电动力学中衰减机械系统的非线性振荡方法

衰减机械系统的非线性振荡可用来研究长约瑟夫逊结的电动力学方程式，而这方程式等同于弱衰减机械系统的非线性振荡。本文应用的方法是将控制方程线性化及结合谐波平衡法（线性谐波平衡法）而产生色散关系，再把平均法应用在弱非线性的耗散系统中得到非常准确的瞬变反应。在此提出的方法不仅考虑能量耗散，而且利用简单的线性代数等式关系来代替冗长及复杂的分析近似解。     

MODAL SYNTHESIS METHOD FOR NORM COMPUTATION OF H∞ DECENTRALIZED CONTROL SYSTEMS (Ⅱ)

When using H ∞ techniques to design decentralized controllers for large systems,the whole system is divided into subsystems, which are analysed using H∞ control theory before being recombined. An analogy was established with substructural analysis in structural mechanics, in which H ∞ decentralized control theory corresponds to substructural modal synthesis theory so that the optimal H ∞ norm of the whole system corresponds to the fundamental vibration frequency of the whole structure. Hence, modal synthesis methodology and the extended Wittrick-Williams algorithm were transplanted from structural mechanics to compute the optimal H∞ norm of the control system. The orthogonality and the expansion theorem of eigenfunctions of the subsystems H∞ control are presented in part (Ⅰ)of the paper. The modal synthesis method for computation of the optimal H ∞ norm of decentralized control systems and numerical examples are presented in part (Ⅱ).     

MODAL SYNTHESIS METHOD FOR NORM COMPUTATION OF H_∞ DECENTRALIZED CONTROL SYSTEMS (II)

IntroductionThecorrespondencebetweenH∞ decentralizedcontrolandmodalsynthesistheoryispresentedinpart (I)ofthepaper[1].WheretheorthogonalityandtheexpansiontheoremofeigenfunctionsofsubsystemsH∞ controlareintroduced .Basedontheseresults,thefollowingsectionspresentthemodalsynthesismethodforthecomputationoftheoptimalH∞ normofthedecentralizedcontrolsystemsandnumericalexamples.Notethatthroughoutthepaperequation(I_n)denotesequation (n)inpart (I)ofthepaper[1].1　OptimalParameterComputationforGlob…     

H∞分散控制系统范数计算的模态综合法(Ⅱ)

在大系统控制中，H∞分散控制方法将整个系统划分成一系列子系统分别研究，然后综合设计大系统的分散控制器，这与结构力学中的子结构分析技术类似．本着这一思想建立了分散H∞控制与子结构振动分析的模拟关系、分散控制系统的最优H∞范数与整体结构一阶本征值之间的对应关系，进而利用结构力学中的模态综合法和扩展Wittriek-Williams算法计算这一参数．论的第(Ⅰ)部分主要介绍系统H∞控制及其本征函数的正交性和展开定理；第(Ⅱ)部分介绍分散控制系统最优H∞范数计算的模态综合法及数值算例。     

强Van der Pol振子的谐波与修正算法

引入谐波平衡近似解的符号运算与同伦延拓法,获得了强Van der Pol振子的解析近似极限环与稳定响应.为提高其近似精度,给出了谐波解的修正算法,并与数值模拟比较.结果表明,该算法非常精确可靠,是研究强非线性动力学系统的有效分析方法.     

THREE-DIMENSIONAL INTERACTIONS OF CIRCULAR CRACK IN TRANSVERSELY ISOTROPIC PIEZOELECTRIC SPACE WITH RESULTANT SOURCES

Exact solutions in form of elementary functions were derived for the stress and electric displacement intensity factors of a circular crack in a transversely isotropic piezoelectric space interacting with various stress and charge sources: force dipoles, electric dipoles, moments, force dilatation and rotation. The circular crack includes penny-shaped crack and external circular crack and the locations and orientations of these resultant sources with respect to the crack are arbitrary. Such stress and charge sources may model defects like vacancies, foreign particles, and dislocations. Numerical results are presented at last.     

MODAL SYNTHESIS METHOD FOR NORM COMPUTATION OF H ∞ DECENTRALIZED CONTROL SYSTEMS ( Ⅰ )

When using H ∞ techniques to design decentralized controllers for large systems,the whole system is divided into subsystems, which are analysed using H ∞ control theory before being recombined. An analogy was established with substructural analysis in structural mechanics, in which H∞ decentralized control theory corresponds to substructural modal synthesis theory so that the optimal H∞ norm of the whole system corresponds to the fundamental vibration frequency of the whole structure. Hence, modal synthesis methodology and the extended Wittrick-Williams algorithm were transplanted from structural mechanics to compute the optimal H ∞ norm of the control system. The orthogonality and the expansion theorem of eigenfunctions of the subsystems H∞ control are presented in part ( Ⅰ ) of the paper. The modal synthesis method for computation of the optimal H∞ norm of decentralized control systems and numerical examples are presented in part ( Ⅱ ).     

声辐射问题的二级分形有限元方法

利用分形有限元和常规有限元相结合的方法对中低频段声辐射问题进行了分析，由于引用了分形比α和能够自动满足无限远辐射边界条件的全域插值函数，大大降低了未知量的个数，从而可以在较短的计算时间和较低的内存消耗的条件下高效地解决问题，计算实例表明这种方法对于求解无界域声场问题是有效的。     

Nonstationary probability densities of system response of strongly nonlinear single-degree-of-freedom system subject to modulated white noise excitation

The nonstationary probability densities of system response of a single-degree-of -freedom system with lightly nonlinear damping and strongly nonlinear stiffness subject to modulated white noise excitation are studied.Using the stochastic averaging method based on the generalized harmonic functions,the averaged Fokker-Planck-Kolmogorov equation governing the nonstationary probability density of the amplitude is derived. The solution of the equation is approximated by the series expansion in terms of a set...     

A heterogeneous boundedly rational expectation model for housing market

This research aims to test the housing price dynamics when considering heterogeneous boundedly rational expectations such as naive expectation, adaptive expectation and biased belief. The housing market is investigated as an evolutionary system with heterogeneous and competing expectations. The results show that the dynamics of the expected housing price varies substantially when heterogeneous expectations are considered together with some other endogenous factors. Simulation results explain some stylized phenomena such as equilibrium or oscillation, convergence or divergence, and over-shooting or under-shooting. Furthermore, the results suggest that variation of the proportion of groups of agents is basically dependent on the selected strategies. It also indicates that control policies should be chosen carefully in consistence with a unique real estate market during a unique period since certain parameter portfolio may increase or suppress oscillation.