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The system represented in the figure is composed of two rigid assemblies articulated in two points and connected to several springs as indicated. Each beam segment weighs 2 kgf/m, and the 5 kgf weight is concentrated at the end F. The stiffness constant k=1000N/m and the length L=1m . The system is operating in the xz plane. Determine, justifying the expressions used, the frequencies and natural modes of the system

Determine, justifying the expressions used, the frequencies and natural modes of the system

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I'm wondering why "$\theta_A$" and "$J_A \theta_A$" are in the opposite direction. Can someone explain it?

In the solutions they rotate in this direction

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enter image description here

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    You shall provide the link to the original/previous post. – r13 Mar 10 '22 at 19:17
  • already did it. –  Mar 11 '22 at 20:06
  • I think you need to carefully review your question, and provide more direct material tied to the question. I am still quite confused about what you have read in the past and what you have done. It is very difficult for people to jump around posts and still maintain interest in the subject. – r13 Mar 11 '22 at 20:23
  • already review it @r13 –  Mar 12 '22 at 15:31

1 Answers1

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I think the sketch below explains why they are in the opposite direction. Note that the direction of $J_A \theta_A$ indicates the direction of rotation of the sub-frame, and the rotation angle, $\theta_A$, is measured from the displaced member to its original position, which was set as the datum.

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ADD: Hope this sketch helps to understand the equation and clear your question.

enter image description here

r13
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  • thanks for the answer but in the solutions they rotate in a different direction, that is why i was asking it –  Mar 12 '22 at 19:35
  • The system will articulate in both directions. Note that the forces in the springs are reversed, so the rotations, in the last sketch you posted. – r13 Mar 13 '22 at 02:12
  • ok, but can you explain the terms in yellow in the equation for bar A? –  Mar 14 '22 at 13:51
  • It looks like an equilibrium equation, but I am not sure I agree with it without knowing the full context. – r13 Mar 14 '22 at 14:32
  • ok, but why the "-x2" and the "x4" ? I still didnt understand why "-x2" and "x4" –  Mar 15 '22 at 13:40
  • Me neither, and that's why I expressed my disagreement on the previous comment. – r13 Mar 15 '22 at 15:50
  • The only thing I can point out is F = k*x, and the equation is the summation of moments, which should be zero for the system. I sense there is a mistake, but uncertain about it. – r13 Mar 15 '22 at 17:48