Lateral vibration of a non-linear viscoelastic beam under intial axial tension

✍ Scribed by F.A. Cozzarelli; J.J. Wu; S. Tang

• Publisher: Elsevier Science
• Year: 1970
• Tongue: English
• Weight: 819 KB
• Volume: 13
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1016/s0022-460x(70)81170-1

✦ Synopsis

The free lateral vibration of a simply-supported metallic beam under axial creep deformation is considered. The constitutive law is formulated with stress power functions in the primary and secondary creep terms; the instantaneous linear elastic deformation is also included. For better physical visualization, a non-linear Maxwell-Kelvin model is used to represent the constitutive law. A reduction to various special models is also obtained. It is assumed that the initial stress is much greater than the increments of stress caused by the oscillation, and a perturbation technique is employed. In the present study, the perturbation essentialIyresults in replacing a non-linear viscoelastic problem by an equivalent linear viscoelastic problem. Analytical solutions for the Maxwell-Kelvin model and for the special models are obtained. Numerical results for a stainless steel and an aluminum alloy are also presented and discussed.