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[answered] MEEM 5702 Final Exam Fall 2016 Consider the beam shown in t


i want to know how to do this problem. it is a structural problem about continuous system.


MEEM 5702 Final Exam Fall 2016 Consider the beam shown in the figure below. The beam is made of steel, 200 mm wide, 100 mm thick and 1000 mm long. The beam is simply

 

supported 250 mm inboard from each end in the Z direction. The beam is loaded at one end with a force, Z ( t ) = 25sin(2? 500t ) N (in the z direction). The damping is assumed to be approximated as

 

2% modal damping.

 

Determine the following:

 

1. The natural frequency and mode shape of the first 5 modes for transverse bending about the Y

 

axis (in the XZ plane).

 

2. The frequency response function (plot) for the response at the center of the beam (Z direction)

 

due to an input at the location of the force described above.

 

3. The total response (plot: displacement vs. time) of the beam at the center in the Z direction,

 

assuming the beam starts at rest.

 

4. Which mode of the beam is the largest contributor to the response described in part 3.

 

5. Which mode(s) do not contribute to the response described in part 3.

 

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