改进了基于雅可比椭圆函数的随机平均法,用于预测高斯白噪声激励下硬弹簧及软弹簧系统的随机响应.引入包含雅可比椭圆正弦函数、余弦函数及delta函数的雅可比椭圆函数变换,导出关于响应幅值和相位的随机微分方程.应用随机平均原理,将响...改进了基于雅可比椭圆函数的随机平均法,用于预测高斯白噪声激励下硬弹簧及软弹簧系统的随机响应.引入包含雅可比椭圆正弦函数、余弦函数及delta函数的雅可比椭圆函数变换,导出关于响应幅值和相位的随机微分方程.应用随机平均原理,将响应幅值近似为Markov扩散过程,建立其平均的It随机微分方程.响应幅值的稳态概率密度由相应的简化Fokker-Planck-Kolmogorov方程解出,进而得到系统位移和速度的稳态概率密度.以Duffing-Van der Pol振子为例,研究了硬弹簧及软弹簧情形下的随机响应,通过与Monte-Carlo数值模拟结果比较证实了本文方法的可行性及精度.展开更多
The classical Hardy theorem asserts that f and its Fourier transform f can not both be very rapidly decreasing. This theorem was generalized on Lie groups and also for the Fourier-Jacobi transform. However, on SU（1, ...The classical Hardy theorem asserts that f and its Fourier transform f can not both be very rapidly decreasing. This theorem was generalized on Lie groups and also for the Fourier-Jacobi transform. However, on SU（1, 1） there are infinitely many “good” functions in the sense that f and its spherical Fourier transform y both have good decay. In this paper, we shall characterize such functions on SU（1, 1）.展开更多
文摘改进了基于雅可比椭圆函数的随机平均法,用于预测高斯白噪声激励下硬弹簧及软弹簧系统的随机响应.引入包含雅可比椭圆正弦函数、余弦函数及delta函数的雅可比椭圆函数变换,导出关于响应幅值和相位的随机微分方程.应用随机平均原理,将响应幅值近似为Markov扩散过程,建立其平均的It随机微分方程.响应幅值的稳态概率密度由相应的简化Fokker-Planck-Kolmogorov方程解出,进而得到系统位移和速度的稳态概率密度.以Duffing-Van der Pol振子为例,研究了硬弹簧及软弹簧情形下的随机响应,通过与Monte-Carlo数值模拟结果比较证实了本文方法的可行性及精度.
基金Project supported by Grant-in-Aid for Scientific Research(C)of Japan(No.16540168)the National Natural Science Foundation of China(No.10371004).
文摘The classical Hardy theorem asserts that f and its Fourier transform f can not both be very rapidly decreasing. This theorem was generalized on Lie groups and also for the Fourier-Jacobi transform. However, on SU（1, 1） there are infinitely many “good” functions in the sense that f and its spherical Fourier transform y both have good decay. In this paper, we shall characterize such functions on SU（1, 1）.
