Axioms,
Год журнала:
2024,
Номер
13(9), С. 596 - 596
Опубликована: Авг. 31, 2024
This
paper
examines
the
stability
behavior
of
nonlinear
dynamical
motion
a
vibrating
cart
with
two
degrees
freedom
(DOFs).
Lagrange’s
equations
are
employed
to
establish
mechanical
regulating
system
examined
motion.
The
proposed
approximate
solutions
(ASs)
this
estimated
through
use
multiple-scales
method
(MSM).
These
considered
novel
as
MSM
is
being
applied
new
model.
Secular
terms
have
been
eliminated
meet
solvability
criteria,
and
every
instance
resonance
that
arises
categorized,
where
them
concurrently.
Therefore,
modulation
developed
based
on
representations
unknown
complex
function
in
polar
form.
for
steady
state
calculated
using
corresponding
fixed
points.
achieved
displayed
graphically
illustrate
impact
manipulating
system’s
parameters
compared
numerical
(NSs)
original
equations.
comparison
shows
great
deal
consistency
solution,
which
indicates
accuracy
method.
criteria
Routh–Hurwitz
assess
instability
zones.
value
model
exhibited
by
its
wide
range
applications
involving
ship
motion,
swaying
architecture,
transportation
infrastructure,
rotor
dynamics.
Axioms,
Год журнала:
2024,
Номер
13(9), С. 596 - 596
Опубликована: Авг. 31, 2024
This
paper
examines
the
stability
behavior
of
nonlinear
dynamical
motion
a
vibrating
cart
with
two
degrees
freedom
(DOFs).
Lagrange’s
equations
are
employed
to
establish
mechanical
regulating
system
examined
motion.
The
proposed
approximate
solutions
(ASs)
this
estimated
through
use
multiple-scales
method
(MSM).
These
considered
novel
as
MSM
is
being
applied
new
model.
Secular
terms
have
been
eliminated
meet
solvability
criteria,
and
every
instance
resonance
that
arises
categorized,
where
them
concurrently.
Therefore,
modulation
developed
based
on
representations
unknown
complex
function
in
polar
form.
for
steady
state
calculated
using
corresponding
fixed
points.
achieved
displayed
graphically
illustrate
impact
manipulating
system’s
parameters
compared
numerical
(NSs)
original
equations.
comparison
shows
great
deal
consistency
solution,
which
indicates
accuracy
method.
criteria
Routh–Hurwitz
assess
instability
zones.
value
model
exhibited
by
its
wide
range
applications
involving
ship
motion,
swaying
architecture,
transportation
infrastructure,
rotor
dynamics.
