... by the balance of linear momentum. The natural frequencies for the in-plane and out-of-plane vibrations are calculated by both the Galerkin method and differential quadrature method. It can be found that natural frequencies of the in-plane vibrations are much higher than those in the out-of-plane case, which...

...Oliver M. O’Reilly, Professor; Peter C. Varadi, Mem. ASME We consider the dynamics of a closed loop of inextensible string which is undergoing an axial motion. At each instant, one material point of the string is in contact with a singular supply of linear momentum (also known as an external...