Nonlinear Dynamic Pre-Diagnostic Analysis of Lima Metro Line 1 Using the Duffing Oscillator Model

Abstract

This paper adapts Duffing’s nonlinear model to evaluate the vibration response of the slabs of Line 1 of the Lima Metro (Peru). The procedure consisted of reformulating the classical oscillator as a nonlinear autonomous system in state space and calibrating its dynamic parameters under operating conditions representative of the infrastructure. Unlike traditional linear approaches, the formulation incorporates variable stiffness and loss of dissipative capacity, enabling the analysis of stability, parametric sensitivity, and global behavior in the phase plane. From the local stability study, two quantitative indicators of vibration performance were defined: the characteristic dissipation time (τ) and the dynamic margin (MD). For the calibrated parameters, the system exhibits asymptotic stability with τ = 0.189 s and MD = 0.050, indicating rapid dissipation but with a relatively small dynamic margin. The sensitivity analysis showed that decreasing the damping increases the dissipation time by 32%, evidencing greater persistence of residual vibrations. The proposed model links physical parameters with measurable metrics, serving as a quantitative pre-diagnostic tool in Structural Health Monitoring (SHM) systems to support railway maintenance decisions.