304
7 Forced Vibration Analysis of Multiple Degrees of Freedom System
Prob. 7.7
7.7 The discs of four degrees of freedom torsional problem is shown in the figure.
Determine the rotations of four discs for a torque T applied to disc 4 by using
two normal coordinates. The first two frequencies and mode shapes are
p
2
=
0.1530
1.502
K
I
and [] =
⎡
⎢
⎢
⎣
0.406 −0.475
0.707 −0.467
0.904 0.024
1.000 1.000
⎤
⎥
⎥
⎦
Also determine the torque between the first and the second discs. Solve the
problem by mode superposition method. Also determine the necessary values
using mode-acceleration method. Compare the values obtained from both the
methods.
7.8 Figure shows a structural steel beam with E = 205 × 10
9 N/m
2 , I = 400 cm
4 ,
L = 400 cm and m = 10 kg/m. Determine the displacement response of the
system to a suddenly applied force of 400kN applied at the left mass.
Prob. 7.8
7.9 Lumped mass representation of a uniform beam having flexural rigidity El is
shown. Determine the displacements of the masses due to constant force P
acting on them.
Prob.7.9
P
P