Premium
Solution of dynamic response of SDOF system using piecewise Lagrange polynomial
Author(s) -
Liu J. L.
Publication year - 2001
Publication title -
earthquake engineering and structural dynamics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.218
H-Index - 127
eISSN - 1096-9845
pISSN - 0098-8847
DOI - 10.1002/eqe.24
Subject(s) - piecewise , mathematics , piecewise linear function , lagrange polynomial , extension (predicate logic) , polynomial , interval (graph theory) , line (geometry) , mathematical analysis , mathematical optimization , computer science , geometry , combinatorics , programming language
Abstract 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. Copyright © 2001 John Wiley & Sons, Ltd.