The stability and vibration of an elastic rod with a circular cross section under the constraint of a cylinder is discussed. The differential equations of dynamics of the constrained rod are established with Euler＇s ...The stability and vibration of an elastic rod with a circular cross section under the constraint of a cylinder is discussed. The differential equations of dynamics of the constrained rod are established with Euler＇s angles as variables describing the attitude of the cross section. The existence conditions of helical equilibrium under constraint are discussed as a special configuration of the rod. The stability of the helical equilibrium is discussed in the realms of statics and dynamics, respectively. Necessary conditions for the stability of helical rod are derived in space domain and time domain, and the difference and relationship between Lyapunov＇s and Euler＇s stability concepts are discussed. The free frequency of flexural vibration of the helical rod with cylinder constraint is obtained in analytical form.展开更多
As part of the design and machining of the RFQ accelerator in the Compact Pulsed Hadron Source （CPHS） project at Tsinghua University, the design process of the undercuts and dipole stabilizer rods is presented in th...As part of the design and machining of the RFQ accelerator in the Compact Pulsed Hadron Source （CPHS） project at Tsinghua University, the design process of the undercuts and dipole stabilizer rods is presented in this paper. In particular, the relationship between the inter-vane voltage slope and the local frequency of the undercut section is described quantitatively. With the identification of modes existing in the cavity, the specific parameters are optimized by the SUPERFISH and MAFIA codes. In addition, the water-cooling requirement of the dipole stabilizer rods is briefly discussed.展开更多
基金the National Natural Science Foundation of China (10472067)
文摘The stability and vibration of an elastic rod with a circular cross section under the constraint of a cylinder is discussed. The differential equations of dynamics of the constrained rod are established with Euler＇s angles as variables describing the attitude of the cross section. The existence conditions of helical equilibrium under constraint are discussed as a special configuration of the rod. The stability of the helical equilibrium is discussed in the realms of statics and dynamics, respectively. Necessary conditions for the stability of helical rod are derived in space domain and time domain, and the difference and relationship between Lyapunov＇s and Euler＇s stability concepts are discussed. The free frequency of flexural vibration of the helical rod with cylinder constraint is obtained in analytical form.
基金Supported by the '985 Project' of the Ministry of Education of China
文摘As part of the design and machining of the RFQ accelerator in the Compact Pulsed Hadron Source （CPHS） project at Tsinghua University, the design process of the undercuts and dipole stabilizer rods is presented in this paper. In particular, the relationship between the inter-vane voltage slope and the local frequency of the undercut section is described quantitatively. With the identification of modes existing in the cavity, the specific parameters are optimized by the SUPERFISH and MAFIA codes. In addition, the water-cooling requirement of the dipole stabilizer rods is briefly discussed.
