An Integral Equation Approach for the Generation of Seismic Power Spectral Density Functions

1980 ◽  
Vol 102 (3) ◽  
pp. 264-270 ◽  
Author(s):  
C. Sundararajan ◽  
G. D. Gupta
Keyword(s):  
Integral Equation ◽  
Spectral Density ◽  
Power Spectral Density ◽  
Response Spectrum ◽  
Inequality Constraint ◽  
Density Functions ◽  
Equation Approach ◽  
Power Spectral ◽  
Integral Equation Approach ◽  
Spectral Density Functions

An integral equation approach is presented for the generation of seismic power spectral density functions from specified response spectra. First, the problem of generating the response spectrum consistent power spectral density function is formulated as an integral equation with an inequality constraint, and then the equation is solved by collocation technique. An example problem is solved and the convergence of the solution is studied. The convergence study indicates that even with only about a hundred collocation points, extremely good accuracy can be achieved.

Generating Seismic Design Power Spectral Density Functions

1989 ◽  
Vol 5 (2) ◽  
pp. 351-368 ◽  
Author(s):  
John T. Christian
Keyword(s):  
Spectral Density ◽  
Density Function ◽  
Power Spectral Density ◽  
Response Spectrum ◽  
Response Spectra ◽  
Spectral Density Function ◽  
Density Functions ◽  
Power Spectral Density Function ◽  
Power Spectral ◽  
Spectral Density Functions

The most widely used way to describe earthquake motions for purposes of design is the response spectrum, but it is often difficult to apply a response spectrum when dealing with multiple degrees of freedom or with complex representations of structural behavior. The power spectral density function, which is a more fundamental description of the frequency content of ground motion, has found increasing use and is essential in the most popular methods of developing artificial earthquake time histories. Although in theory the response spectrum and the power spectral density are closely related, in practice it has proven difficult to compute one from the other. Two integration schemes described in the literature have been implemented in an interactive micro-computer program SPEED and are found to give substantially identical results. When they are used to find a power spectral density function that corresponds to a standard design response spectrum, the results do not converge at frequencies above 10 Hz. Possible explanations for this lie in the shape of the prescribed standard response spectra, the methodology used to generate them, and the lack of statistical variation at high frequencies. When power spectral density functions are calculated for response spectra determined from a statistical evaluation of strong motion across the full range of frequencies, the calculations converge rapidly.

scholarly journals A search for X-ray reprocessing echoes in the power spectral density functions of AGN

2016 ◽  
Vol 461 (2) ◽  
pp. 1642-1655 ◽  
Author(s):  
D. Emmanoulopoulos ◽  
I. E. Papadakis ◽  
A. Epitropakis ◽  
T. Pecháček ◽  
M. Dovčiak ◽  
...  
Keyword(s):  
Spectral Density ◽  
Power Spectral Density ◽  
Density Functions ◽  
X Ray ◽  
Power Spectral ◽  
Spectral Density Functions

scholarly journals Rotor Blades Diagnosis Method Based on Differences in Phase Shifts

2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Rafał Grądzki ◽  
Paweł Lindstedt ◽  
Zbigniew Kulesza ◽  
Błażej Bartoszewicz
Keyword(s):  
Phase Shift ◽  
Spectral Density ◽  
Power Spectral Density ◽  
Cross Correlation ◽  
Technical Condition ◽  
Rotor Blades ◽  
Density Functions ◽  
Power Spectral ◽  
Spectral Density Functions ◽  
Diagnosis Method

In this work, an innovative diagnosis method of rotor blades is presented. A measurement signal of blade tip displacement is divided into two observation zones, in which two peaks of an additional template signal are introduced. Cross-correlation and power spectral density functions of the measurement and template signals in these two distinct zones are calculated. Next, the phase shift between the two cross-correlation functions is obtained by calculating the ratio of the two power spectral density functions. The changes in parameters of an analytical description of this phase shift are used to determine a distinct and easy-to-analyze image of the technical condition of the tested blade. A graphical portrait indicating the technical condition of all blades in the annulus is developed. Although not directly measured, environmental signals (e.g., external disturbances and sensor’s noise) affecting the diagnostic process are included in the method. It is demonstrated that, by using the proposed signal processing technique, a negative influence of these disturbances is eliminated and the reliability of the machine technical condition indications is improved. The approach is demonstrated using experimental results of turbine engine blade displacements. High effectiveness of the method and measurement equipment has been confirmed in a wide range of analyzed tip-timing results obtained in different periods of the measurement process.

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