Shape Memory Alloy(SMA)is a typical material with memory effect,and it is widely used in many engineering fields.Based on the elastic theory and Galerkin method,a vibration system of SMA beam with rigid constraints is...Shape Memory Alloy(SMA)is a typical material with memory effect,and it is widely used in many engineering fields.Based on the elastic theory and Galerkin method,a vibration system of SMA beam with rigid constraints is proposed.The non⁃smooth transformation was employed to deal with the discontinuous position,and the original system was turned into an approximate equivalent system associated with the Dirac function.Then,using the stochastic averaging method,the drift and diffusion coefficients of the corresponding Fokker Planck Kolmogorov equation were described.Lastly,the approximate probability response of the system was formulated analytically.Meanwhile,numerical simulation was carried out to verify the effectiveness of analytical results.Furthermore,stochastic bifurcation was discussed.Results show that the stationary probability response of the system was affected by the increase of noise amplitude and restitution force,and a certain restitution value and damping could induce P⁃bifurcation.展开更多
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
A feedback control optimization method of partially observable linear structures via stationary response is proposed and analyzed with linear building structures equipped with control devices and sensors. First, the p...A feedback control optimization method of partially observable linear structures via stationary response is proposed and analyzed with linear building structures equipped with control devices and sensors. First, the partially observable control problem of the structure under horizontal ground acceleration excitation is converted into a completely observable control problem. Then the It6 stochastic differential equations of the system are derived based on the stochastic averaging method for quasi-integrable Hamiltonian systems and the stationary solution to the Fokker-Plank-Kolmogorov （FPK） equation associated with the It6 equations is obtained. The performance index in terms of the mean system energy and mean square control force is established and the optimal control force is obtained by minimizing the performance index. Finally, the numerical results for a three-story building structure model under E1 Centro, Hachinohe, Northridge and Kobe earthquake excitations are given to illustrate the application and the effectiveness of the proposed method.展开更多
考虑生物生长过程中受到的不可预知的跳跃性的环境扰动,运用一类非高斯噪声建立了随机的基因转录调控系统. 利用 Monte Carlo 法得到了系统的稳态概率密度函数,研究了非高斯噪声的各个参数对蛋白质浓度的影响,发现噪声强度不能够诱导基...考虑生物生长过程中受到的不可预知的跳跃性的环境扰动,运用一类非高斯噪声建立了随机的基因转录调控系统. 利用 Monte Carlo 法得到了系统的稳态概率密度函数,研究了非高斯噪声的各个参数对蛋白质浓度的影响,发现噪声强度不能够诱导基因开关,而稳定性指标和偏斜参数能够作为基因开关的控制参量. 进一步研究了非高斯噪声作用下系统从一个态跃迁到另一个态的平均首通时间(MFPT) ,并讨论了各个参数不同的作用机理.展开更多
研究了Lévy稳定噪声激励下的双稳Duffing-van der Pol振子,利用Monte Carlo方法,得到了振幅的稳态概率密度函数.分析了Lévy稳定噪声的强度和稳定指数对概率密度函数的影响,通过稳态概率密度的性质变化,讨论了噪声振子的随机...研究了Lévy稳定噪声激励下的双稳Duffing-van der Pol振子,利用Monte Carlo方法,得到了振幅的稳态概率密度函数.分析了Lévy稳定噪声的强度和稳定指数对概率密度函数的影响,通过稳态概率密度的性质变化,讨论了噪声振子的随机分岔现象,发现了不仅系统参数和噪声强度可以视为分岔参数,Lévy噪声的稳定指数α的改变也能诱导系统出现随机分岔现象.展开更多
