A NUMERICAL METHOD FOR THE TRANSIENT RESPONSE OF NONLINEAR SYSTEMS,
Abstract
Numerical integration equations are derived for determining the response of nonlinear systems subjected to transient loads. The numerical method consists of approximating the nonlinear variables and the forcing functions in the differential equations over a short interval of time by their mean value, by a straight line, or by a parabola. This allows for Duhamel integral type solutions for the nonlinear terms. A step by step solution follows which uses an iteration method during each increment of the solution. The sufficient condition for the convergence of the iteration method is presented for the case of N numerical equations. A scaling law is presented which eliminates linear damping from the equation of motion by a prescribed transformation. Example problems of a one-degree-of-freedom system and a twodegree-of-freedom system are solved by the numerical integration equations and the solutions are compared with response curves obtained from analog computers at NRL.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 21, 1963
- Accession Number
- AD0414807
Entities
People
- G. J. O'hara
- P. F. Cunniff
Organizations
- United States Naval Research Laboratory