摄动法

• In this method , a new perturbation technique called linearization - correction method was used to linearize the nonlinear equations in the model , and then the wavelet precise integration method was used to calculate the sensitivity of the response . at last the stochastic perturbation method is used to analyse the variance and expectation of sediment concentration , rate and depth of flow . the calculated result was high agreement with that result of monte carlo method
  在该方法中，采用了一种拟摄动法对模型中的非线性方程进行线性化，然后采用小波配置法对模型方程进行空间离散，最后用随机有限元方法求得模型中水流速度，水深和泥沙浓度的统计特性，计算结果和montecarlo法模拟结果吻合得很好。
• The result of a case studying shows that the settlement calculated by large strain consolidation theory is large than that by infinite strain theory during the consolidation procession , but the final settlements calculated by both theories are same . more general assumptions than that in the classical consolidation theory is adopted and the exact analytical solution of nonlinear finite strain self - weight consolidation based on this assumption is obtained . by applying same experiment data , the comparison of the solutions of linear and nonlinear finite strain theory , as well as the numerical solution from finite element method is presented
  对此模型求得到了某些特殊条件下的lagrange级数解答，并通过尾矿沉降池实例分析，验证了所得解答的合理性和有效性；建立了土体在堆积过程中的大应变固结模型，通过其对称性构造出相似变量之后，由摄动法求得了近似解析解答，并通过试验数据与传统的线性化固结理论的解答相比较，显示了传统线性化固结理论在该问题上的局限性。
• A detailed study is made in this dissertation on the applicability of the classical perturbation methods to the dynamical systems with time delays , and on the global view of local bifurcations and the complex dynamical behaviors of several duffing systems under different delayed state feedback control
  本文详细研究经典摄动法直接应用于时滞动力系统时的有效性及适用性问题，用不同方法系统分析了时滞状态反馈下的duffing系统关于时滞的大范围分叉模式和复杂动力学行为。
• By use of - perturbation method with spatial discretization , the hydraulic transient system controlled by quasilinear partial differential equation was converted to a time - continuous linear system , so that the inverse problem of hydraulic transients under limited pressure could be sol ed with the optimal control theory for time - continuous systems
  采用-摄动法并经过空间离散，将由拟线性偏微分方程控制的有压瞬变流系统转化为时间连续线性系统，从而使有压瞬变流限压控制反问题能应用时间连续系统最优控制理论来求解。
• The first - order perturbation method correct for forcing decoupling method based on perturbation theory is put forward to decrease error ; iii . the complex modal method is introduced into analysis of non - classical damping systems to eliminate error of forcing decoupling method , and improve the complex modal response spectrum , which can apply to design of non - classical damping systems ; iv . for exerting the energy dissipation capability of each device , a two - step optimum method , whose controlling function is extremum expectation of interbedded displacement , is put forward to optimize the number and position of device ; v . the problem of iterative method applied to analyze energy dissipation systems is indicate , and give some primary advice based on pilot study
  为改善上述缺点，本文进行了以下的研究工作：在忽略耗能器附加质量的基础上，推导出适用于耗能减震结构的摄动法，减少振型分解法在迭代计算过程中的工作量，加快计算速度；针对运动方程的强行解耦所产生的误差，根据摄动法原理，对其进行一阶摄动修正；为消除强行解耦振型分解法用于非比例阻尼结构分析时产生的误差，引入状态空间对系统进行复模态分析，并改进了基于复模态理论的、适用于非比例阻尼结构设计的双反应谱方法；对于耗能器的数量和位置优化进行了一些探讨和研究。
• For a warm dusty plasma with variable dust charge , the modulational instability of the dust - acoustic waves can be described by the nonlinear schrodinger equation ( iut 4 - auxx + b | u | 2u = 0 ) . it shows that the dust - acoustic wave is modulational stable in this dusty plasma . only the dark soliton exists in warm dusty plasma with variable dust charge
  通过约化摄动法，得到了描述尘埃微粒电荷可变的热尘埃等离子体中尘埃声波的非线性薛定谔方程( iu _ t + u _ ( xx ) + | u | ~ 2u = 0 ) ，不论是单离子温度情形，还是两离子温度情形，尘埃微粒电荷可变的热尘埃等离子体中的尘埃声波是调制稳定的，仅存在暗孤子(包络穴)
• Then the unified approach can be applied to it to acquire the ensemble random evolutionary response . since the normal probability density function ( pdf ) may lead to instability of some sample systems when the random parameters taking sufficiently small negative values , an arch - like pdf and a more adaptable - pdf , together with the matching chebyshev polynomial approximation and gegenbauer polynomial approximation , are suggested . numerical examples show that the suggested methods are effective
  相比较而言，随机模拟法的结果无疑是最可靠的，但是它的计算量嫌大；随机摄动法的计算量远小于随机模拟法，但是它要求随机摄动量必须是一个小量；正交展开法的计算精度好于随机摄动法，其得到结果与随机模拟法得到的结果几乎吻合，其计算量略多于随机摄动法，但与随机模拟法相比要少的多，不过计算前的准备工作较费时。
• The research work on the chaos is carried out in chapter 5 . the properties of chaos sensitively dependent on the initial conditions and the perturbations are proved and a method of controlling chaos of duffing oscillator is investigated as well . in chapter 6 , the bifurcation and chaos of continuous nonlinear systems are researched
  第五章用正规摄动法给出了一维非线性微分方程的通解，并以此为基础解析地证明了混沌运动对初值的敏感依赖性和对扰动的敏感依赖性，并以杜芬振子为例子以验证，研究了杜芬振子的混沌运动控制的多谐扰动法。