An exact solution to cavitation is found tension of ac lass ofCauchy elastic membranes. The constitutive relationship of materialsis based on Hookean elastic law and finite logarithmic strain mea-Sure. A variable tran...An exact solution to cavitation is found tension of ac lass ofCauchy elastic membranes. The constitutive relationship of materialsis based on Hookean elastic law and finite logarithmic strain mea-Sure. A variable transformation is used in solving the two-pointboundary-value problem of nonlinear ordinary Different equation. Asimple formula to calculate the critical stretch for cavitation isderived. As the nu- Merical results, the bifurcation curvesdescribing void nucleation and suddenly rapidly growth of the cavityAre obtained. The boundary layers of displacements and stresses nearthe cavity wall are observed.展开更多
The relation between the Lyapunov exponent spectrum of a periodically excited non-autonomous dynamical system and the Lyapunov exponent spectrum of the corresponding autonomous system is given and the validity of the ...The relation between the Lyapunov exponent spectrum of a periodically excited non-autonomous dynamical system and the Lyapunov exponent spectrum of the corresponding autonomous system is given and the validity of the relation is verified theoretically and computationally. A direct method for calculating the Lyapunov exponent spectrum of non-autonomous dynamical systems is suggested in this paper, which makes it more convenient to calculate the Lyapunov exponent spectrum of the dynamical system periodically excited. Following the definition of the Lyapunov dimension D-L((A)) of the autonomous system, the definition of the Lyapunov dimension D-L of the non-autonomous dynamical system is also given, and the difference between them is the integer 1, namely, D-L((A)) - D-L = 1. For a quasi-periodically excited dynamical system, similar conclusions are formed.展开更多
机电惯容是一种新型惯容装置,可利用电路网络实现高阶机械阻抗,具有性能和空间上的优势。由于海上风力机的机舱空间有限,研究了位于浮式平台中的机电惯容系统对漂浮式海上风力机载荷的影响。根据直流电机的特性,电机轴的转矩输出与电机...机电惯容是一种新型惯容装置,可利用电路网络实现高阶机械阻抗,具有性能和空间上的优势。由于海上风力机的机舱空间有限,研究了位于浮式平台中的机电惯容系统对漂浮式海上风力机载荷的影响。根据直流电机的特性,电机轴的转矩输出与电机回路中的电流呈线性关系,因此针对所建立的机电惯容,重点研究了所有由单个电阻、电容、电感组成的电路网络对漂浮式风力机减振性能的影响。为了降低优化过程中的复杂度,首先建立了3自由度(Degree of freedom,DOF)漂浮式海上风力机模型,随后优化了含有电路网络模型的输入输出传递函数的H2范数,得到电路网络最优参数。最后,基于美国可再生能源实验室的5 MW基准风力机模型对优化结果进行了仿真分析。仿真结果表明,在不考虑装置工作行程的情况下,所建立的机电惯容调谐质量阻尼器(Mechatronic inerter tuned mass damper,MITMD)系统可以有效减少风力机系统的结构载荷。相较于减振装置位于机舱中的情况,建立在平台中的MITMD系统可以同时减轻塔基和塔顶转轴处的载荷。MITMD的控制效果以运动位移为代价,因此在实际应用中需要折中考虑减振效果和装置的工作行程。展开更多
Dynamical cavitation and oscillation of an anisotropic two-family fiber-reinforced incompressible hyper-elastic sphere subjected to a suddenly applied constant boundary dead load are examined within the framework of f...Dynamical cavitation and oscillation of an anisotropic two-family fiber-reinforced incompressible hyper-elastic sphere subjected to a suddenly applied constant boundary dead load are examined within the framework of finite elasto-dynamics.An exact differential equation between the radius of the cavity and the applied load is obtained.The curves for the variation of the maximum radius of the cavity with the load and the phase diagrams are obtained by vibration theories and numerical computation.It is shown that there exists a critical value for the applied load.When the applied load is larger than the critical value,a spherical cavity will suddenly form at the center of the sphere.It is proved that the evolution of the cavity radius with time follows that of nonlinear periodic oscillation,and oscillation of the anisotropic sphere is not the same as that of the isotropic sphere.展开更多
基金the National Natural Science Foundation of China(No.19802012)the Scientific Research Foundation for Relurned Overseas Chinese Scholarsthe Scientific Research Foundation for Key Teachers in Chinese Universities
文摘An exact solution to cavitation is found tension of ac lass ofCauchy elastic membranes. The constitutive relationship of materialsis based on Hookean elastic law and finite logarithmic strain mea-Sure. A variable transformation is used in solving the two-pointboundary-value problem of nonlinear ordinary Different equation. Asimple formula to calculate the critical stretch for cavitation isderived. As the nu- Merical results, the bifurcation curvesdescribing void nucleation and suddenly rapidly growth of the cavityAre obtained. The boundary layers of displacements and stresses nearthe cavity wall are observed.
