建立了改进的基于Jacobi椭圆函数的随机平均法,用于预测有界噪声激励作用下硬弹簧和软弹簧系统的随机响应.通过引入基于Jacobi椭圆函数的变换,导出关于响应幅值和激励与响应之间相位差的随机微分方程,应用随机平均原理,将响应幅值近似...建立了改进的基于Jacobi椭圆函数的随机平均法,用于预测有界噪声激励作用下硬弹簧和软弹簧系统的随机响应.通过引入基于Jacobi椭圆函数的变换,导出关于响应幅值和激励与响应之间相位差的随机微分方程,应用随机平均原理,将响应幅值近似为一个Markov扩散过程,建立其平均的Ito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,研究了硬刚度及软刚度情形下的随机响应,通过与Monte Carlo数值模拟结果比较证实了此方法的可行性及精度.由于广义调和函数是基于线性系统的精确解,Jacobi椭圆函数是基于非线性系统的精确解,研究结果表明基于Jacobi椭圆函数的随机平均法得到的结果与Monte Carlo模拟方法更接近.因此与基于广义调和函数的随机平均相比,基于Jacobi椭圆函数更加精确,因为它是基于保守的非线性系统.展开更多
The title compound 6?-chloro-4?-methylene-3 H-spiro [isoben zofura-1,3?-isochroman], C_(17)H_(13)ClO_2, was prepared and characterized by IR, NMR, HRMS and single-crystal X-ray diffraction. This compound has a bisbenz...The title compound 6?-chloro-4?-methylene-3 H-spiro [isoben zofura-1,3?-isochroman], C_(17)H_(13)ClO_2, was prepared and characterized by IR, NMR, HRMS and single-crystal X-ray diffraction. This compound has a bisbenzannulated [5,5]-spiroketals skeleton. It crystallizes in orthorhombic, space group P212121 with a = 13.383(3), b = 7.6120(17), c = 13.793(3) ?, Z = 4, Dc= 1.275 g/cm^3, μ = 0.28 mm^(–1), F(000) = 592, wR = 0.1443 and R = 0.0557. The preliminary biological test showed that the title compound has good anti-bacterial activities in vitro.展开更多
文摘建立了改进的基于Jacobi椭圆函数的随机平均法,用于预测有界噪声激励作用下硬弹簧和软弹簧系统的随机响应.通过引入基于Jacobi椭圆函数的变换,导出关于响应幅值和激励与响应之间相位差的随机微分方程,应用随机平均原理,将响应幅值近似为一个Markov扩散过程,建立其平均的Ito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,研究了硬刚度及软刚度情形下的随机响应,通过与Monte Carlo数值模拟结果比较证实了此方法的可行性及精度.由于广义调和函数是基于线性系统的精确解,Jacobi椭圆函数是基于非线性系统的精确解,研究结果表明基于Jacobi椭圆函数的随机平均法得到的结果与Monte Carlo模拟方法更接近.因此与基于广义调和函数的随机平均相比,基于Jacobi椭圆函数更加精确,因为它是基于保守的非线性系统.
基金National Key Technology Support Program(No.2015BAD11B02)Agricultural Science and Technology Innovation Program(ASTIP,No.CAASASTIP-2014-LIHPS-04)
文摘The title compound 6?-chloro-4?-methylene-3 H-spiro [isoben zofura-1,3?-isochroman], C_(17)H_(13)ClO_2, was prepared and characterized by IR, NMR, HRMS and single-crystal X-ray diffraction. This compound has a bisbenzannulated [5,5]-spiroketals skeleton. It crystallizes in orthorhombic, space group P212121 with a = 13.383(3), b = 7.6120(17), c = 13.793(3) ?, Z = 4, Dc= 1.275 g/cm^3, μ = 0.28 mm^(–1), F(000) = 592, wR = 0.1443 and R = 0.0557. The preliminary biological test showed that the title compound has good anti-bacterial activities in vitro.
