非保守力下温度场中FGM圆板的非线性力学行为

研究了温度场中非保守功能梯度材料(FGM)圆板的非线性力学行为。基于经典板理论,推导了受非保守力作用的FGM圆板在温度场中的控制微分方程。采用打靶法分析了由陶瓷二氧化锆和金属钛合金两相材料组成的非保守FGM圆板在均匀和非均匀升温场中的非线性力学行为。给出了不同均匀升温和非均匀升温场下,FGM圆板在非保守载荷作用下的平衡路径和平衡构形。分析并讨论了均匀和非均匀升温、材料梯度指数对非保守圆板过屈曲和弯曲行为的影响。结果表明:温度场中,非保守FGM圆板发生弯曲而纯陶瓷圆板会发生过屈曲行为;当梯度指数p=2,非保守载荷q=52时,均匀升温场中非保守圆板的变形大于非均匀升温场中非保守圆板的变形。     

非保守非线性刚-弹-液-控耦合分析动力学及其应用研究

非保守非线性刚-弹-液-控耦合分析动力学是与航天动力学和多体动力学相关的重要研究课题之一, 研究这一理论和应用课题具有重要理论意义和实际应用价值. 本研究建立了非保守非线性两类变量的刚-弹-液-控耦合分析动力学的Hamilton型拟变分原理, 并以该Hamilton型拟变分原理的泛函为依据, 分析了刚-弹-液-控耦合中的刚-弹耦合、刚-液耦合与弹-液耦合、控-刚耦合的特点. 借助于Lagrange-Hamilton体系, 从Hamilton型拟变分原理出发推导出非保守非线性刚-弹-液-控耦合系统的Lagrange方程, 并应用该Lagrange方程推导出系统的控制方程. 进一步以该控制方程为依据, 分析了刚-弹-液-控耦合中的刚-弹耦合、刚-液耦合与弹-液耦合、控-刚耦合的机理. 从两个方面概要地研究了非保守非线性刚-弹-液-控耦合系统的Lagrange方程的应用: 一方面, 应用该Lagrange方程建立了相应的有限元计算模型, 分析了这类计算模型的优越性; 另一方面, 应用系统的控制方程对实际问题进行解析的分析讨论, 说明了应用解析的分析讨论来研究问题与应用数值的、定量的分析方法来研究问题的互补特性. 最后, 讨论了几个相关的问题.      

NON-CONSERVATIVE NONLINEAR RIGID-ELASTIC-LIQUID- CONTROL COUPLING ANALYTICAL DYNAMICS AND ITS APPLICATIONS$^{\bf 1)}$

非保守非线性刚-弹-液-控耦合分析动力学是与航天动力学和多体动力学相关的重要研究课题之一, 研究这一理论和应用课题具有重要理论意义和实际应用价值. 本研究建立了非保守非线性两类变量的刚-弹-液-控耦合分析动力学的Hamilton型拟变分原理, 并以该Hamilton型拟变分原理的泛函为依据, 分析了刚-弹-液-控耦合中的刚-弹耦合、刚-液耦合与弹-液耦合、控-刚耦合的特点. 借助于Lagrange-Hamilton体系, 从Hamilton型拟变分原理出发推导出非保守非线性刚-弹-液-控耦合系统的Lagrange方程, 并应用该Lagrange方程推导出系统的控制方程. 进一步以该控制方程为依据, 分析了刚-弹-液-控耦合中的刚-弹耦合、刚-液耦合与弹-液耦合、控-刚耦合的机理. 从两个方面概要地研究了非保守非线性刚-弹-液-控耦合系统的Lagrange方程的应用: 一方面, 应用该Lagrange方程建立了相应的有限元计算模型, 分析了这类计算模型的优越性; 另一方面, 应用系统的控制方程对实际问题进行解析的分析讨论, 说明了应用解析的分析讨论来研究问题与应用数值的、定量的分析方法来研究问题的互补特性. 最后, 讨论了几个相关的问题.     

