Power spectral density function

One of the most striking chaotic phenomena in generic Hamiltonian systems is the onset of nonstationary fluctuations with extremely long-time memories [5-8], Usually, the nonstationarity is characterized by the infrared catastrophe that is, the power spectral density function S(f) satisfies S(f) V(v > 1) for f O. 

Since the optic fiber probe has time response characteristic of the nanosecond level, limited by the response of the light detector, the response of signals will have essentially no time lag. Thus another method for describing optic output signals for particle concentration is to analyze the power spectrum. The power spectral density function of random signals can express the frequency structure of signals by the mean square value. The power spectral density function Sx(/) can be defined as ... 

There is no closed-form solution for the auto-correlation function or the power spectral density function of this nonlinear system. Therefore, an equivalent linear system is utilized to obtain the approximated mean of the spectral density estimator. Multiplying Equation (3.76) with x(t - t) and taking expectation yields ... 

In addition to being characterized by a PDF, signals can be characterized in the frequency domain by their power spectral density functions, which are Fourier transforms of the autocorrelation functions. White signals, which are uncorrelated from sample to sample, have a delta function autocorrelation or a flat (constant) power spectral density. Ocean signals, in general, are much more colorful and are not limited to being stationary. 

Peak picking on (averaged normalized) Power Spectral Density functions is a quick way to look to eigenfrequencies and mode shapes and can be recommended for an on side quality check of the measurements. 

The evolutionary power spectral density function was modeled as a Kanai-Tajimi filter with a Shinozuka-Sato (Shinozuka and Sato 1967) modulating function. 

This work used the power spectral density function Sxx introduced by Clough and Penzien (1975),... 

Lai, S.P. 1982. Statistical characterization of strong ground motions using power spectral density function. Bulletin of the Seismological Society of America 72 259-274. 

Figure 17.2.5 (A) Time correlation function, (B) power spectral density function, and (C) probability density function of the time series in Figure 17.2.4C. Adapted with permission from reference (8).

Since the design time histories meet response spectrum enveloping requirement and power spectral density function requirement and the components of design time histories in each direction are statistically independent, the deisgn time histories are acceptable. The critical damping values are consistent with Reg. Guide 1.61 and ASME Code Case N-411-1. 

Nonstationary power spectral density functions for the displacement response of a dam reservoir system subjected to a simple but nonstationary random acceleration excitation are obtained by a frequency domain approach due to Shinozuka. These spectral response solutions are new and are checked satisfactorily in the limiting stationary case and against the corresponding solution obtained previously by a time domain approach. For the range of frequency ratio Oj- representing dam reservoir interaction effect, it is found that the displacement spectral peak value increases with increasing dam flexibility. The location of the spectral peak is at a nearly constant value of f2Qj- (w/o) ) (c x/ s) 0.6, which means that the peak spectral response is at... 

This frequency response functions enter the modified Priestley s formulation of Sec. 2, resulting in evolutionary output power spectral density functions for deflection and moments, respectively. We... 

A Computer-oriented algorithm for nonstationary random vibrations of polygonal Kirchhoff-plates has been developed. A fast and accurate BEM for calculation of undamped frequency response function has been used. Light hysteretic damping has been introduced subsequently, and the modified spectral Priestley-formulation has been applied in order to calculate evolutionary output power spectral density functions. It is hoped that this solution strategy will be of interest for workers in the field of probabilistic structural dynamics. 

Using Blenkarn s (1970) ice force records obtained at Cook Inlet, Alaska, Fig. 1, the averaged power spectral density function. Fig. 2, is obtained. 

The mean square response given by Eqn. 8, for the averaged power spectral density function shown in Fig. 2, la given in Fig. 4. 

Fig. 7. Power spectral density functions of the radial displacement component of the...

Functions like f(/) are actually power spectral density functions. An estimation by means... 

A Bayesian framework is used to update the spectral density model with site-specific records (Radu and Grigoriu 2014). The power spectral density function g/y) is only available in... 

Cottone G, Di Paola M (2010) New representation of power spectral density function and correlation function by means of fractional spectral moments. Prob Eng Mech 25 348-353... 

Finally, in the particular case in which the modulating function presented in Eq. 2 figures as a t) = 1, the process is called stationary. Note that in this case the power-spectral density function depends only on the circular frequency and not on the time. 

Once the power-spectral density function G(ct), t) is defined, the rth sample of ground acceleration process can be generated via the superposition of N harmonics as follows (e.g., Shinozuka and Deodatis 1988) ... 

Clearly, the proper definition of the power-spectral density functirai is the crucial step to address the stochastic modeling of the seismic action. In the context of defining spectrum-compatible ground motion processes, the issue consists in determining which is the inverse relationship between the power-spectral density function and the target response spectrum. It has to be emphasized that the evaluation of the response-spectrum-compatible power-spectral... 

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