基金the National Natural Science Foundation of China(No.19772027)the Science Foundation of Shanghai Municipal Commission of Education(99A01)the Science Foundation of Shanghai Municipal Commission of Science and Technology(No.98JC14032)
文摘The relation between the Lyapunov exponent spectrum of a periodically excited non-autonomous dynamical system and the Lyapunov exponent spectrum of the corresponding autonomous system is given and the validity of the relation is verified theoretically and computationally. A direct method for calculating the Lyapunov exponent spectrum of non-autonomous dynamical systems is suggested in this paper, which makes it more convenient to calculate the Lyapunov exponent spectrum of the dynamical system periodically excited. Following the definition of the Lyapunov dimension D-L((A)) of the autonomous system, the definition of the Lyapunov dimension D-L of the non-autonomous dynamical system is also given, and the difference between them is the integer 1, namely, D-L((A)) - D-L = 1. For a quasi-periodically excited dynamical system, similar conclusions are formed.
文摘机电惯容是一种新型惯容装置,可利用电路网络实现高阶机械阻抗,具有性能和空间上的优势。由于海上风力机的机舱空间有限,研究了位于浮式平台中的机电惯容系统对漂浮式海上风力机载荷的影响。根据直流电机的特性,电机轴的转矩输出与电机回路中的电流呈线性关系,因此针对所建立的机电惯容,重点研究了所有由单个电阻、电容、电感组成的电路网络对漂浮式风力机减振性能的影响。为了降低优化过程中的复杂度,首先建立了3自由度(Degree of freedom,DOF)漂浮式海上风力机模型,随后优化了含有电路网络模型的输入输出传递函数的H2范数,得到电路网络最优参数。最后,基于美国可再生能源实验室的5 MW基准风力机模型对优化结果进行了仿真分析。仿真结果表明,在不考虑装置工作行程的情况下,所建立的机电惯容调谐质量阻尼器(Mechatronic inerter tuned mass damper,MITMD)系统可以有效减少风力机系统的结构载荷。相较于减振装置位于机舱中的情况,建立在平台中的MITMD系统可以同时减轻塔基和塔顶转轴处的载荷。MITMD的控制效果以运动位移为代价,因此在实际应用中需要折中考虑减振效果和装置的工作行程。
基金supported by the National Natural Science Foundation of China (Grant Nos.10772104 and 10872045)the innovation project of Shanghai Municipal Education Commission (Grant No.09YZ12)Shanghai Leading Academic Discipline Project (Grant No.S30106)
文摘Dynamical cavitation and oscillation of an anisotropic two-family fiber-reinforced incompressible hyper-elastic sphere subjected to a suddenly applied constant boundary dead load are examined within the framework of finite elasto-dynamics.An exact differential equation between the radius of the cavity and the applied load is obtained.The curves for the variation of the maximum radius of the cavity with the load and the phase diagrams are obtained by vibration theories and numerical computation.It is shown that there exists a critical value for the applied load.When the applied load is larger than the critical value,a spherical cavity will suddenly form at the center of the sphere.It is proved that the evolution of the cavity radius with time follows that of nonlinear periodic oscillation,and oscillation of the anisotropic sphere is not the same as that of the isotropic sphere.
