3.19 Techniques for Analysing Earthquake Response
123
3.20 An accelerometer with damping ζ = 0.70 is used to measure a periodic
motion with the displacement given by the equation
x = A sin p 1 t + B sin p 2 t
3.21 A vehicle idealised as shown is moving over a surface having a sine curve
having an amplitude Y s and wave length l. Determine the transmissibility of
the motion.
Prob. 3.21
3.22 An instrument is attached to a rubber mounting having a static deflection of
3.6 mm. The supporting structure vibrates at a frequency of 30 Hz. Determine
the percentage reduction in the transmitted support motion.
3.23 A machine of mass 400 kg is supported on springs with a static deflection
of 5 mm. If the machine has a rotating unbalance of 0.2 kgm, determine the
force transmitted to the floor at 1000 rpm.
3.24 Write the equation for the force vibration of a single DOF system in terms of
the loss factor η at resonance.
3.25 A viscously damped spring–mass system is initially at rest. If the system is
actuated by a harmonic force of frequency ω = p =
k
m
, determine the
equation of its motion.
3.26 Two gears at two ends are being driven by an electric motor placed centrally on
the shaft. If the torque experienced by the rotor is T = T 0 cos ω t, determine
the resulting torsional vibration. The ends may be assumed to be changed for
the purpose of the analysis. The following values are assumed:
T 0 = 200 N m, ω = 100 Hz,
J 0 = mass moment of whole of the rotor = 0.08 kgm
2 ,
diameter of the shaft = 0.032 m,
length of the shaft on the either side of the motor = 0.45 m,
123
3.20 An accelerometer with damping ζ = 0.70 is used to measure a periodic
motion with the displacement given by the equation
x = A sin p 1 t + B sin p 2 t
3.21 A vehicle idealised as shown is moving over a surface having a sine curve
having an amplitude Y s and wave length l. Determine the transmissibility of
the motion.
Prob. 3.21
3.22 An instrument is attached to a rubber mounting having a static deflection of
3.6 mm. The supporting structure vibrates at a frequency of 30 Hz. Determine
the percentage reduction in the transmitted support motion.
3.23 A machine of mass 400 kg is supported on springs with a static deflection
of 5 mm. If the machine has a rotating unbalance of 0.2 kgm, determine the
force transmitted to the floor at 1000 rpm.
3.24 Write the equation for the force vibration of a single DOF system in terms of
the loss factor η at resonance.
3.25 A viscously damped spring–mass system is initially at rest. If the system is
actuated by a harmonic force of frequency ω = p =
k
m
, determine the
equation of its motion.
3.26 Two gears at two ends are being driven by an electric motor placed centrally on
the shaft. If the torque experienced by the rotor is T = T 0 cos ω t, determine
the resulting torsional vibration. The ends may be assumed to be changed for
the purpose of the analysis. The following values are assumed:
T 0 = 200 N m, ω = 100 Hz,
J 0 = mass moment of whole of the rotor = 0.08 kgm
2 ,
diameter of the shaft = 0.032 m,
length of the shaft on the either side of the motor = 0.45 m,