Fatigue damage spectrum

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The Fatigue Damage Spectrum (FDS) of a vibration is obtained by tracing the fatigue damage experienced by a linear Single Degree of Freedom System (SDOF) according to its natural frequency, for given damping ratio and for a given value of parameter b (this parameter comes from the Basquin law representing the Wöhler curve of the material constituting the structure).

In physics, the degree of freedom (DOF) of a mechanical system is the number of independent parameters that define its configuration. It is the number of parameters that determine the state of a physical system and is important to the analysis of systems of bodies in mechanical engineering, aeronautical engineering, robotics, and structural engineering.

Contents

Regardless of the vibratory signal studied (sinusoidal vibration, shock, random or composite vibration); the FDS can be obtained directly from the time history signal. The method consists of :

In the case of stationary random vibration, the Power spectral density (PSD) of the vibration can be directly used for the FDS calculation.

Spectral density Relative importance of certain frequencies in a composite signal

The power spectrum of a time series describes the distribution of power into frequency components composing that signal. According to Fourier analysis, any physical signal can be decomposed into a number of discrete frequencies, or a spectrum of frequencies over a continuous range. The statistical average of a certain signal or sort of signal as analyzed in terms of its frequency content, is called its spectrum.

Note

Vibrations can damage a mechanical system as a result of several processes, among which are:

FDS is used according to the second criterion. The first criterion is considered with the Extreme response spectrum (ERS).

The Extreme Response Spectrum (ERS) is defined as a curve giving the value of the highest peak of the response of a linear Single Degree of Freedom System to vibration, according to its natural frequency, for a given damping ratio. The response is described here by the relative movement of the mass of this system in relation to its support. The x-axis refers to the natural frequency and the y-axis to the highest peak multiplied by the square of the quantity, by analogy with the relative displacement shock response spectrum.

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