Random Vibration Fatigue
Random Vibration Fatigue
Random Vibration Fatigue
Excitations
Mithun
Introduction
Testing the product to failure will teach many important things about the
component/structure weaknesses and ways to improve it. Random
responses study is the key for real kind of application.
Failures can be due to :
Exceeding of safe threshold levels
Fatigue failures
Sine vs Random
Amplitude vs Time
history for sinusoidal
vibration
Amplitude vs Time
history for random
vibration
Gaussian Distribution
In random vibration, it may be desired to predict the probability of a
response exceeding a particular value.
Amplitude / RMS
Power Spectral Density
Power spectral density function (PSD) shows the strength of the
variations(energy) as a function of frequency.
Figure: Spring-mass-damper
system
M=mass
General Equation C=viscous damping coefficient
K=spring stiffness
X= absolute displacement of mass
Y= base input displacement
z (Relative displacement) = x– y
Design of components under Random
Loads
The equipment design is indented in avoiding mechanical failure and
equipment malfunction.
X(t) = response
threshold “α”
For loads with variable (but regular) amplitude levels, the fatigue life is computed
by computing the fractional damage in the material due to one cycle of
loading with amplitude level Si.
If Ni cycles are required for failure with loading of amplitude Si, the fractional
damage due to one such cycle is 1/Ni
Thus, the total fractional damage due to a loading with ‘k’ different amplitude
levels is given by Miners Rule