Application of Taylor Matrix Method to the Solution of Longitudinal Vibration of Rods

The present study introduces a novel and simple matrix method for the solution of longitudinal vibration of rods in terms of Taylor polynomials. The proposed method converts the governing partial differential equation of the system into a matrix equation, which corresponds to a system of linear algebraic equations with unknown Taylor coefficients. Then the solution is obtained easily by solving these matrix equations. Both free and forced vibrations of the system are studied; particular and general solutions are determined. The method is demonstrated by an illustrative example using symbolic computation. Comparison of the numerical solution obtained in this study with the exact solution is quite good.