具有非轴对称刚度转轴的分岔

研究具有非轴对称刚度转轴的１／２亚谐共振和分岔,首先用Ｈａｍｉｌｔｏｎ原理导出运动微分方程,这是刚度系数周期性变化的参数激励方程,然后用多尺度法求得平均方程分岔响应方程和定常解,最后用奇异性理论分析分岔响应方程和定常解的稳定性,得到了局部分岔集和不同区域的不同分岔响应曲线。     

求强非线性系统次谐共振解的MLP方法

定义了一个新的参数变换α=α(ε,nω₀/m,ω₁),扩展了改进的LP方法的应用范围,使该方法能够求强非线性系统的次谐共振解.研究了Duffing方程的1/3亚谐和3次超谐共振解以及Vander Pol-Mathieu方程1/2亚谐共振解,这些例子说明近似解和数值解相当吻合.     

变速度轴向运动粘弹性梁的动态稳定性

研究速度变化的轴向运动粘弹性梁在亚谐波共振及组合共振范围内的参数振动．通过平均法,在运动参数激励频率为2倍固有频率或为两阶固有频率之和附近时得到了自治的常微分方程组．在参数激励频率和激励振幅平面上,可以找到由于共振而产生的失稳区域,并应用数值方法验证了理论推导结果的正确性．分析了粘弹性阻尼,速度和预紧张力对失稳区域的影响．粘弹性阻尼使得共振失稳区域减小,而速度和预紧张力使共振失稳区域在频率-振幅平面上发生漂移．     

次线性Duffing系统的多重次调和解

本文证明了，次线性Ｄｕｆｆｉｎｇ系统存在无穷多个高阶次调和解及次调和解列是无界的。     

Double‐mode modeling of nonlinear flexural vibration analysis for a symmetric rectangular honeycomb sandwich thin panel by the homotopy analysis method

Nonlinear flexural vibration of a symmetric rectangular honeycomb sandwich thin panel with simply supported along all four edges is studied in this paper. The nonlinear governing equations of the symmetric rectangular honeycomb sandwich panel subjected to transverse excitations are simplified to a set of two ordinary differential equations by the Galerkin method. Based on the homotopy analysis method, the average equations of the primary resonance and harmonic resonance are obtained. The influence of structural parameters, the transverse exciting force amplitude, and transverse damping to the symmetric rectangular honeycomb sandwich panel are discussed by using the analytic approximation method. Compared with the results obtained by single‐mode modeling technique, the results obtained by double‐mode modeling technique change the softening and hardening nonlinear characteristics when Ω ≈ ω₁, ω₁/3, and ω₂/3.     

Polynomial Asymptotic Representation of Subharmonic Functions in a Half-Plane

Let u(z) be a subharmonic function in a half-plane such that its Riesz measure is concentrated on the finite system of rays.In the paper the connection between the behavior of u(z) and the distribution of its measure (including boundary measure) is investigated in terms of polynomial asymptotic representations.     

一类三维系统的次调和解与不变环面的分支

讨论一类三维自治系统的闭轨在周期扰动下的分支问题.利用Poincare映射与积分流形定理,得到扰动系统存在次调和解和不变环面的条件,以及次调和解的鞍结点分支.     

电力系统奇阶次谐波分叉的数值模拟

本文用Runge-Kutta方法与Galerkin方法揭示了电力系统中一些鲜为人知的物理理过程。例如低频谐振与磁滞回环的变异之间的联系;次谐波分叉的两极分化;分频谐振与基频谐振共存的频率范围等等。     

Uniformly convergent difference schemes for first boundary value problem for elliptic differential equations with a small parameter at the highest detivative

In this paper we consider the Dirichlet problem for elliptic differential equations. A special difference scheme is constructed from the necessary condition of uniform convergence. We also prove the uniform convergence and the asymptotic behavior of the solution of the difference problem, and give the error estimate.     

Saddle-Node Bifurcations of Cycles in a Relief Valve

We extend the asymptotic perturbation (AP) method to the studyof a linear partial differential equation with nonlinear boundaryconditions. A relief valve under the combined effects of static anddynamic loadings is considered with the following resonances between thenth linear mode and the external periodic excitation: primaryresonance, subharmonic resonance of order one-half or one-third,superharmonic resonance of order-two or order-three and combinationresonance. The AP method uses two different procedures for thesolutions: introducing an asymptotic temporal rescaling and balancing ofthe harmonic terms with a simple iteration. We obtain amplitude andphase modulation equations and determine external force-response andfrequency-response curves. Stability of steady-state motions is alsoinvestigated. Saddle-node bifurcations of cycles are observed and underappropriate conditions the performance of the relief valve may beunsatisfactory due to the presence of jumps and hysteresis effects inthe system response. Global analysis is used in order to exclude theexistence of modulated motion. The validity of the method is highlightedby comparing approximate solutions with results of the numericalintegration.