Chapter 15
Random Vibrations
15.1 Introduction
During the last three decades, a great deal of activity has taken place in studying
the loads acting on the structure in a realistic manner and the necessary response
thereof. The analytical methods during this period have made tremendous strides,
and a need has been felt to account for the load in its truer perspective. The dynamic
loads which have been considered in all the previous chapters have fixed or definite
values of amplitude, frequency, period and phase. But for many cases, such as wave
forces on offshore structures, earthquake effects on buildings, bridges and dams, air
pressure on aeroplanes and vibration of ships in rough seas, there is an uncertainty
involved with the exactness of the loading parameters. These uncertainties are related
to the random time functions.
The input to the problem, that is the loading, is rather complex and extremely
irregular in many cases. Exact mathematical representation of them is practically
impossible. The only rational way to deal with such cases is to treat them as random
process, so that the loading can be treated in a probabilistic sense. The input being
random, the response of the structure will also be random [1–7].
15.2 Random Process
Based on the behaviour of the parameters, a process may be categorised into the
following two types: deterministic process and random process.
If an experiment is conducted a number of times under identical conditions and
the records obtained are always alike, then the process is termed as deterministic.
If an experiment is conducted a number of times, maintaining the variables identified by the experimenter same in all cases, but the output or records continually differ
from each other, then the process is said to be random. The degree of randomness
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
M. Mukhopadhyay, Structural Dynamics,
https://doi.org/10.1007/978-3-030-69674-0_15
527
Random Vibrations
15.1 Introduction
During the last three decades, a great deal of activity has taken place in studying
the loads acting on the structure in a realistic manner and the necessary response
thereof. The analytical methods during this period have made tremendous strides,
and a need has been felt to account for the load in its truer perspective. The dynamic
loads which have been considered in all the previous chapters have fixed or definite
values of amplitude, frequency, period and phase. But for many cases, such as wave
forces on offshore structures, earthquake effects on buildings, bridges and dams, air
pressure on aeroplanes and vibration of ships in rough seas, there is an uncertainty
involved with the exactness of the loading parameters. These uncertainties are related
to the random time functions.
The input to the problem, that is the loading, is rather complex and extremely
irregular in many cases. Exact mathematical representation of them is practically
impossible. The only rational way to deal with such cases is to treat them as random
process, so that the loading can be treated in a probabilistic sense. The input being
random, the response of the structure will also be random [1–7].
15.2 Random Process
Based on the behaviour of the parameters, a process may be categorised into the
following two types: deterministic process and random process.
If an experiment is conducted a number of times under identical conditions and
the records obtained are always alike, then the process is termed as deterministic.
If an experiment is conducted a number of times, maintaining the variables identified by the experimenter same in all cases, but the output or records continually differ
from each other, then the process is said to be random. The degree of randomness
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
M. Mukhopadhyay, Structural Dynamics,
https://doi.org/10.1007/978-3-030-69674-0_15
527