper for vibration control of stay cables. The efficiency and accuracy of the proposed method is also verified by comparing the results with those obtained by using Runge-Kutta direct integration technique. A new time history analysis method is provided for the research on the stay cable vibration control.     

智能结构有限元动力模型的建立及主动振动控制和抑制

采用一种新的压电板单元，建立了含有分布压电传感元件和执行元件结构（智能结构）的有限元动力模型。利用两种反馈控制律，研究了智能结构振动控制与抑制的问题，并提出了智能结构主动振动控制和抑制的一种方法。最后，提供了数值示例，说明本文提出方法的应用。     

The hybrid control of vibration of thin plate with active constrained damping layer

This paper concerns in the active and passive hybrid control of vibration of the thin plate with Local Active Constrained damping Layer (LACL). The governing equations of system are formulated based on the constitutive equations of elastic, viscoelastic, piezoelectric materials. Galerkin method and GHM method are employed to transform partial differential equations into ordinary ones with a lower dimension. LQR method of classical control theory is used in simulating calculation. Numeral results show that the active and passive hybrid control manner obtained in this paper is a better one for vibration control of the plate. Project supported by the National Science Foundation of China (19632001) and the Research Foundation of Xian Jiaotong University     

Nonlinear dynamic buckling of a viscoelastic model under impact loading

A simple nonlinear buckling analysis is applied to a one-degree-of-freedom arch under impact loading in which viscous damping may also be included. Such a loading consists of a falling body striking centrally the joint mass of the arch in such a way that a completely plastic impact can be postulated. When there is no damping the exact dynamic buckling load for such a kind of loading-associated with an unbounded motion can be established by using a static criterion (approach). More specifically, it was shown that the dynamic buckling load corresponds to that unstable equilibrium state where the total potential energy of the system is zero. Furthermore, it was proved that the second variation of the total potential energy at the foregoing unstable equilibrium state is negative definite. This implies that the curve loading versus displacement resulting by the vanishing of the total potential energy has always a maximum on the afore mentioned unstable state. It was also found that the system may become sensitive to initial conditions. If damping is included the foregoing static criterion yields lower bound buckling estimates. These findings were verified by employing a highly efficient approximate technique as well as the numerical scheme of Runge-Kutta for solving any nonlinear initial-value problem.     

带支撑广义Maxwell粘弹性阻尼耗能结构风振响应分析

工程中粘弹性阻尼器的安装通过支撑与结构进行连接,但在安装粘弹性阻尼器的耗能结构随机响应分析中,为了简化计算过程,将支撑的刚度看作无穷大或者忽略支撑刚度的影响。实际上,对支撑刚度的影响加以考虑更能符合工程实际。针对考虑支撑刚度影响的粘弹性阻尼耗能结构风振响应分析过程复杂的问题,提出了一种求解考虑支撑影响的广义Maxwell粘弹性阻尼耗能结构基于Davenport谱风振响应的简明解析解法。在广义Maxwell粘弹性阻尼器微分型本构模型基础上,给出了考虑支撑刚度的粘弹性阻尼器等效本构关系。将粘弹性阻尼器等效本构关系与结构运动方程联立,采用复模态法将其解耦,获得结构风振响应的统一表达式。将耗能结构在Davenport风速谱下的系列响应功率谱密度函数分解为频域响应函数与Davenport功率谱密度函数的乘积形式,基于随机振动理论中谱矩的定义,对响应功率谱密度函数积分后获得无积分项的系列响应谱矩表达式。在算例中通过与虚拟激励法计算结果对比,验证了所提解法的准确性,并分析了支撑刚度在耗能系统中的影响。     

Parametric vibration stability and active control of nonlinear beams

The vibration stability and the active control of the parametrically excited nonlinear beam structures are studied by using the piezoelectric material. The velocity feedback control algorithm is used to obtain the active damping. The cubic nonlinear equation of motion with damping is established by employing Hamilton’s principle. The multiple-scale method is used to solve the equation of motion, and the stable region is obtained. The effects of the control gain and the amplitude of the external force on the stable region and the amplitude-frequency curve are analyzed numerically. From the numerical results, it is seen that, with the increase in the feedback control gain, the axial force, to which the structure can be subjected, is increased, and in a certain scope, the structural active damping ratio is also increased. With the increase in the control gain, the response amplitude decreases gradually, but the required control voltage exists a peak value.     

