Engineering Dynamics: Connected Systems

[VonDanglewanger]

Homework Statement

A uniform bar ABCD having a mass of 4.25kg is pivoted at B shown in Figure below. The bar ABCD is
supported at A and D by springs having stiffness’s of 12kN/m and 2kN/m respectively. A torsional spring
of stiffness 100Nm/rad is also present at the pivot B and a damper is located at C having a coefficient of
damping of 6kNs/m. A discrete mass of 6.75kg is at D. Beam ABCD is connected to another beam EFG by
Link DG. The Link has negligible mass. Beam EFG is also uniform and has a mass of 7.1kg/m and is pivoted
at E and carries a mass of 8kg and a spring of stiffness 10kN/m at F. Determine:

(a) the equivalent mass-spring-damping system at A;
(b) the natural frequency of the system.

My thoughts at a solution involve moving the mass and spring from F to D to find the equivalent mass-spring system at D. I would then calculate the equivalent mass of lever EFG, which I believe would be transmitted through lever DG to point D. Adding the equivalent mass of lever EFG to the mass at D would give me a new value for the equivalent mass at D which means I could treat the whole thing as a linear system and work back from D referring everything to point A as instructed.

Question: Does this appear to be a logical solution? What do I do about the torsional spring at pivot B, can I somehow convert it into a linear spring constant?

 

[paisiello2]

The way you state it doesn't sound correct.

For example, I am not entirely sure what you mean by "moving the mass and spring from F to D". If you literally mean this then I don't think this will give you the correct answer.

The correct approach I think would be to develop a displacement relationship between all the points.

BTW, there appear to be some typos in the written description since it doesn't match the diagram 100%.