深海采矿柔性立管系统非线性有限元模拟

在海洋环境载荷及集矿机牵引作用下,深海采矿柔性立管系统的动力学响应涉及几何非线性和非保守载荷的双重非线性源.基于三维固体有限变形理论建立数学模型,在完全拉格朗日格式下推导了系统运动平衡方程,针对非保守载荷的等效计算、非线性切线刚度矩阵及非线性方程的数值求解等关键问题提出了有效处理方案.根据处理方案开发了数值计算程序,并...     

Modeling and identification of electro-elastic nonlinearities in ultrasonic power transfer systems

Nonlinear Dynamics - We establish a nonlinear non-conservative mathematical framework for the acoustic-electro-elastic dynamics of the response of a piezoelectric disk to high-level acoustic...     

Nonlinear Dynamics and Stability of a Two D.O.F. Elastic/Elasto-Plastic Model System

The local and global nonlinear dynamics of a two-degree-of-freedom model system is studied. The undeflected model consists of an inverted T formed by three rigid bars, with the tips of the two horizontal bars supported on springs. The springs exhibit an elasto-plastic response, including the Bauschinger effect. The vertical rigid bar is subjected to a conservative (dead) or non-conservative (follower) force having static and periodic components. First, the method of multiple scales is used for the analysis of the local dynamics of the system with elastic springs. The attention is focused at modal interaction phenomena in weak excitation at primary resonance and in hard sub-harmonic excitation. Three different asymptotic expansions are utilised to get a structural response for typical ranges of excitation parameters. Numerical integration of the governing equations is then performed to validate results of asymptotic analysis in each case. A full global nonlinear dynamics analysis of the elasto-plastic system is performed to reveal the role of plastic deformations in the stability of this system. Static 'force-displacement' curves are plotted and the role of plastic deformations in the destabilisation of the system is discussed. Large-amplitude non-linear oscillations of the elasto-plastic system are studied, including the influence of material hardening and of static and sinusoidal components of the applied force. A practical method is proposed for the study of a non-conservative elasto-plastic system as a non-conservative elastic system with an 'equivalent' viscous damping. This revised version was published online in July 2006 with corrections to the Cover Date.     

非线性动力学问题的一个显式精细积分算法

对非线性动力学问题,给出了一个显式的精细积分算法,适用于多自由度,强非线性,非保守系统,算例表明本方法精度高,计算量较少。     

FREE VIBRATION OF A SIMPLY SUPPORTED BEAM UNDER A NON-CONSERVATIVE DISTRIBUTED LOAD

对受非保守载荷的简支梁在后屈曲附近的自由振动进行了研究. 基于可伸长梁的大变形理论,建立了受沿轴线分布切向非保守力作用的简支梁后屈曲附近自由振动的几何非线性模型. 在小振幅和谐振动假设下,简化得到后屈曲梁线性振动的控制方程. 采用打靶法求解振动问题的控制方程,给出了前三阶固有频率与载荷之间的特征关系曲线. 结果表明：非保守载荷作用下梁的振动响应与保守载荷作用下梁的振动响应有着明显不同.     

连续介质分析动力学及其应用

综述了国内和国外学者研究连续介质分析动力学问题的进展,阐明了本文主要论述将Lagrange方程应用于连续介质动力学的问题.论文采用Lagrange-Hamilton体系,分别论述了非保守非线性弹性动力学、不可压缩黏性流体动力学、黏弹性动力学、热弹性动力学、刚--弹耦合动力学和刚--液耦合动力学的Lagrange方程及其应用.论述了应用Lagrange方程建立有限元计算模型的问题. 最后,展望了将Lagrange方程应用于连续介质动力学问题的研究前景.      

