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Final_Project

#Problem 1

1.a

Beam Deflection b. We used the Monte Carlo method for this part of the problem in order to determine the mean and standard deviatrion for the maximum deflection if b and h are normally dist. with q=50N/m.

#Problem 2 in order to solve for the system of equations for 6,10,20 segments, the following functions were used:

central_difference_6q.m

central_difference_10q.m

central_difference_20q.m

![alt text] (https://github.uconn.edu/nam12022/Final_Project/blob/master/Problem2graph.png) #Problem 3 in order to solve for the system of equations for 6,10,20 segments, the following functions were used:

central_difference_6p.m

central_difference_10p.m

central_difference_20p.m

![alt text] (https://github.uconn.edu/nam12022/Final_Project/blob/master/Plot3a.png) ![alt text] (https://github.uconn.edu/nam12022/Final_Project/blob/master/plot3b.png) ![alt text] (https://github.uconn.edu/nam12022/Final_Project/blob/master/Plot3c.png) #Problem 4

These the 6 segment beam yielded frequencies: f1 = 141.7854 f2 = 529.1503 f3 = 1.0583e+03

These the 10 segment beam yielded frequencies: f1 = 143.8803 f2 = 561.4373 f3 = 1.2118e+03

These the 20 segment beam yielded frequencies: f1 = 144.7715 f2 = 575.5213 f3 = 1.2816e+03 ![alt text] (https://github.uconn.edu/nam12022/Final_Project/blob/master/Prob4.png)