SECOND-ORDER ASYMPTOTIC APPROXIMATION OF FLEXURAL VIBRATIONS IN ELASTIC RODS
Hipolito Irago, J.M. Viaño · Mathematical Models and Methods in Applied Sciences · 1998
We address the approximation of the eigenvalues and eigenfunctions of the spectral problem derived from the linearized elastic system for a rod. The geometric properties of domain (area of cross-section is very small with respect to its length) allow us to use an asymptotic method as principal tool using the diameter of cross-section as a small parameter ∊. We characterize zeroth- and second-order terms. Convergence results to the zeroth-order term have already been studied elsewhere. Here we analyze several questions related to the second-order term as an improvement on the zeroth-order approximation that includes Timoshenko and torsion effects.