Post-divergence and post-flutter analysis of sub-tangentially loaded and damped Beck column using a nonlinear FE procedure

Both post-divergence and post-flutter behaviors of damped Beck columns subjected to a sub-tangentially follower force are rigorously explored using an exact co-rotational frame element. First a linear stability theory of the damped Beck column is summarized using a stability map. A geometrically nonlinear frame element based on the co-rotational formulation is then formulated including mass matrix, Rayleigh damping matrix, and load-correction stiffness matrix due to circulatory forces. The dynamic FE analysis is performed using Newmark integration method. Finally a Beck column model is parametrically analyzed in order to investigate non-linear stability characteristics of the internally and externally damped non-conservative system. In particular, interesting nonlinear behaviors of Beck column quite different from those predicted by the linear theory are reported through static and dynamic nonlinear analysis with variation of sub-tangentiality of the follower force.     

Destabilization paradox due to breaking the Hamiltonian and reversible symmetry

Stability of a linear autonomous non-conservative system in the presence of potential, gyroscopic, dissipative, and non-conservative positional forces is studied. The cases when the non-conservative system is close to a gyroscopic system or to a circulatory one are examined. It is known that marginal stability of gyroscopic and circulatory systems can be destroyed or improved up to asymptotic stability due to action of small non-conservative positional and velocity-dependent forces. The present paper shows that in both cases the boundary of the asymptotic stability domain of the perturbed system possesses singularities such as “Dihedral angle” and “Whitney umbrella” that govern stabilization and destabilization. In case of two degrees of freedom, approximations of the stability boundary near the singularities are found in terms of the invariants of matrices of the system. As an example, the asymptotic stability domain of the modified Maxwell-Bloch equations is investigated with an application to the stability problems of gyroscopic systems with stationary and rotating damping.     

Analytical dynamics of continuous medium and its application

综述了国内和国外学者研究连续介质分析动力学问题的进展,阐明了本文主要论述将Lagrange方程应用于连续介质动力学的问题.论文采用Lagrange-Hamilton体系,分别论述了非保守非线性弹性动力学、不可压缩黏性流体动力学、黏弹性动力学、热弹性动力学、刚--弹耦合动力学和刚--液耦合动力学的Lagrange方程及其应用.论述了应用Lagrange方程建立有限元计算模型的问题. 最后,展望了将Lagrange方程应用于连续介质动力学问题的研究前景.     

A discrete approach for a generalized Beck’s column in parametric resonance

A Galerkin projection based on non-standard bases is conceived to derive an equivalent discrete model of a continuous system under non-conservative forces. The problem of deriving a discrete model capable of describing critical and post-critical scenarios for non-selfadjoint systems is discussed and an heuristic rule for a proper choice of trial functions is given. The procedure is utilized to analyze the effect of non-conservative autonomous and non-autonomous (pulsating) forces acting on a linearly damped Beck’s column involving geometrical nonlinearities. The linear and nonlinear behaviours arising from the analysis of the proposed discrete model are in good agreement with those observed through the unavoidably more involved direct continuous approach. Critical scenarios for the autonomous and non-autonomous cases are investigated and the multiple scales method is applied in order to obtain the bifurcation equations in the neighborhood of a Hopf bifurcation point in primary parametric resonance. A comparison between critical and post-critical continuous and discrete model is performed adopting two control parameters, namely the amplitudes of the static and dynamic components of the forces, playing the role of detuning and bifurcation parameters, respectively.     

A generalized variational principle for potentializable operators

For non-conservative mechanical systems (non-potential operators), classical energetic variational principles do not hold true. In the present paper, a generalized variational principle, valid for non-linear and non-conservative systems, is deduced by means of “potentializable” operators. A systematic inclusion or boundary conditions in problems dealing with such operators is proposed and examples from continuum mechanics are presented.     

