1.9 Types of Analysis
13
If the records of the dynamic load and the corresponding responses are taken
many times under identical conditions, and both the records obtained are alike in all
cases, then the vibration is said to be deterministic. In this, the analyst has perfect
control over all the variables related to the problem.
If the records of the dynamic load and the corresponding responses are taken
many times, when all other conditions under the control are maintained the same,
but the records are found to differ continually from each other, then the vibration
is said to be random. This unpredictability associated with the input and output of
the problem is referred to as randomness. The degree of randomness depends on the
understanding of the effects of different parameters involved and the ability to control
them. Chapter 15 of the book deals with random vibration, whereas the treatment in
other remaining chapters is deterministic vibration.
1.10 Linear and Nonlinear Vibration
If the basic components associated with the vibration analysis, such as the spring,
mass and the damper behave linearly, then the emanated vibration is referred to as
linear vibration. In this case, the differential equation of motion is linear.
On the other hand if one or more of the basic components behave in a nonlinear
manner, the resulting vibration is said to be nonlinear vibration. In this case, the
analyst will have to deal with nonlinear differential equation of motion. It may be
mentioned that the linear analysis of vibration is more straight forward, whereas the
nonlinear analysis of vibration is more mathematically involved.
References
1. M. R. Cohen and I. E. Drabkin, A Source Book on Greek Science, Harvard University Press,
Cambridge, 1958
2. A. D. Dimarogonas, The origins of vibration theory, Journal of Sound and Vibration, V. 140,
No. 2, 1993, pp. 181–189
3. M. G. Evans, The Physical Philosophy of Aristotle, The University of New Mexico Press,
Albuquerque, 1964.
4. S. P. Timoshenko, History of Strength of Materials, McGraw-Hill, New York 1953
5. J. W. Strutt [Lord Rayleigh], The Theory of Sound, Dover, 1945.
6. F. Dinca and C. Theodosin, Nonlinear and Random Vibration, Academic Press Inc., 1973.
7. S. H. Crandall and W. D. Mark, Random Vibration in Mechanical Systems, Academic Press,
New York, 1963.
8. J. D. Robson, Random Vibration, Edinburgh University Press, Edinburgh, U. K., 1964.
9. D. E. Newland, An Introduction to Random Vibrations and Spectral Analysis, Longman,
London, 1975.
10. R.W.Clough and J. Penzien, Dynamics of Structures, McGraw-Hill Inc., 1993
11. S.O. Rice, Mathematical Analysis of Random Noise, Dover Publications, New York, 1954
12. J.S. Bendat, Principles and Applications for Random Noise Theory, John Wiley & Sons, New
York, 1966
13
If the records of the dynamic load and the corresponding responses are taken
many times under identical conditions, and both the records obtained are alike in all
cases, then the vibration is said to be deterministic. In this, the analyst has perfect
control over all the variables related to the problem.
If the records of the dynamic load and the corresponding responses are taken
many times, when all other conditions under the control are maintained the same,
but the records are found to differ continually from each other, then the vibration
is said to be random. This unpredictability associated with the input and output of
the problem is referred to as randomness. The degree of randomness depends on the
understanding of the effects of different parameters involved and the ability to control
them. Chapter 15 of the book deals with random vibration, whereas the treatment in
other remaining chapters is deterministic vibration.
1.10 Linear and Nonlinear Vibration
If the basic components associated with the vibration analysis, such as the spring,
mass and the damper behave linearly, then the emanated vibration is referred to as
linear vibration. In this case, the differential equation of motion is linear.
On the other hand if one or more of the basic components behave in a nonlinear
manner, the resulting vibration is said to be nonlinear vibration. In this case, the
analyst will have to deal with nonlinear differential equation of motion. It may be
mentioned that the linear analysis of vibration is more straight forward, whereas the
nonlinear analysis of vibration is more mathematically involved.
References
1. M. R. Cohen and I. E. Drabkin, A Source Book on Greek Science, Harvard University Press,
Cambridge, 1958
2. A. D. Dimarogonas, The origins of vibration theory, Journal of Sound and Vibration, V. 140,
No. 2, 1993, pp. 181–189
3. M. G. Evans, The Physical Philosophy of Aristotle, The University of New Mexico Press,
Albuquerque, 1964.
4. S. P. Timoshenko, History of Strength of Materials, McGraw-Hill, New York 1953
5. J. W. Strutt [Lord Rayleigh], The Theory of Sound, Dover, 1945.
6. F. Dinca and C. Theodosin, Nonlinear and Random Vibration, Academic Press Inc., 1973.
7. S. H. Crandall and W. D. Mark, Random Vibration in Mechanical Systems, Academic Press,
New York, 1963.
8. J. D. Robson, Random Vibration, Edinburgh University Press, Edinburgh, U. K., 1964.
9. D. E. Newland, An Introduction to Random Vibrations and Spectral Analysis, Longman,
London, 1975.
10. R.W.Clough and J. Penzien, Dynamics of Structures, McGraw-Hill Inc., 1993
11. S.O. Rice, Mathematical Analysis of Random Noise, Dover Publications, New York, 1954
12. J.S. Bendat, Principles and Applications for Random Noise Theory, John Wiley & Sons, New
York, 1966