Mathematical Model for the Free Variation of an Arc with Varying Radius of Curvature

摘要

A mathematical model for the symmetric and antisymmetric free vibrations of an arc with varying radius of curvature is developed. The arc is approximated by a discrete set of equations and the model is developed for varying cross sectional geometry (taper and thickness). Digital computer solutions for the matrix eigenvalue problem are discussed for the pinned-pinned and clamped-radially guided boundary conditions. Vibration coefficients are presented for various elliptical cases with taper and thickness variations. (Author)