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I'm trying to do some symbolic calculation like this:

Substitute (11.2) into the last two of equations (11.1) and, in turn, substitute these into the first of equations(11.1),

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I want to obtain a fourth-order differential equation that is

enter image description here

I have read some material in official documentation, but i still don't know how to do this in Mathematica. Can somebody help me about this, or just tell me to which book/website I should refer so that I can do the calculation in Mathematica.

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You can refer to this post: mathematica.stackexchange.com/a/6428/1871 –  xzczd Apr 16 at 4:29
    
+1 for solid mechanics :-) –  Philipp Apr 16 at 7:41
    
@xzczd Thank you! I'm reading the page you give me right now. –  Osora Apr 17 at 7:25
    
In addition, to avoid downvotes I suggest you to show your specific effort on solving this rather than just pasted the question here and vaguely said you have "read some material". BTW, you forgot to give the definition of $\rho$. –  xzczd Apr 17 at 11:02
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