Stability and vibration of a helical rod constrained by a cylinder
Stability and vibration of a helical rod constrained by a cylinder作者机构：Department of Engineering Mechanics Shanghai Jiao Tong University Shanghai 200030 China
出 版 物：《Acta Mechanica Sinica》 (力学学报（英文版）)
年 卷 期：2007年第23卷第2期
页 面：215-219页
核心收录：
学科分类：08[工学] 080102[工学-固体力学] 0801[工学-力学（可授工学、理学学位）]
基 金：the National Natural Science Foundation of China (10472067)
主 题：Thin elastic rod . Cylinder constraint Stability.Flexural vibration
摘 要：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.
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