介电弹性作动器主动隔振模糊控制试验研究

采用模糊控制策略,开展介电弹性作动器的主动隔振性能试验研究。基于介电弹性材料的Maxwell应力模型建立了作动器的力电耦合模型,分析了作动器的非线性特性;针对隔振系统设计了Mamdani型模糊控制器,建立了控制电压信号与振动响应之间的关系;在此基础上,开展了介电弹性作动器主动隔振试验研究,并与加速度反馈控制进行了对比。试验结果表明,在相同驱动电压的情况下,基于模糊控制策略的主动隔振性能要优于加速度反馈控制,且能够显著降低由于非线性驱动力导致的倍频响应幅值,有助于提高隔振系统的稳定性。     

Analysis of frequency-domain vibration response of thin plate attached with viscoelastic free layer damping

To predict the vibration response of viscoelastic composite structure, two key issues need to be conducted, one is introducing the constitutive model of viscoelastic material into the analysis model and the other is describing the real damping behavior of viscoelastic composite structure. The emphasis of this study is to obtain the effects of frequency dependence on the vibration response of viscoelastic composite structure and the method of introducing two kinds of damping (viscoelastic material damping and remaining equivalent viscous damping). Vibration response analysis in frequency domain was investigated for viscoelastically damped plate. A cantilever plate attached with the ZN_1 viscoelastic free layer damping (FLD) was chosen to demonstrate the developed method. Frequency-domain response of the composite plate were solved and the obtained results were compared with the experimental values for the purpose of assessing the rationality of the proposed method. In addition, in order to obtain the effects of viscoelastic material parameters on vibration response of viscoelastic composite structure, a detailed parametric analysis was performed. This study shows that the frequency dependent characteristic of viscoelastic material has significant influence on the vibration response in the resonant region and acceptable results can be achieved in the non-resonant region if frequency dependent parameters are substituted by average values of the viscoelastic parameters reasonably in the analysis process.     

Vibration analysis and active control of nearly periodic two-span beams with piezoelectric actuator/sensor pairs

The piezoelectric materials are used to investigate the active vibration control of ordered/disordered periodic two-span beams. The equation of motion of each sub-beam with piezoelectric patches is established based on Hamilton's principle with an assumed mode method. The velocity feedback control algorithm is used to design the controller. The free and forced vibration behaviors of the two-span beams with the piezoelectric actuators and sensors are analyzed. The vibration properties of the disordered two-span beams caused by misplacing the middle support are also researched. In addition, the effects of the length disorder degree on the vibration performances of the disordered beams are investigated. From the numerical results, it can be concluded that the disorder in the length of the periodic two-span beams will cause vibration localizations of the free and forced vibrations of the structure, and the vibration localization phenomenon will be more and more obvious when the length difference between the two sub-beams increases. Moreover, when the velocity feedback control is used, both the forced and the free vibrations will be suppressed. Meanwhile, the vibration behaviors of the two-span beam are tuned.     

Optimal control of the dynamic response of an anisotropic plate with various boundary conditions

The problem of minimising the dynamic response of an anisotropic rectangular plate with minimum possible expenditure of force is presented for various cases of boundary conditions. The plate has a principal direction of anisotropy rotated at an arbitrary angle relative to the coordinate axes. This orientation angle has been taken as an optimisation design parameter. The control problem is formulated as an optimisation problem by using a performance index, which comprises a weight sum of the control objective and penalty function of the control force. The explicit solutions for the closed-loop distributed control function is obtained by means of Liapunov-Bellman theory. To assess the present solution, numerical results are presented to illustrate the effect of anisotropy ratio, orientation angle, aspect ratio and boundary conditions on the control process.     

