Torsional vibrations of the constant rod sections

Abstract

The article presents a method of algebraic polynomials of the third degree for solving the differential equation of torsional vibrations of a rod with geometric and physical characteristics variable along its length. The numerical results were compared with the exact, analytically obtained values of the torsional vibration frequencies, and the error of the algebraic polynomial method was estimated. Calculations for various coefficients of exponentially varying polar moment of inertia of the rod are made with an accuracy of up to five significant digits.