108
Mechanical shock
factor
for
transformation, which also implicitly also that
if
there
are
several
resonances,
the Q
factor varies little with
the frequencies.
- A
very short phenomenon, which will induce
the
response
of
few
cycles,
is
replaced
by a
vibration
of
much large duration, which will produce
a
relatively
significant
number
of
cycles
of
stress
in the
system
and
will
be
able
to
thus damage
the
structures sensitive
to
this phenomenon
in a
non-representative manner
[KER 84].
- The
maximum
responses
are the
same,
but the
acceleration signals x(t)
are
very
different.
In a
sinusoidal
test,
the
system reaches
the
maximum
of its
response
at
its
resonance
frequency. The
input
is
small
and it is the
resonance which makes
it
possible
to
reach
the
necessary
response.
Under
shock,
the
maximum response
is
obtained
at a frequency
more characteristic
of the
shock itself [CZE 67].
- The
swept sine individually excites resonances,
one
after
another, whereas
a
shock
has a
relatively broad spectrum
and
simultaneously excites several modal
responses which
will
combine.
The
potential mechanisms
of
failure
related
to the
simultaneous excitation
of
these modes
are not
reproduced.
4.4.2. Simulation
of
shock
response
spectra
using
a
fast
swept
sine
J.R.
Pagan
and
A.S. Baran [FAG
67]
noted
in
1967 that certain shapes
of
shock,
such
as the
terminal peak
saw
tooth pulse excite
the
high
frequencies of
resonance
of
the
shaker
and
suggested
the use of a
fast
swept sine wave
to
avoid this problem.
They
saw
moreover
two
advantages there: there
is
neither residual velocity
nor
residual displacement
and the
specimen
is
tested according
to two
directions
in the
same
test.
The
first
work carried
out by
J.D. Crum
and R.L
Grant [CRU
70]
[SMA 74a]
[SMA
75], then
by
R.C. Rountree
and
C.R. Freberg [ROU
74] and
D.H. Trepess
and
R.G.
White [TRE
90]
uses
a
drive signal
of the
form:
where A(t)
and
E(t)
are two
time functions,
the
derivative
of
<j)(t)
being
the
instantaneous pulsation
of
x(t).
The
response
of a
linear one-degree-of-freedom mechanical system
to a
sinewave excitation
of frequency
equal
to the
natural
frequency of the
system
can be
written
in
dimensionless
form
(Volume
1,
Chapter
5) as: