Problem 4

Redo lab 10 for a circular plate with radius R = 1 m and thickness t = 0.003 m. Use the same material properties and the function P(t) shown. Apply the point force P at the center of the plate and fix half of the plate’s circumference. Use 10 modes for modal superposition. 

Hint: generate and mesh a quarter of the circle then use the “Symmetry” operation to complete the circle. This way you will have a node exactly at the center of the circle. Do not forget to “sweep”.

In your report provide the following:

1) small screenshots of the first 10 natural modes of vibration with displacement z shown via the “Contour Plot”. Organize them all on the same page

2) table of the first 10 natural frequencies of vibration

3) history plot of displacement z of the center of the plate obtained from (all curves must be on the same chart):

a. direct analysis (1000 increments)

b. modal superposition analysis (1000 increments)

c. direct result analysis (200 increments)

d. modal superposition result analysis (200 increments)

4) history plot of displacement z of the center of the plate obtained from (all curves must be on the same chart):

a. modal superposition analysis (200 increments, based on 5 modes)

b. modal superposition analysis (200 increments, based on 10 modes)

c. modal superposition analysis (200 increments, based on 20 modes)

5) comment on the results of comparisons in 3) and 4)