Abstract: A mechanical wave or vibration propagating through
granular media exhibits a specific signature in time. A coherent
pulse or wavefront arrives first with multiply scattered waves (coda)
arriving later. The coherent pulse is micro-structure independent i.e.
it depends only on the bulk properties of the disordered granular
sample, the sound wave velocity of the granular sample and hence
bulk and shear moduli. The coherent wavefront attenuates (decreases
in amplitude) and broadens with distance from its source. The
pulse attenuation and broadening effects are affected by disorder
(polydispersity; contrast in size of the granules) and have often been
attributed to dispersion and scattering. To study the effect of disorder
and initial amplitude (non-linearity) of the pulse imparted to the
system on the coherent wavefront, numerical simulations have been
carried out on one-dimensional sets of particles (granular chains).
The interaction force between the particles is given by a Hertzian
contact model. The sizes of particles have been selected randomly
from a Gaussian distribution, where the standard deviation of this
distribution is the relevant parameter that quantifies the effect of
disorder on the coherent wavefront. Since, the coherent wavefront is
system configuration independent, ensemble averaging has been used
for improving the signal quality of the coherent pulse and removing
the multiply scattered waves. The results concerning the width of the
coherent wavefront have been formulated in terms of scaling laws. An
experimental set-up of photoelastic particles constituting a granular
chain is proposed to validate the numerical results.
Abstract: This paper presents the scaling laws that provide the
criteria of geometry and dynamic similitude between the full-size
rotor-shaft system and its scale model, and can be used to predict the
torsional vibration characteristics of the full-size rotor-shaft system by
manipulating the corresponding data of its scale model. The scaling
factors, which play fundamental roles in predicting the geometry and
dynamic relationships between the full-size rotor-shaft system and its
scale model, for torsional free vibration problems between scale and
full-size rotor-shaft systems are firstly obtained from the equation of
motion of torsional free vibration. Then, the scaling factor of external
force (i.e., torque) required for the torsional forced vibration problems
is determined based on the Newton’s second law. Numerical results
show that the torsional free and forced vibration characteristics of a
full-size rotor-shaft system can be accurately predicted from those of
its scale models by using the foregoing scaling factors. For this reason,
it is believed that the presented approach will be significant for
investigating the relevant phenomenon in the scale model tests.