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
As one of the oldest creatures on the earth, the tortoises have formed a nearly perfect shell structure after millions of years of evolution In this paper, Chinese tortoise shell is studied. Firstly, the scanni...As one of the oldest creatures on the earth, the tortoises have formed a nearly perfect shell structure after millions of years of evolution In this paper, Chinese tortoise shell is studied. Firstly, the scanning model of the tortoise shell is established by means of computer tomography （CT） scanning technology and MIMICS software. Secondly, the solid model of three-dimensional structure of the tortoise shell is constructed by using geomagic studio reverse engineering software. Afterwards, the compression numerical simulation of the tortoise shell structure under low strain rate is conducted with the help of finite element software LS-DYNA. Finally, load-bearing characteristics of the tortoise shell structure and dome-shaped structure are compared and analyzed. The results show that compared withthe dome-shaped structure with the same volume, tortoise shell structure has a higher structural rigidity and can withstand higher pressure. Therefore, tortoise shell structure provide some reference to the design of armored vehicles, sheltersand other types of thin shell structures.展开更多
To improve the efficiency and amplify the exciting force of a shake table,a novel variable stiffness mechanism(VSM)constructed by four leaf spring-lever combinations(LSLCs)was designed.Three VSMs were installed in par...To improve the efficiency and amplify the exciting force of a shake table,a novel variable stiffness mechanism(VSM)constructed by four leaf spring-lever combinations(LSLCs)was designed.Three VSMs were installed in parallel on the traditional hydraulic shake table to constitute a resonant shake table(RST).The static model of the VSM and the dynamic model of the RST were constructed by considering the large deflection of leaf springs and the geometrical nonlinearity of L-shaped levers.The variable stiffness property of LSLCs was analyzed and verified through static experiments.The simulation and vibration experiments on the dynamic properties of the RST prototype were conducted.The results show that compared with traditional shake tables,the RST consumes lower exciting force in a specified frequency bandwidth when outputting the same displacement of vibration.Under a harmonic vibrational excitation,the RST is effective for vibration enhancement using broadband frequency resonance and can save energy to some extent.The broadband resonance technology exhibits considerable potential in practical engineering applications.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.
文摘As one of the oldest creatures on the earth, the tortoises have formed a nearly perfect shell structure after millions of years of evolution In this paper, Chinese tortoise shell is studied. Firstly, the scanning model of the tortoise shell is established by means of computer tomography （CT） scanning technology and MIMICS software. Secondly, the solid model of three-dimensional structure of the tortoise shell is constructed by using geomagic studio reverse engineering software. Afterwards, the compression numerical simulation of the tortoise shell structure under low strain rate is conducted with the help of finite element software LS-DYNA. Finally, load-bearing characteristics of the tortoise shell structure and dome-shaped structure are compared and analyzed. The results show that compared withthe dome-shaped structure with the same volume, tortoise shell structure has a higher structural rigidity and can withstand higher pressure. Therefore, tortoise shell structure provide some reference to the design of armored vehicles, sheltersand other types of thin shell structures.
基金The National Natural Science Foundation of China(No.41876218,51905210)。
文摘To improve the efficiency and amplify the exciting force of a shake table,a novel variable stiffness mechanism(VSM)constructed by four leaf spring-lever combinations(LSLCs)was designed.Three VSMs were installed in parallel on the traditional hydraulic shake table to constitute a resonant shake table(RST).The static model of the VSM and the dynamic model of the RST were constructed by considering the large deflection of leaf springs and the geometrical nonlinearity of L-shaped levers.The variable stiffness property of LSLCs was analyzed and verified through static experiments.The simulation and vibration experiments on the dynamic properties of the RST prototype were conducted.The results show that compared with traditional shake tables,the RST consumes lower exciting force in a specified frequency bandwidth when outputting the same displacement of vibration.Under a harmonic vibrational excitation,the RST is effective for vibration enhancement using broadband frequency resonance and can save energy to some extent.The broadband resonance technology exhibits considerable potential in practical engineering applications.
