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I would like to know how I go about calculating the resonance frequency for an object, given its material properties and dimensions. For example, a small rectangle $X$ by $Y$ by $Z$ dimensions, I would assume the material properties necessary are the Young's modules, $E$, and density, $\rho$.

And then how would this extend to other shaped objects?

Thank you in advance.

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  • $\begingroup$ In the general case, you will use a finite element software such as Ansys to do a modal analysis of the object. Young's modulus and E are the same thing. $\endgroup$ – James Jan 19 '18 at 14:48
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    $\begingroup$ Thank you, I am aware that Young's modulus and E are the same, I wrote it in the form of "parameter name, symbol" as is the general practise. $\endgroup$ – Dave Jan 19 '18 at 15:36
  • $\begingroup$ Oh, right! Sorry I missed that. $\endgroup$ – James Jan 19 '18 at 15:57
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    $\begingroup$ That's no problem, thanks for trying to help. But outside of using finite element modelling tool, is there some back of the envelope calculations that you are aware of to calculate resonance for a block of material. I've got COMSOL and can plug parameters into that, but I am looking more for a way to compare or have an idea of the result before running the model, and to help improve my understanding of the physics involved. $\endgroup$ – Dave Jan 19 '18 at 16:10

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