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Lalanne C. Mechanical Vibrations and Shock. Fatigue Damage (Volume 4) PDF

Lalanne C. Mechanical Vibrations and Shock. Fatigue Damage (Volume 4)
Hermes Penton Science, 2002. — 352 pages. — ISBN: 1903996066.

Having established the relationships which provide the response of a linear system with one degree of freedom to a random vibration, Volume 4 is devoted to the calculation of damage fatigue. It presents the hypotheses adopted to describe the behaviour of a material subjected to fatigue, the laws of damage accumulation, together with the methods for counting the peaks of the response, used to establish a histogram when it is impossible to use the probability density of the peaks obtained with a Gaussian signal. The expressions of mean damage and of its standard deviation are established. A few cases are then examined using other hypotheses (mean not equal to zero, taking account of the fatigue limit, non linear accumulation law, etc.).

Fatigue damage to a system with one-degree-of-freedom is one of the two criteria adopted for comparing the severity of different vibratory environments, the second being the maximum response of the system.

This criterion is also used to create a specification reproducing on the equipment the same effects as all the vibrations to which it will be subjected in its useful lifetime. This volume focuses on calculation of damage caused by random vibration.

This requires:
- having the relative response of the system under vibration represented by its PSD or by its rms value. Chapter 1 establishes all the useful relationships for that calculation. In Chapter 2 is described the main characteristics of the response.
- knowledge of the fatigue behaviour of the materials, characterized by S-N curve, which gives the number of cycles to failure of a specimen, depending on the amplitude of the stress applied. In Chapter 3 are quoted the main laws used to represent the curve, emphasizing the random nature of fatigue phenomena, followed by some measured values of the variation coefficients of the numbers of cycles to failure.
- determination of the histogram of the peaks of the response stress, supposed here to be proportional to the relative displacement. When the signal is Gaussian stationary, as was seen in Volume 3 the probability density of its peaks can easily be obtained from the PSD alone of the signal. When this is not the case, the response of the given one-degree-of-freedom system must be calculated digitally, and the peaks then counted directly. Numerous methods, ranging from the simplest (counting of the peaks) to the most complex (rainflow) have been proposed and are presented, with their disadvantages, in Chapter 5.
- choice of a law of accumulation of the damage caused by all the stress cycles thus identified. In Chapter 4 are described the most common laws with their limitations.

All these data are used to estimate the damage, characterized statistically if the probability density of the peaks is available, and deterministically otherwise (Chapter 6), and its standard deviation (Chapter 7).

Finally, in Chapter 8 are provided a few elements for damage estimation from other hypotheses concerning the shape of the S-N curve, the existence of an endurance limit, the non linear accumulation of damage, the law of distribution of peaks, and the existence of a non-zero mean value.

Contents:

Introduction

Response of a linear one degree-of-freedom linear system to random vibration
Average value of response of a linear system
Response of perfect bandpass filter to random vibration
PSD of response of a single-degree-of-freedom linear system
Rms value of response to white noise
Rms value of response of a linear one-degree-of-freedom system subjected to bands of random noise
Rms value of the absolute acceleration of the response
Transitory response of dynamic system under stationary random excitation
Transitory response of dynamic system under amplitude modulated white noise excitation

Characteristics of the response of a one-degree-of-freedom linear system to random vibration
Moments of response of a one-degree-of-freedom linear system: irregularity factor of response
Autocorrelation function of response displacement
Average numbers of maxima and minima per second
Equivalence between transfer functions of bandpass filter and one-degree-of-freedom linear system

Concepts of material fatigue
Introduction
Damage arising from fatigue
Characterization of endurance of materials
Factors of influence
Other representations of S-N curves
Prediction of fatigue life of complex structures
Fatigue in composite materials

Accumulation of fatigue damage
Evolution of fatigue damage
Classification of various laws of accumulation
Miner's method
Modified Miner's theory
Henry's method
Modified Henry's method
H. Corten and T. Dolan's method
Other theories

Counting methods for analysing random time history
General
Peak count method
Peak between mean-crossing count method
Range count method
Range-mean count method
Range-pair count method
Hayes counting method
Ordered overall range counting method
Level-crossing count method
Peak valley peak counting method
Fatigue-meter counting method
Rainflow counting method
NRL counting method (National Luchtvaart Laboratorium)
Evaluation of time spent at given level
Influence of levels of load below fatigue limit on fatigue life
Test acceleration
Presentation of fatigue curves determined by random vibration tests

Damage by fatigue undergone by a one-degree-of-freedom mechanical system
Introduction
Calculation of fatigue damage due to signal versus time
Calculation of fatigue damage due to acceleration spectral density
Equivalent narrow band noise
Comparison of S-N curves established under sinusoidal and random loads
Comparison of theory and experiment
Influence of shape of power spectral density and value of irregularity factor
Effects of peak truncation
Truncation of stress peaks

Standard deviation of fatigue damage
Calculation of standard deviation of damage: J.S. Bendat's method
Calculation of standard deviation of damage: S.H. Crandall, W.D. Mark and G.R. Khabbaz method
Comparison of W.D. Mark and J.S. Bendat's results
Statistical S-N curves

Fatigue damage using other assumptions for calculation
S-N curve represented by two segments of a straight line on logarithmic scales (taking into account fatigue limit)
S-N curve defined by two segments of straight line on log-lin scales
Hypothesis of non-linear accumulation of damage
Random vibration with non zero mean: use of modified Goodman diagram
Non Gaussian distribution of instantaneous values of signal
Non-linear mechanical system

Appendices
Gamma function
Definition
Properties
Approximations for arbitrary x
Incomplete gamma function
Definition
Relation between complete gamma function and incomplete gamma function
earson form of incomplete gamma function
Various integrals
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