Numerical methods for determining the periodic solution of non - linear oscillation systems 具有系统参数的非线性动力系统周期解方法
In this paper , a linear oscillation motor is introduced , for the shortage of to - and - fro equipment . the mathematic model of this type of motor is established . to finding out its distributing of magnetic field , the program of finite analysis method is worked out 本文针对传统往复运动设备的缺点,提出了一种能量型永磁直线振荡电机,建立了直线振荡电机的数学模型;利用有限元分析方法,编制了直线振荡电机磁场有限元分析程序;分析了直线振荡电机在各种励磁状态下的磁场分布;验证了所设计模型的合理性。
Coordinate transformation , matrix , vectors , newton ' s law , conservation theorems , simple harmonic oscillator , non - linear oscillations , gravitation , euler ' s equation when auxiliany condition are imposed , the delta notation , lagrangian and hamilitonian dynamics , central - force motion , dynamics of a system o f particles , motion of noninertial reference frame , dynamics of rigid body , coupled oscillations , orthogonality of the eigenvectors , continuous system 座标变换、矩阵、向量、牛顿定律、守恒定律、简谐振动、非线性振动、引力、尤拉式方程式及附加条件、符号、拉格兰及汉米尔顿力学、中心运动、多粒子系统动力学、非惯性参考座标运动、刚体动力学、耦会振动、本微向量正交性、连续系统。
A state space model for parts of non - linear oscillation systems is put forward , and the concealed analytical solution for the systems is deduced . a numerical calculation method is presented and the calculation precision is improved greatly through using iterative method . finally the presented numerical method is extended to solve differential equations with complex stiffness matrix 导出了一类非线性振动系统的状态空间模型,在此模型中给出了非线性振动系统的隐式解析解,提出了相应的数值计算方法,并利用迭代法有效地提高了计算精度,最后将该数值方法推广应用到复刚度振动方程的数值求解计算中。