研究基于分数阶黏弹性材料构造的Van der pol减振系统在外部宽带噪声激励下的随机稳定性和随机分岔行为.考虑约束条件的影响,引入非平滑Zhuravlev变换,将碰撞系统转化为无碰撞的动力学系统.利用一组拟周期函数近似替换分数阶微分,通过...研究基于分数阶黏弹性材料构造的Van der pol减振系统在外部宽带噪声激励下的随机稳定性和随机分岔行为.考虑约束条件的影响,引入非平滑Zhuravlev变换,将碰撞系统转化为无碰撞的动力学系统.利用一组拟周期函数近似替换分数阶微分,通过随机平均法得到系统的It8随机微分方程,根据最大Lyapunov指数法和奇异边界理论分类讨论系统的随机稳定性,利用拟Hamilton系统随机平均法分析系统在线性It8方程下的随机分岔行为,得到D-分岔的临界条件,进一步求出与系统幅值相关的稳态概率密度函数.使用MATLAB绘制稳态概率密度曲线,直观展现系统发生的稳态变化.结果表明,当分数阶阶次和噪声强度在一定阈值内变化时,可诱导系统产生P-分岔行为.展开更多
Intercritical annealing（IA） at various temperatures followed by quenching and partitioning（IAQP） treatments was conducted on a cold-rolled Fe-0.2C-1.42Si-l.87Mn（wt%） sheet steel.Optimized microstructure and enha...Intercritical annealing（IA） at various temperatures followed by quenching and partitioning（IAQP） treatments was conducted on a cold-rolled Fe-0.2C-1.42Si-l.87Mn（wt%） sheet steel.Optimized microstructure and enhanced mechanical properties were achieved through appropriate adjustment of IA temperatures.The steel which was annealed at1,033 K for 600 s,then quenched to 573 K and partitioned at 693 K for 20 min,designated as 1033 QP steel,exhibits maximum 16.3 vol% retained austenite（RA） with good mechanical properties（ultimate tensile strength 886 MPa and total elongation 27%）.It was found that the thermal and mechanical stabilities of RA are mainly influenced by the combined effect of its average carbon content and amount of adjacent martensite.Furthermore,the transformation-induced plasticity effect increased the peak n-values observed at the second stage of the work hardening of IAQP steels.展开更多
Multi<span style="font-family:Verdana;">-</span><span style="font-family:Verdana;">objective optimization problem (MOOP) is an important class of optimization problem that ensures...Multi<span style="font-family:Verdana;">-</span><span style="font-family:Verdana;">objective optimization problem (MOOP) is an important class of optimization problem that ensures users </span><span style="font-family:Verdana;">to </span><span style="font-family:Verdana;">model a large variety of real world applications. In this paper an advanced transformation technique has been proposed to solve MOOP. An algorithm is suggested and the computer application of algorithm has </span><span style="font-family:Verdana;">been </span><span style="font-family:Verdana;">demonstrated by a flow chart. This method is comparatively easy to calculate. Applying on different types of examples, the result indicate</span><span style="font-family:Verdana;">s</span><span style="font-family:Verdana;"> that the proposed method gives better solution than other methods and it is less time consuming. Physical presentation and data analysis represent the worth of the method more compactly.</span>展开更多
文摘研究基于分数阶黏弹性材料构造的Van der pol减振系统在外部宽带噪声激励下的随机稳定性和随机分岔行为.考虑约束条件的影响,引入非平滑Zhuravlev变换,将碰撞系统转化为无碰撞的动力学系统.利用一组拟周期函数近似替换分数阶微分,通过随机平均法得到系统的It8随机微分方程,根据最大Lyapunov指数法和奇异边界理论分类讨论系统的随机稳定性,利用拟Hamilton系统随机平均法分析系统在线性It8方程下的随机分岔行为,得到D-分岔的临界条件,进一步求出与系统幅值相关的稳态概率密度函数.使用MATLAB绘制稳态概率密度曲线,直观展现系统发生的稳态变化.结果表明,当分数阶阶次和噪声强度在一定阈值内变化时,可诱导系统产生P-分岔行为.
基金financially supported by the National Natural Science Foundation of China (No. 51174251)the National Basic Research Program of China (No. 2010CB630803)
文摘Intercritical annealing（IA） at various temperatures followed by quenching and partitioning（IAQP） treatments was conducted on a cold-rolled Fe-0.2C-1.42Si-l.87Mn（wt%） sheet steel.Optimized microstructure and enhanced mechanical properties were achieved through appropriate adjustment of IA temperatures.The steel which was annealed at1,033 K for 600 s,then quenched to 573 K and partitioned at 693 K for 20 min,designated as 1033 QP steel,exhibits maximum 16.3 vol% retained austenite（RA） with good mechanical properties（ultimate tensile strength 886 MPa and total elongation 27%）.It was found that the thermal and mechanical stabilities of RA are mainly influenced by the combined effect of its average carbon content and amount of adjacent martensite.Furthermore,the transformation-induced plasticity effect increased the peak n-values observed at the second stage of the work hardening of IAQP steels.
文摘Multi<span style="font-family:Verdana;">-</span><span style="font-family:Verdana;">objective optimization problem (MOOP) is an important class of optimization problem that ensures users </span><span style="font-family:Verdana;">to </span><span style="font-family:Verdana;">model a large variety of real world applications. In this paper an advanced transformation technique has been proposed to solve MOOP. An algorithm is suggested and the computer application of algorithm has </span><span style="font-family:Verdana;">been </span><span style="font-family:Verdana;">demonstrated by a flow chart. This method is comparatively easy to calculate. Applying on different types of examples, the result indicate</span><span style="font-family:Verdana;">s</span><span style="font-family:Verdana;"> that the proposed method gives better solution than other methods and it is less time consuming. Physical presentation and data analysis represent the worth of the method more compactly.</span>
