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Aerospace Structural Dynamics AE31002Tutorial Sheet 1

1. Consider the frame shown in the fig-ure below. The upper deck is rigid and

having a mass of 2.98kg/cm. Deter-mine the natural frequency of the structure.

Assume 1) the mass of the column and wallare negligible; and 2) the top platform is suf-ficiently rigid to prevent rotation at the topsof the columns. Column Ix = 3433.91cm

4.Ans. 4.49cps

2. Determine the natural period

for the system shown below.

Assume that the beam and the springs sup-porting the weight W are mass-less.Ans. T = 2L

Wg

L3EI+2kL3

3. Determine the natural frequency ofthe fixed beam as shown below,

carrying a concentrated weight W at itscenter. Neglect the mass of the beam.

Ans. f= 4

3EIgW

4. Determine the torsional spring con-stant of the steel propeller shaft shown.

Ans. 6.6 106 N-m/rad

5. The boom AB of the crane shown is auniform steel bar of length 10m and areaof cross section 2500mm2. A weight W is

suspended while the crane is stationary.The cable CDEBF is made of steel andhas a cross sectional area of 100mm2.

Neglecting the effect of the cable CDEB,find the equivalent spring constant of thesystem in the vertical direction.

Ans. keq = 26.4304 106

N/m

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