Civil Engineering Reference
In-Depth Information
Vibration analysis of SDOF
and MDOF systems in
the wavelet domain
The simplest approach in studying the response of a structural system to
an external dynamic excitation is to idealize the system as a linear single-
degree-of-freedom (SDOF) system comprising a mass body, a spring
representing the system stiffness and a dashpot representing the energy
dissipation mechanism of the system. In many of the cases, the dynamic
excitation to which the system is subjected is a seismic ground motion
process. The seismic motions are known to be highly nonstationary with
time-varying statistical characteristics and are also characterized by time-
dependent frequency content due to the dispersion of the constituent waves.
Different solution procedures have been proposed to obtain the nonstation-
ary system response; however, the specific modulating functions used in the
approach determined the nature of the nonstationarity to be considered in
the analysis. Moreover, the time-varying frequency content of input excita-
tions has not been considered. With the development of the wavelet-based
analytical technique, it has become possible to tackle the frequency non-
stationarities as well. In this chapter, we will see how to use the discretized
version of the continuous wavelet transform to obtain the nonstationary
response of a SDOF system subjected to seismic ground motion excitation.
The basic idea to solve system equations of motion in the wavelet domain is
clearly explained in this chapter.
2.1 WAVELET-BASED DISCRETIZATION
OF GROUND MOTIONS
The seismic ground motion processes are transient and contain finite
energy. Thus, these processes may be well represented by statistical func-
tionals of wavelet coefficients. Let us consider the earthquake excitation
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