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Summary: Numerical Continuation of Periodic Orbits for Harmonically Forced Nonlinear
Systems
Michael W. Sracic
Graduate Research Assistant, Ph.D Candidate
mwsracic@wisc.edu
&
Matthew S. Allen
Assistant Professor
msallen@engr.wisc.edu
Department of Engineering Physics
University of Wisconsin-Madison
534 Engineering Research Building
1500 Engineering Drive
Madison, WI 53706
ABSTRACT
A nonlinear structure will often respond periodically when it is excited with a sinusoidal force. Several methods are available
that can compute the periodic response for various drive frequencies, which is analogous to the frequency response function
for a linear system. The simplest approach would be to compute a sequence of simulations where the equations of motion are
integrated until damping drives the system to steady state, but that approach suffers from a number of drawbacks. Recently,
numerical methods have been proposed that use a solution branch continuation technique to find the free response of
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