On the Motion of a Naturally Curved and Twisted Slender Rod

Abstract

A set of equations describing the motion of a naturally curved and twisted slender elastic rod is determined in this thesis. In particular, a study of the vibration of a helical spring is made, and the natural frequencies from the theory presented are compared with those from a simpler theory. Comparison of the two theories shows that the simpler theory is valid for most springs. The simpler theory is then used to show how the natural frequencies for a helical spring can be obtained when the spring is subjected to any boundary conditions. Finally, an analytical and experimental study of the vibration of a helical spring clamped at both ends is made in order to investigate the validity of the theory presented.