排序方式: 共有24条查询结果,搜索用时 93 毫秒
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计算非线性振动系统高阶渐近解的Normal Form方法 总被引:1,自引:0,他引:1
利用非线性振动理论,计算非一笥振动系统的高阶渐近解,从理论上讲无任何障碍,但由于计算工作需要进行积分等十分繁琐冗长的运算,使得人们只能非线性振动系统的一阶和二阶近似,而为了研究在退化情况下,非线性动力系统的复杂动力学行为、分岔特性,必须计算该系统的高阶近似解,本文给出了一种Normal Form方法计算高阶渐近解的实用方法,利用这种方法可非常方便地计算出非线性振动系统的七阶近似解。 相似文献
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The construction of homoclinic and heteroclinic orbitals in asymmetric strongly nonlinear systems based on the Pad'e approximant 下载免费PDF全文
In this paper, the extended Pad'e approximant is used to construct the homoclinic and the heteroclinic trajectories in nonlinear dynamical systems that are asymmetric at origin. Meanwhile, the conservative system, the autonomous system, and the nonautonomous system equations with quadratic and cubic nonlinearities are considered. The disturbance parameter varepsilon is not limited to being small. The ranges of the values of the linear and the nonlinear term parameters, which are variables, can be determined when the boundary values are satisfied. New conditions for the potentiality and the convergence are posed to make it possible to solve the boundary-value problems formulated for the orbitals and to evaluate the initial amplitude values. 相似文献
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A new hysteretic nonlinear model of quad iced bundle conductors is constructed. The bifurcation equation is obtained by applying the undetermined fundamental frequency method of the complex normal form. The transition set and bifurcation diagrams for the singularity are presented. Then the corresponding relations between the unfolding parameters and the system parameters are given, and the sensitivity parameters and its range of values are obtained to analyze and to control the galloping of the quad iced bundle conductor. 相似文献
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研究弹性细杆Kirchhoff模型及其相关演化系统, 是深入考察宏观、微观柔性体拓扑结构与稳定性问题的重要依据. 以DNA弹性细杆数学模型为背景, 考虑截面非对称性特征的影响, 构造新的复数形式Kirchhoff系统. 在此基础上, 结合复变量扭矩设解形式, 获得了非对称截面系统的有效抗弯刚度; 并通过相关理论在高维系统简化过程中的应用, 得到了对应于原有系统的单变量二阶常微分方程. 此外, 将DNA分子具备的抗弯刚度周期变化特征转化为针对有效抗弯刚度的周期摄动形式, 以期从总体上减少理论分析对于数值积分 相似文献
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类Pade逼近方法在二维非线性振动系统的应用 总被引:1,自引:0,他引:1
提出一种求解强非线性系统同异宿轨道解析解的改进类Pad\'{e}逼近方法, 该方法在分析带有扰动参数的系统时无需预先限定参数的取值范围. 首先研究了具有三次非线性项的系统,分析其产生同宿或异宿轨道时参数的取值范围, 分别提出直接体现参数的同宿及异宿解的设解通式, 据此获得了一类强非线性下的自治系统方程的同宿及异宿解. 其次, 对于非自治系统, 研究了具有三次非线性项系统的强迫振动, 直接考虑扰动参数对整个系统的影响, 得到了满足同(异)宿边界条件的周期解. 最后, 构造了两种不同形式的异宿解, 从而减少了保守系统异宿解的计算量. 借助数值模拟验证了该方法的有效性及精确性. 相似文献
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The static bifurcation of the parametrically excited strongly
nonlinear oscillator is studied. We consider the averaged equations
of a system subject to Duffing--van der Pol and quintic strong
nonlinearity by introducing the undetermined fundamental frequency
into the computation in the complex normal form. To discuss the
static bifurcation, the bifurcation problem is described as a
3-codimensional unfolding with $Z_{2}$ symmetry on the basis of
singularity theory. The transition set and bifurcation diagrams for
the singularity are presented, while the stability of the zero
solution is studied by using the eigenvalues in various parameter
regions. 相似文献
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The Shilnikov sense Smale horseshoe chaos in a simple 3D
nonlinear system is studied. The proportional integral derivative
(PID) controller is improved by introducing the quadratic and cubic
nonlinearities into the governing equations. For the discussion of
chaos, the bifurcate parameter value is selected in a reasonable
regime at the requirement of the Shilnikov theorem. The analytic
expression of the Shilnikov type homoclinic orbit is accomplished.
It depends on the series form of the manifolds surrounding the
saddle-focus equilibrium. Then the methodology is extended to
research the dynamical behaviours of the simplified
solar-wind-driven-magnetosphere-ionosphere system. As is
illustrated, the Lyapunov characteristic exponent spectra of the two
systems indicate the existence of chaotic attractor under some
specific parameter conditions. 相似文献
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STUDYINGTHEFOCALVALUEOFORDINARYDIFFERENTIALEQUATIONSBYNORMALFORMTHEORYZhangQichang(张琪昌)(TianjinUniversity.Tianjin300072.P.R.C... 相似文献