Mathematical justification of stretching and torsional vibration models for elastic rods

✍ Scribed by H. Irago; J.M. Viaño

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 174 KB
• Volume: 189
• Category: Article
• ISSN: 0045-7825
• DOI: 10.1016/s0045-7825(99)00411-9

✦ Synopsis

Our goal in this work is to derive from the three-dimensional elasticity and using the asymptotic analysis, the one-dimensional evolution models for the stretching and the torsion of linearly elastic rods. More precisely, starting with the three-dimensional scaled dynamical problem and assuming the speci®c mass independent of the diameter e of the transversal section of the rod, we obtain the classical stretching and torsional models in the zeroth and second-order terms of an asymptotic expansion of the (scaled) threedimensional solution in powers of e (small parameter).