# 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
edited Jan 20
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.