128
3 Forced Vibration of Single Degree of Freedom System
assumed as sinusoidal with an amplitude of 75 mm and length of 30 m. When
fully loaded, the weight of the automobile is 18 kN. The effective stiffness
of the automobile suspension is 14000 N/m and the damping ratio of the
system is 0.4. Determine (a) the amplitude of the vertical motion, (b) when
the vehicle is travelling at 60 km/hr and the speed of the vehicle that would
produce a resonant condition.
3.49 For a SDF viscously damped system, show that the energy dissipated per
cycle is given by
W =
π F
2
0
k
=
2η ζ
(1 − η 2 ) 2 + (2η ζ ) 2
3.50 A machine component is vibrating with the motion
y = 0.5 sin 30π t + 1.0 sin π t
Determine the vibration record that would be obtained with an accelerometer
having ζ = 0.15 and ω = 1000 Hz.
References
1. R.A. Anderson, Fundamentals of Vibration, McMillan Co., New York, 1967.
2. J.M. Biggs, Introduction to Structural Dynamics, McGraw-Hill Book Inc., New York, 1964.
3. R.W. Clough and J. Penzien, Dynamics of Structures, 2nd Edition, McGraw-Hill Book Inc.,
New York, 1993.
4. Roy R. Craig, Jr., Structural Dynamics, John Wiley & Sons, 1981.
5. J.P. Den Hartog, Mechanical Vibrations, Fourth Edition, McGraw-Hill Book Inc., 1956.
6. D.G. Fertis, Dynamics and Vibrations of Structures, 2nd edition, John Wiley & Sons, New
York, 2000.
7. L.S. Jacobsen and R.S. Ayer, Engineering Vibrations, McGraw-Hill Book Inc, 1958.
8. L. Meirovitch, Elements of Vibration Analysis, McGraw-Hill Book Inc., New York, 1975.
9. W.T. Thomson, Theory of Vibration with Applications, Prentice Hall, New Jersey, 1972.
10. M. Paz, Structural Dynamics Theory and Computations, Second Edition, CBS Publication and
Distribution, New Delhi, 1983.
3 Forced Vibration of Single Degree of Freedom System
assumed as sinusoidal with an amplitude of 75 mm and length of 30 m. When
fully loaded, the weight of the automobile is 18 kN. The effective stiffness
of the automobile suspension is 14000 N/m and the damping ratio of the
system is 0.4. Determine (a) the amplitude of the vertical motion, (b) when
the vehicle is travelling at 60 km/hr and the speed of the vehicle that would
produce a resonant condition.
3.49 For a SDF viscously damped system, show that the energy dissipated per
cycle is given by
W =
π F
2
0
k
=
2η ζ
(1 − η 2 ) 2 + (2η ζ ) 2
3.50 A machine component is vibrating with the motion
y = 0.5 sin 30π t + 1.0 sin π t
Determine the vibration record that would be obtained with an accelerometer
having ζ = 0.15 and ω = 1000 Hz.
References
1. R.A. Anderson, Fundamentals of Vibration, McMillan Co., New York, 1967.
2. J.M. Biggs, Introduction to Structural Dynamics, McGraw-Hill Book Inc., New York, 1964.
3. R.W. Clough and J. Penzien, Dynamics of Structures, 2nd Edition, McGraw-Hill Book Inc.,
New York, 1993.
4. Roy R. Craig, Jr., Structural Dynamics, John Wiley & Sons, 1981.
5. J.P. Den Hartog, Mechanical Vibrations, Fourth Edition, McGraw-Hill Book Inc., 1956.
6. D.G. Fertis, Dynamics and Vibrations of Structures, 2nd edition, John Wiley & Sons, New
York, 2000.
7. L.S. Jacobsen and R.S. Ayer, Engineering Vibrations, McGraw-Hill Book Inc, 1958.
8. L. Meirovitch, Elements of Vibration Analysis, McGraw-Hill Book Inc., New York, 1975.
9. W.T. Thomson, Theory of Vibration with Applications, Prentice Hall, New Jersey, 1972.
10. M. Paz, Structural Dynamics Theory and Computations, Second Edition, CBS Publication and
Distribution, New Delhi, 1983.