基于非保守体力的大变形固结有限元法

考虑土体固结过程中体力的非保守特点,完善了T.L.描述的大变形固结平衡方程,并以伴生体力代替非保守体力,提出了相应的大变形固结增量有限元列式. 当忽略土体体积应变的影响时,改进的大变形固结平衡方程及其有限元法均可退化为基于保守体力的传统形式. 采用自主开发的程序对大变形自重固结算例进行分析,结果初步表明:传统方法低估了地基固结度,但高估了地基沉降量和超静孔隙水压力. 基于非保守体力的大变形固结分析在理论上能够更合理地预测地基的固结性状.      

非保守弹性动力学初值问题的简单Gurtin型拟变分原理

按照广义力和广义位移之间的对应关系,将弹性动力学基本方程卷积乘上相应的虚量,然后积分且代数相加,并利用体积力和面积力均为伴生力这一特征,建立了非保守系统初值问题的简单Gurtin型五类变量的完全拟变分原理.更进一步地还建立了非保守系统初值问题的简单Gurtin型不完全拟变分原理和有条件不完全拟变分原理.在建立非保守系统初值问题的各类简单Gurtin型拟变分原理的同时,还将变积方法推广为卷变积方法.最后,介绍了寻求伴生力的方法.     

On the numerical solution to two fluid models via a cell centered finite volume method

A new method for the discretization of nonlinear systems of partial differential equations occurring in the numerical simulation of two phase flows is proposed. This method is based on a cell centered finite volume discretization on possibly unstructured meshes and aims to approximate three-dimensional stationary and evolution problems in arbitrary geometries. We are able to consider conservative and non-conservative systems of equations and the method belongs to the class of shock-capturing upwind ones. In the paper we put the emphasis on the treatment of terms involving first-order derivatives since we deal with the change of type (hyperbolic to non-hyperbolic). One of the features of the method is that it does not rely a priori on the hyperbolic character of the convection operator. The method is illustrated on a classical numerical benchmark and we refer to the bibliography concerning various and numerous applications in the context of two phase flows.     

非匀质地基上正交异性矩形厚板的动态稳定

本文把伽辽金法和富里哀级数相结合,用以分析非匀质地基上的自由边正交异性矩形厚板的动态稳定。在板的自由边上作用着均匀分布的非保守跟随力,力的方向受到控制,使其与加载边的转角成定比。分析基于理论,因此包括了剪切变形的影响。力是非保守的,会有颤振和发散两种形式的失稳,力是保守的,只会有发散形式的失稳。     

On a stationarity principle for non-conservative dynamical systems

A stationarity principle for non-conservative, holonomic dynamical systems is formulated. It is based on the notion of Gâteaux directional derivative. Its relation to the classical and variational principle with non-commutative variational rules is discussed.     

The Validity Range of Low Fidelity Structural Membrane Models

Three classes of structural models can be considered for the characterization of thin extensible pressurized membranes. A low-fidelity, linear model assumes that all of the membrane’s resistance to a transverse pressure is provided from geometric stress-stiffening, and that movement along the membrane is purely out-of-plane. A medium-fidelity model can include geometric nonlinearity (finite strains, non-conservative pressure loads); while the highest level of membrane modeling assumes material nonlinearity: specifically, hyperelasticity. Common modeling applications such as performance prediction, failure prevention, and structural optimization all require repeated function evaluations. As computational cost is proportional to model fidelity, what is the validity range of the two lower fidelity models discussed above? The presence of a large pre-tension within the membrane is known to lessen the role of nonlinear elastic effects: the range of linear transverse deformation increases with pre-tension. Conversely, very low pre-tensions require the use of a nonlinear model, as the linear model becomes unbounded. This work studies the Hencky–Campbell problem for model validation purposes: hydrostatic inflation of a thin flat circular membrane, clamped along its boundary, with an arbitrary initial tension. A full-field, non-contact visual image correlation system is used to estimate the material properties of the rubber membrane, measure the state of pre-tension in the circular sheet, and document the displacement and strain fields as a function of applied pressure. The resulting data set is then compared directly with numerical simulations, in order to estimate the location of the surface of data points wherein a particular low fidelity model (either linear or geometrically nonlinear) loses its predictive capability.