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31.
常微分方程技术及其在固体力学计算中的应用 总被引:2,自引:0,他引:2
常微分方程(ODE——Ordinary Differential Equation)边值问题的最新计算求解技术的迅速发展推出了一批高质高效的通用软件,而工程中大量的ODE问题并非呈现为这些求解器(Solver)所接受的标准形式。然而,运用一些简单的ODE变换技巧可以将大量的不同类型的特殊问题转化为标准形式。本文列举了若干常用的变换技巧,并广泛地应用于各种固体力学问题的计算中,使大量的ODE问题在形式上得到统一,得以用标准的ODE Solver方便有效地求解。 相似文献
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车-桥系统耦合振动响应的简便计算 总被引:13,自引:1,他引:13
依据振动理论推导出了二自由度模型车辆与桥梁系统竖向耦合振动微分方程,采用模态分析的离散化方法,将复杂的偏微分方程问题转化为变系数常微分方程问题,并将微分方程数值积分的Runge-Kutta方法引入到该时变系统的振动响应计算中,使复杂的耦合响应问题得到简便的解决。通过算例验证了该方法的有效性和简便性。该方法只需要直接数值积分,具有公式简单,编程方便,计算速度快等优点,特别适合于工程实际问题的计算,并且不仅适用于匀速运动车辆,也适用于变速运动车辆。 相似文献
34.
The differential quadrature method (DQM) has been applied successfully to solve numerically many problems in the fluid mechanics. But it is only limited to the flow problems in regular regions. At the same time, here is no upwind mechanism to deal with the convective property of the fluid flow in traditional DQ method. A local differential quadrature method owning upwind mechanism (ULDQM) was given to solve the coupled problem of incompressible viscous flow and heat transfer in an irregular region. For the problem of flow past a contraction channel whose boundary does not parallel to coordinate direction, the satisfactory numerical solutions were obtained by using ULDQM with a few grid points. The numerical results show that the ULDQM possesses advantages including well convergence, less computational workload and storage as compared with the low-order finite difference method. 相似文献
35.
Principal parametric and three-to-one internal resonances of flexible beams undergoing a large linear motion 总被引:7,自引:0,他引:7
A set of nonlinear differential equations is established by using Kane‘s method for the planar oscillation of flexible beams undergoing a large linear motion. In the case of a simply supported slender beam under certain average acceleration of base, the second natural frequency of the beam may approximate the tripled first one so that the condition of 3 : 1 internal resonance of the beam holds true. The method of multiple scales is used to solve directly the nonlinear differential equations and to derive a set of nonlinear modulation equations for the principal parametric resonance of the first mode combined with 3 : 1 internal resonance between the first two modes. Then, the modulation equations are numerically solved to obtain the steady-state response and the stability condition of the beam. The abundant nonlinear dynamic behaviors, such as various types of local bifurcations and chaos that do not appear for linear models, can be observed in the case studies. For a Hopf bifurcation,the 4-dimensional modulation equations are reduced onto the central manifold and the type of Hopf bifurcation is determined. As usual, a limit cycle may undergo a series of period-doubling bifurcations and become a chaotic oscillation at last. 相似文献
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本文从一类变系数二阶微分方程的一个通解入手,分析了一类非均质楔形直杆的纵向自由振动,得到了这类直杆在一种边界条件下的频率方程和振型函数. 相似文献
38.
Chaos is closely associated with homoclinic orbits in deterministic nonlinear dynamics. In this paper, analytic expressions of homoclinic orbits for some (2+1)- dimensional nonlinear Schrodinger-like equations are constructed based on Hirota's bilinear method, including long wave-short wave resonance interaction equation, generalization of the Zakharov equation, Mel'nikov equation, and g-Schrodinger equation are constructed based on Hirota's bilinear method. 相似文献
39.
SELF-ADAPTIVE STRATEGY FOR ONE-DIMENSIONAL FINITE ELEMENT METHOD BASED ON ELEMENT ENERGY PROJECTION METHOD 总被引:1,自引:0,他引:1
Based on the newly-developed element energy projection (EEP) method for computation of super-convergent results in one-dimensional finite element method (FEM), the task of self-adaptive FEM analysis was converted into the task of adaptive piecewise polynomial interpolation. As a result, a satisfactory FEM mesh can be obtained, and further FEM analysis on this mesh would immediately produce an FEM solution which usually satisfies the user specified error tolerance. Even though the error tolerance was not completely satisfied, one or two steps of further local refinements would be sufficient. This strategy was found to be very simple, rapid, cheap and efficient. Taking the elliptical ordinary differential equation of second order as the model problem, the fundamental idea, implementation strategy and detailed algorithm are described. Representative numerical examples are given to show the effectiveness and reliability of the proposed approach. 相似文献
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