Abstract: The differential matrices of derivatives are constructed by using barycentric Lagrange interpolation which has good numerical stability and high computing precision. The barycentric interpolation collocation method for analyzing the vibration problems under arbitrary excitation is presented. The vibration differential equation and two initial conditions are transformed into a set of algebraic equation system and two algebraic equations respectively. Applying attached method to impose initial conditions, a new set of algebraic equation system which has n variables and n+2 equations is obtained. The new algebraic equation system is solved by using least-square method. The velocity and acceleration of vibration is directly computed by using differential matrices. For vibration problems under pulse excitations, dividing the time domain into two intervals according to the characters of excitation, the displacements of vibration in the two intervals are computed respectively. The displacement and velocity at the end of first interval are taken as the initial conditions of vibration in the second interval. The numerical examples indicate that the proposed method has high computing precision in analysis of vibration under pulse excitations.

Key words: Barycentric interpolation, Collocation method, Numerical analysis, Pulse excitation, Vibration