Multiple Periodic Solutions of a Nonlinear Suspension Bridge System of Partial Differential Equations

A nonlinear system of partial differential equations is presented to model the vertical motions of the roadbed and main cable of suspension bridge. The model is subjected to periodic forcing and numerical methods are presented for the computation of the periodic responses in the system.Newton's method, continuation algorithms and Floquet theory are used to produce bifurcation diagrams which capture the multiplicity and stability of the periodic solutions. Separable solutions are investigated using methods for ordinary differential equations while general solutions are investigated using a finite difference scheme and an implicit-explicit initial value solver.The method of steepest descent is used to find entirely new branches of periodic solutions. Multiple periodic solutions are found, including subharmonic solutions whose period is a multiple of the period of the forcing.