Project 3 Partner: Lado Tonia and Diego Torrejon

Division of the Work: Part 1,2 – Collaborative Part 3,4 – Diego Part 5,6 – Mostly Lado and Diego Web Page – Mostly Kevin

Part 1 Run tacoma.m with wind speed W=80 km/hr and initial conditions y=y'= θ'=0, θ=.001. The bridge is stable in the torsional dimension if small disturbances in θ die out; unstable if they grow far beyond original size. Which occurs for this value of W? MATLAB code Drag this link to new tab for movie

Part 2 Replace the trapezoid method by fourth-order Runge Kutta to improve accuracy. Also, add new figure windows to plot y(t) and θ(t). MATLAB code

Part 3 The system is torsionally stable for W=50 km/hr. Find the magnification factor for a small initial angle. That is, set θ(0)= 10-3 and find the ratio of the maximum angle θ(t), 0 ≤ t ≤ ∞, to θ(0). Is the magnification factor approximately consistent for initial angles θ(0) = 10 -4, 10-5,...? Results >> tacoma3([0 1000],[0 0 .001 0],.04,3) magFac =7.9556e+004 MATLAB code

Part 4 Find the minimum wind speed W for which a small disturbance θ(0) = 10 -3 has a magnification factor of 100 or more. Can a consistant magnification factor be defined for this W? Results >> tacoma4([0 1000],[0 0 .001 0],.04,3); W = 58 magFac = 75.753927529200425 W = 59 magFac = 1.004609555513187e+002 MATLAB code

Part 5 Design and implement a method for computing the minimum wind speed in step 4, to within 0.5 * 10 -3 km/hr. Results >> secTacoma(55,65) W=58.9887968710310 magFac=100.0000780565943 Secant Method Matlab Code

Part 6 Try some larger values of W. Do all extremely small initial angles eventually grow to catastrophic size?

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