Nonlinear dynamic response and dynamic buckling of shallow spherical shells with circular hole

In this paper, the nonlinear equations of motion for shallow spherical shells with axisymmetric deformation including transverse shear are derived. The nonlinear static and dynamic response and dynamic buckling of shallow spherical shells with circular hole on elastically restrained edge are investigated. By using the orthogonal point collocation method for space and Newmark-β scheme for time, the displacement functions are separated and the nonlinear differential equations are replaced by linear algebraic equations to seek solutions. The numerical results are presented for different cases and compared with available data.     

大型直线振动筛动态仿真的研究

本文对我国首次设计的27m^2大型直线振动筛进行了动态仿真,探索了大型筛分机械动态仿真理论方法和试验技术,改进了大型筛体的设计,为我国生产大型振动筛探索了可行之路。     

Nonlinear vibration analysis of isotropic cantilever plate with viscoelastic laminate

The nonlinear vibration of an isotropic cantilever plate with viscoelastic laminate is investigated in this article. Based on the Von Karman’s nonlinear geometry and using the methods of multiple scales and finite difference, the dimensionless nonlinear equations of motion are analyzed and solved. The solvability condition of nonlinear equations is obtained by eliminating secular terms and, finally, nonlinear natural frequencies and mode-shapes are obtained. Knowing that the linear vibration of this type of plate does not have exact solution, Ritz method is employed to obtain semi-analytical nonlinear mode-shapes of transverse vibration of this plate. Airy stress function and Galerkin method are employed to reduce nonlinear PDEs into an ODE of duffing type. Stability of plate and chaotic behavior are investigated by Runge–Kutta method. Poincare section diagrams are in good agreement with results of Lyapunov criteria.     

大型索网天线机电耦合动力学建模与主动变形控制

索网天线因其折叠收纳比高、质量轻以及口径大等优点,成为众多空间任务的首选天线形式,但反射面精度较低限制了大型索网天线的在轨性能指标。在索网天线竖向张力索中加入压电陶瓷堆(PZT)作动器,通过主动控制提高反射面的形面精度。首先,将张紧的索网天线分为含有作动器的主动索单元和不含作动器的被动索单元,通过压电本构方程、几何方程和哈密顿原理推导出主动索单元的动力学模型,并与被动索单元一起组装得到索网天线的机电耦合动力学模型。然后,根据天线反射面的初始形面误差和所建立的天线机电耦合动力学模型,基于模型预测控制(MPC)方法计算出各作动器的控制输入电压曲线。最后,以一个10m口径的索网天线为算例,验证本文所建立的模型和控制方法的有效性。     

转动基中斜拉索的非线性动力学分析

给出了转动基中柔性斜拉索的运动学描述方法，建立了该系统的运动学控制方程。利用多尺度摄动方法，得到了斜拉索的内共振模式。利用Melnikov方法和留数定理，分析了转动基中斜拉索的全局发岔与混沌性 质，并用数值方法模拟了该系统的混沌运动。     

粘弹性大变形动力响应的有限元分析

本文基于ＴｏｔａｌＬａｇｒａｎｇｉａｎ增量叠加方法，采用Ｋｉｒｃｈｈｏｆｆ应力增量和Ｇｒｅｅｎ应变增量表示的动力虚功方程和Ｋｉｒｃｈｈｏｆｆ应力－Ｇｒｅｅｎ应变的单积分型本构关系，导出粘弹性大变形的动力变分方程。依此采用Ｎｅｗｍａｒｋ法和八节点轴对称等参数元与二十节点三维等参数元编制了轴对称及三维问题的动力响应计算程序，典型例题的计算结果表明分析符合结构的物理性质。