FinalProject_group34

#Problem 1 This problem created the function shape_simple_support.m, which takes the input q(distributed load) and x(distance along beam) and it outputs w(deflection of the beam). This problem is solved with Euler-Bernoulli beam equation, with the transverse loading P=0 and initial conditions omega=0

1.a

1.b

A Monte Carlo approach is used to solve for the mean and standard deviation of the maximum deflection of the beam for a loading q=50N/m if b and h are randomly distributed variables b and h.

The function montecarlo_model takes input N and outputs the Mean and Standard deviation. For example the code was run with N=10 and the Mean was -.0013 and the standard deviation was 3.5271e-04 ![ Monte Carlo Output] (montecarlo_model_example.png)

#Problem 2

2.a

This problem was solved with the function central_difference_6.m ##2.b This problem was solved with the function central_difference_10.m ##2.c This problem was solved with the function central_difference_20.m ##2.d This was plotted with the script problem_2_plot.m ##2.e The analytical and numerical approaches produce similar results as can be seen by the 2 plots. There is slight variation for the number of segments as can be seen in the plot from 2.d

#Problem 3 ##3.a This problem is solved with the function central_difference_6_P.m ##3.b This problem is solved with the function central_difference_10_P.m ##3.c This problem is solved with the function central_difference_20_P.m ##3.d These were plotted with plot_6_P.m, plot_10_P.m, and plot_20_P.m

#Problem 4 ##4.a.b.c.d

Used Eigenval(6,0), Eigenval(10,0), and Eigenval(20,0) respectively

6 Segments

First Natural Frequency	Second Natural Frequency	Third Natural Frequency
141.7854	529.1503	1.0583e+03

10 Segments

First Natural Frequency	Second Natural Frequency	Third Natural Frequency
143.8803	561.4373	1.2118e+03

20 Segments

First Natural Frequency	Second Natural Frequency	Third Natural Frequency
144.7715	575.5213	1.2816e+03

##4.e Beloware the plots for 6, 10, and 20 for the 1st, 2nd and 3rd Natural Frequencies Respectively

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