利用数值仿真的方法,对一类M ath ieu方程—欧拉动弯曲问题进行了研究.利用分岔图、相图等揭示了该系统经由倍周期分岔通向混沌的路径,另用时间响应图、相图和功率谱图来表明系统非线性状态.通过分岔图来选择适当的控制参数,利用耦合控...利用数值仿真的方法,对一类M ath ieu方程—欧拉动弯曲问题进行了研究.利用分岔图、相图等揭示了该系统经由倍周期分岔通向混沌的路径,另用时间响应图、相图和功率谱图来表明系统非线性状态.通过分岔图来选择适当的控制参数,利用耦合控制法、x|x|控制法和周期激振力控制法对欧拉动弯曲问题中的混沌行为进行了有效的控制.结果表明,通过这三种方法,都可以将系统的混沌运动控制到稳定的周期轨道。展开更多
Mosquito has the ability to penetrate the skin with painless insertion. It has attracted the researchers to mimic the bite and develop a painless microneedle. Mosquito applies axial compressive load along with frequen...Mosquito has the ability to penetrate the skin with painless insertion. It has attracted the researchers to mimic the bite and develop a painless microneedle. Mosquito applies axial compressive load along with frequency on fascicle to penetrate the human skin and retract if it senses instability prior to insertion. The mechanism of mosquito bite is studied in this work which is divided into two stages for analysis considering different boundary conditions. The probing behaviour of mosquito is considered as stage I and the process of penetration as stage II. An equivalent mechanical model for stage I is proposed and a mathematical model is developed to understand the instability of fascicle in terms of frequency and magnitude of force applied. The governing equation and associated boundary conditions are simplified into Mathieu equation and regions of dynamic instability are obtained through the solution. Results confirm instability of the fascicle during stage I of insertion. The probing behaviour of mosquito is discussed in terms of applied force and vibrating frequency. Horizontal reaction forces exerted by labium on fascicle during buckling improve the stability and enable fascicle to withstand high compressive forces. The analysis and results are utilized to set design guidelines for the development of dynamically stable vibration-assisted microneedle.展开更多
文摘利用数值仿真的方法,对一类M ath ieu方程—欧拉动弯曲问题进行了研究.利用分岔图、相图等揭示了该系统经由倍周期分岔通向混沌的路径,另用时间响应图、相图和功率谱图来表明系统非线性状态.通过分岔图来选择适当的控制参数,利用耦合控制法、x|x|控制法和周期激振力控制法对欧拉动弯曲问题中的混沌行为进行了有效的控制.结果表明,通过这三种方法,都可以将系统的混沌运动控制到稳定的周期轨道。
文摘Mosquito has the ability to penetrate the skin with painless insertion. It has attracted the researchers to mimic the bite and develop a painless microneedle. Mosquito applies axial compressive load along with frequency on fascicle to penetrate the human skin and retract if it senses instability prior to insertion. The mechanism of mosquito bite is studied in this work which is divided into two stages for analysis considering different boundary conditions. The probing behaviour of mosquito is considered as stage I and the process of penetration as stage II. An equivalent mechanical model for stage I is proposed and a mathematical model is developed to understand the instability of fascicle in terms of frequency and magnitude of force applied. The governing equation and associated boundary conditions are simplified into Mathieu equation and regions of dynamic instability are obtained through the solution. Results confirm instability of the fascicle during stage I of insertion. The probing behaviour of mosquito is discussed in terms of applied force and vibrating frequency. Horizontal reaction forces exerted by labium on fascicle during buckling improve the stability and enable fascicle to withstand high compressive forces. The analysis and results are utilized to set design guidelines for the development of dynamically stable vibration-assisted microneedle.
基金Supported by the National Nature Science Foundation of China(51079097)Top Discipline Projects of Shanghai Municipal Education CommissionThe Innovation Projects of 2013 Shanghai Postgraduate Education(the second,20131129)
