Suspension bridge modeling

Abstract

The purpose of this study is to model the suspension bridge that oscillated by the external forces and investigate the phenomenon of resonance that would induce the destructive of the suspension bridge. Theoretically, the resonance will occur when the external frequency of the forces are tend to or equal to the natural frequency of the bridge. Resonance is a phenomenon of wave oscillation that can produce large amplitude even due to small periodic driving forces. A big building can collapse easily by the resonance due to the vibration of earthquake. A high frequency of sound can cause resonance to occur and break the glass or mirror. The mathematical model involves a suspension bridge that suspended at both end and it is vibrating under external forces (marching soldiers). In this model, the oscillation of the suspension bridge will be in linear wave equation form and will be solved by using the methods in Ordinary Differential Equation (ODE’s) and Partial Differential Equation (PDE’s). Different types of graph will be plotted by using MAPLE. Simulation results demonstrated that the bridge will collapse during the first two modes of the vibration when resonance occurred. Different lengths and angles of the suspension bridge also influence the period of the vibration when resonance occurred.