Solution of dynamic response of SDOF system using piecewise Lagrange polynomial. - Liu, J. L. (Earthquake engineering & structural dynamics.)
As an extension of the procedure in which an arbitrary dynamic loading is approximated by piecewise linear segments, the second and third degree piecewise Lagrangian interpolating polynomials are employed to approximate an arbitrary dynamic loading in the Duhamel integral for the solution of dynamic response of a SDOF system. The related formulae are derived. The proposed method offers computational advantage over the traditional step by step solution techniques for comparable accuracy and far better accuracy than the piecewise linear approximation procedure for comparable time interval when the loading cannot be represented by straight line segments.