ON COUPLED LONGITUDINAL AND LATERAL VIBRATIONS OF ELASTIC RODS

✍ Scribed by O.M. O'REILLY

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 429 KB
• Volume: 247
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.2001.3753

✦ Synopsis

In this paper, the coupled longitudinal and lateral vibrations of a rectangular parallelepiped composed of a uniform, isotropic, elastic body are examined. The one-dimensional model for the body was developed by Green, Naghdi and several of their co-workers. It is based on a Cosserat or directed rod theory. The frequency spectrum is found to divide naturally into three regions which are separated by degenerate cases. When the cross-section of the body is square, a natural splitting of the modes occurs. One-half of this split involves motions coupling the axial extension and symmetric lateral deformation of the body. The other half involves asymmetric lateral deformations. The cases of a free}free rod and a cantilevered rod are discussed and the results compared to existing works in the literature which use the three-dimensional theory of elasticity to model the vibrations.