Citation: Barraza-Contreras, J.M.;
Piña-Monarrez, M.R.; Molina, A.;
Torres-Villaseñor, R.C. Random
Vibration Fatigue Analysis Using
a Nonlinear Cumulative Damage
Model. Appl. Sci. 2022, 12, 4310.
https://doi.org/10.3390/
app12094310
Academic Editors:
Alberto Campagnolo and
Alberto Sapora
Received: 29 March 2022
Accepted: 21 April 2022
Published: 24 April 2022
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Article
Random Vibration Fatigue Analysis Using a Nonlinear
Cumulative Damage Model
Jesús M. Barraza-Contreras * , Manuel R. Piña-Monarrez , Alejandro Molina and Roberto C. Torres-Villaseñor
Industrial and Manufacturing Department, Engineering and Technological Institute, Universidad Autónoma de
Ciudad Juárez, Ciudad Juárez 32310, Chihuahua, Mexico; manuel.pina@uacj.mx (M.R.P.-M.);
al187118@alumnos.uacj.mx (A.M.); al153286@alumnos.uacj.mx (R.C.T.-V.)
* Correspondence: al187061@alumnos.uacj.mx; Tel.: +52-656-330-1229
Featured Application: To apply the proposed model and its method, the inputs required are vibra-
tion power spectral density (PSD) and material characteristics, thus the bending stress provoked
by vibration can be determined by using response acceleration. The proposed model incorpo-
rates the damage induced by the stress of the random vibration, then, the fatigue life is estimated.
Thus, for further research, the model can be used to formulate fatigue analysis considering a ma-
terial’s strain or crack growth.
Abstract:
The paper’s content allowed us to determine the fatigue life of a component that is being
subjected to a random vibration environment. Its estimation is performed in the frequency domain
with loading frequencies being closer to the system’s natural frequency. From loads’ amplitude
and their interaction effect, we derive a nonlinear damage model to cumulate the generated fatigue
damage. The exponent value of 0.4 from the Manson–Halford curve damage model was replaced by
a vibration bending stress relation that considers the effect and interaction of loads. The analysis is
performed from a progressive accelerated vibration spectrum to predict the fatigue life estimation.
From this accelerated scenario, the accelerated coefficients and cumulated damage are both deter-
mined. The proposed nonlinear model is based on the following facts: (1) vibration and bending
stress
σ
vb
values are obtained from the response acceleration of power spectral density (PSD) applied
and (2) the model can be applied to any mechanical component analysis where the corresponding
acceleration responses
A
res
and the dynamic load factor
σ
dynamic
values are known. The steps to
determine the expected fatigue damage accumulation D by using the curve damage are given.
Keywords:
fatigue damage; random vibration; resonant frequency; acceleration response; non-linear
accumulative model
1. Introduction
Several systems and components may be subjected to vibrations during their op-
erational life. Random vibration induces fatigue damage by dynamic loads and their
amplitudes [
1
], which causes deflection in the component. The maximum experienced
stresses are generated as a response of the natural frequencies of the component [
2
], mainly
when products are operating close to those natural frequencies (resonance frequency).
Thus, components must be designed to withstand the induced fatigue damage. There-
fore, during product development, it is necessary to validate the component functionality
through durability/validation tests. Furthermore, since predicting the fatigue damage is
a complex process [
3
], nowadays, its accurate prediction is a fundamental engineering
problem. For that purpose, some cumulative damage models have been proposed; some of
these include the modified Steinberg vibration lifetime model [
4
] that considers that the
effects of the vibration are accurate predictions. The synthesis of sine on random vibration
based on fatigue damage spectrum [
5
] preserves not only the induced fatigue damage but
Appl. Sci. 2022, 12, 4310. https://doi.org/10.3390/app12094310 https://www.mdpi.com/journal/applsci
