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Frequency modes of the rectangular shell

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This is task i received from my professor:

The shapes of three natural modes having the frequencies $\omega_1, \omega_2, \omega_3$ of the rectangular shell are presented in the figure. The exciting pressure $p(t)$ applied uniformly all over the one side of the shell has the form $p(t) = Pe^{jωt}$.
Make a sketch of the normal displacement of the gravity point of the shell against frequency, if the excitation frequency varies within bounds $0.5\omega_1< \omega <2\omega_1$ and static displacement of that point equals to $u_0$.

Links to photo of frequency nodes (sorry for low quality)->1 .

Can somebody help me and tell me how i should get started?

asked Jan 14 in Physics Problems by KacperKacper (100 points)
edited Jan 20 by sammy gerbil
Probably this is something to ask your professor about, because there are several things which I do not find clear about the question.

* What is the "gravity point"? Is this the centre of the shell (centre of gravity)?  
* What does "static displacement" mean? If this is the displacement when there is no exciting pressure, isn't this zero?
* The image is also not clear.  I guess for $\omega_1$ the only nodes are at the edges of the shell, for $\omega_2$ there is a node at the centre of the shell but I cannot make out the mode shape for $\omega_3$.

My guess is that this is a question about resonance. The amplitude of vibrations reaches a maximum as the driving frequency approaches the natural frequency of a mode.

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