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This document provides an introduction and background on deriving asymptotic formulas for the eigenvalues of a Timoshenko beam with variable mass density. It discusses: 1) The Timoshenko beam model, which describes transverse vibration of beams and is characterized by two coupled partial differential equations. 2) For a beam with free-free boundary conditions and variable density but constant other parameters, the problem reduces to a system of ordinary differential equations for the eigenvalues. 3) De
- Author
- tosha_fl
- Language
- EN