  In this paper we explore the numerical study. of the Nonlinear Behavior of
Suspension Bridge Models. The study of suspension bridges is one of the classic
problems of mechanical vibrations, one of the most famous collapses of which
was that of the Tacoma Narrows Bridge. This paper covers an initial explanation
of vibrations in a suspension bridge. To do this, three different systems are
going to be simulated: The first being a system where only the vertical
vibrations of the bridge deck are taken into account, the second covering the
vibrations of the main cable and the roadbed, and lastly, a system that takes
both vertical and torsional vibrations into account. A time-frequency analysis
will also be done on all systems with temporal response, Fast Fourier Transform
(FFT) and Continuous Wavelet Transform (CWT), plus in a specific case the use
of Hilbert-Huang transform (HHT). Poincare maps and Lyapunov exponents are used
to characterize the dynamics of the system. In particular, in the vertical and
torsional system, an explanation of why the Tacoma Bridge oscillations have
undergone an abrupt change from vertical to torsional oscillations. Thus,
extremely rich dynamic behaviors are studied by numerical simulation in the
time and frequency domains.
