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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.