AERO4630-Project 4 Solved

Problem 1: Vibrations of a plate

material properties are the same as the cantilever beam from the last project. Let’s put our origin at theLet’s analyze the vibrations of a plate. Consider a plate of dimensions L = 1m, W = 1m and H = 0.001m. The

. We are still using the same equation of motion. So we don’t have to non-dimensionalize anything again.x = 0,y =

0,z = 0

a)     direction) force ofLet’s consider the case where the plate is clamped at the left face x = 0                                                 −z

100N                                                                                                                                                                       0.98L ≤ x ≤ L,0.49W ≤ y ≤

 
together on a single plot.(0.5L,0,H) (0.5L,0.25W,H) (0.5L,0.5W,H) (0.5L,0.75W,H) (0.5L,W,H)
(1b)
Repeat the above problem for L = 2m,W = 2m. How does the frequency and amplitude change?
(1c)
Let’s consider a different case now forapply the force ofpoints listed above (in the same format). Obtain the amplitude and frequency of vibrations of each point.at a corner L = 1m,W = 1m. Let’s clamp two faces,. Obtain the plots for all thex = 0 and y = W and

                                       100N                                  0.98L ≤ x ≤ L,0 ≤ y ≤ 0.02W,z = H
(1d)
Let’s clamp all the side facesforce ofplacement vs time for following points in a single plot:, but this time in the middleand                                               x = 0, .x = L, y = 0 and y = W (for L, = 1m,W = 1m),. Apply the same. Plot the                                                                                                                                  dis-,

100N                                                                                   0.49L ≤ x ≤ 0.51L,0.49W ≤ y ≤ 0.51W,z = H                            z

(0.5L,0.5W,H) (0.25L,0.5W,H) (0.75L,0.5W,H)

(0.5Repeat the plots fordifference in amplitudes and frequencies of all these points? If so, comment on the differences.L,0.25W,H)     (0.5L,0.75W,H) ,                                     ,                                   ,                                      . Is there a

(0.25L,0.25W,H) (0.25L,0.75W,H) (0.75L,0.25W,H) (0.75L,0.75W,H)

Now change the dimensions again topoint change? L = 2m,W = 2m. How do the frequency and amplitudes of each
(1          peat this forplacement of following points of the plate as a function of time on a single plot:  . Once the plate is bent, we let go of the force and see the plate vibrate. Plot the,on a small patch on the top towards the right side, . Obtain the amplitude and frequency of vibration of each point. Re-,                      ,    and subject to a downward (, (L,0,H),and plot these(L,0.25W,dis-H),

                     0.51W,z = H                                                                                                                                                                        z

(L,0.5W,H)(L,0.75W,H) (L,W,H)