本文讨论三稳态van der Pol-Duffing振子的随机P-分岔问题及参数影响.首先由随机平均法导出振动幅值的稳态概率密度函数,再应用突变理论得到系统发生随机P-分岔的临界参数条件.结果表明:参数变化时,系统经两次随机P-分岔,幅值稳态概率...本文讨论三稳态van der Pol-Duffing振子的随机P-分岔问题及参数影响.首先由随机平均法导出振动幅值的稳态概率密度函数,再应用突变理论得到系统发生随机P-分岔的临界参数条件.结果表明:参数变化时,系统经两次随机P-分岔,幅值稳态概率密度分布曲线峰的个数从1增加到3.随机激励的强度、系统阻尼系数对概率密度分布有重要影响,概率密度曲线峰的最大数目与确定性系统吸引子的数目相等.展开更多
基金Sponsored by the National Natural Science Foundation of China(Grant No.11302158)the Natural Science Foundation of Shaanxi Province,China(Grant No.2018JM1044)
文摘Shape Memory Alloy(SMA)is a typical material with memory effect,and it is widely used in many engineering fields.Based on the elastic theory and Galerkin method,a vibration system of SMA beam with rigid constraints is proposed.The non⁃smooth transformation was employed to deal with the discontinuous position,and the original system was turned into an approximate equivalent system associated with the Dirac function.Then,using the stochastic averaging method,the drift and diffusion coefficients of the corresponding Fokker Planck Kolmogorov equation were described.Lastly,the approximate probability response of the system was formulated analytically.Meanwhile,numerical simulation was carried out to verify the effectiveness of analytical results.Furthermore,stochastic bifurcation was discussed.Results show that the stationary probability response of the system was affected by the increase of noise amplitude and restitution force,and a certain restitution value and damping could induce P⁃bifurcation.
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 the National Natural Science Foundation of China under a key grant (No.10332030)the Research Fund for the Doctoral Program of Higher Education of China (No.20060335125)the Zhejiang Provincial Natural Science Foundation of China (No.Y607087).
文摘A feedback control optimization method of partially observable linear structures via stationary response is proposed and analyzed with linear building structures equipped with control devices and sensors. First, the partially observable control problem of the structure under horizontal ground acceleration excitation is converted into a completely observable control problem. Then the It6 stochastic differential equations of the system are derived based on the stochastic averaging method for quasi-integrable Hamiltonian systems and the stationary solution to the Fokker-Plank-Kolmogorov （FPK） equation associated with the It6 equations is obtained. The performance index in terms of the mean system energy and mean square control force is established and the optimal control force is obtained by minimizing the performance index. Finally, the numerical results for a three-story building structure model under E1 Centro, Hachinohe, Northridge and Kobe earthquake excitations are given to illustrate the application and the effectiveness of the proposed method.
文摘考虑生物生长过程中受到的不可预知的跳跃性的环境扰动,运用一类非高斯噪声建立了随机的基因转录调控系统. 利用 Monte Carlo 法得到了系统的稳态概率密度函数,研究了非高斯噪声的各个参数对蛋白质浓度的影响,发现噪声强度不能够诱导基因开关,而稳定性指标和偏斜参数能够作为基因开关的控制参量. 进一步研究了非高斯噪声作用下系统从一个态跃迁到另一个态的平均首通时间(MFPT) ,并讨论了各个参数不同的作用机理.
文摘研究了Lévy稳定噪声激励下的双稳Duffing-van der Pol振子,利用Monte Carlo方法,得到了振幅的稳态概率密度函数.分析了Lévy稳定噪声的强度和稳定指数对概率密度函数的影响,通过稳态概率密度的性质变化,讨论了噪声振子的随机分岔现象,发现了不仅系统参数和噪声强度可以视为分岔参数,Lévy噪声的稳定指数α的改变也能诱导系统出现随机分岔现象.
文摘本文讨论三稳态van der Pol-Duffing振子的随机P-分岔问题及参数影响.首先由随机平均法导出振动幅值的稳态概率密度函数,再应用突变理论得到系统发生随机P-分岔的临界参数条件.结果表明:参数变化时,系统经两次随机P-分岔,幅值稳态概率密度分布曲线峰的个数从1增加到3.随机激励的强度、系统阻尼系数对概率密度分布有重要影响,概率密度曲线峰的最大数目与确定性系统吸引子的数目相等.
