Konya Journal of Engineering Sciences,
Journal Year:
2023,
Volume and Issue:
11, P. 23 - 31
Published: Dec. 27, 2023
In
recent
years,
the
analysis
of
materials
and
elements
with
dimensions
at
nano/micro
levels
has
gained
momentum.
While
analyzing
these
small-scale
elements,
higher-order
elasticity
theories
have
started
to
be
used
instead
classical
(CETs).
One
theories,
which
includes
a
parameter
in
its
constitutive
equations,
is
modified
couple
stress
theory
(MCST).
this
study,
bending
cantilever
perforated
microbeam
investigated
by
MCST
Euler-Bernoulli
(EB)
beam
theory.
First,
perforation
characteristics
are
described
incorporated
into
equation
governing
problem
based
on
found
literature.
Then,
Laplace
transform
applied
equation.
The
known
boundary
conditions
substituted
inverse
obtain
deflection
Mechanics of Advanced Materials and Structures,
Journal Year:
2024,
Volume and Issue:
unknown, P. 1 - 24
Published: March 13, 2024
This
study
presents
a
thermal
vibration
analysis
of
functionally
graded
porous
nanobeams
using
boosting
machine
learning
models
and
semi-analytical
approach.
Nonlocal
strain
gradient
theory
is
employed
to
explore
behavior,
accounting
for
size
effects.
A
approach
solution
utilizing
Fourier
series
Stokes'
transform
establish
an
eigenvalue
problem
capable
examining
vibrational
frequencies
in
both
rigid
deformable
boundary
conditions
presented.
Four
including
(GBoost),
light
(LGBoost),
extreme
adaptive
(AdaBoost)
are
the
impact
seven
crucial
parameters
on
natural
nanobeam.
Sobol
quasi-random
space-filling
method
used
generate
samples
by
varying
input
feature
combinations
different
nanobeam
distributions.
The
model
performance
assessed
statistical
metrics,
visualization
tools,
5-fold
cross-validation,
SHAP
importance.
results
highlight
effectiveness
ML
predicting
frequencies,
particularly
XGBoost,
which
achieved
exceptional
R2
value
0.999,
accompanied
lowest
MAE,
MAPE,
RMSE
values
among
assessed.
LGBoost
AdaBoost
follow
XGBoost
performance,
while
GBoost
exhibits
relatively
lower
effectiveness,
as
highlighted
radar
plots.
revealed
significant
foundation
parameter
frequency
prediction,
with
porosity
coefficients
notably
influencing
higher
modes.
Mechanics Based Design of Structures and Machines,
Journal Year:
2024,
Volume and Issue:
52(10), P. 8216 - 8248
Published: March 17, 2024
This
study
introduces
an
approach
to
analyze
torsional
vibration
in
non-circular
nanowires
within
magnetic
fields,
considering
various
boundary
conditions
on
elastic
foundation.
Analytical
formulas
for
natural
angular
frequencies
are
obtained
using
nonlocal
strain
gradient
theory.
The
analysis
covers
three
cross-sections,
incorporating
the
warping
effect.
Elastic
springs
at
wire
ends
simulate
support
conditions,
restricting
rotation
around
wire's
axis.
torsion
function
axis
is
represented
by
a
Fourier
series,
discretized
spring
points
and
linked
Stokes'
transform
alongside
values.
leads
eigenvalue
problem
that
includes
higher-order
material
size
parameters
(strain
gradient,
nonlocal),
parameters,
function.
study's
novelty
lies
effectively
solving
sections,
addressing
function,
medium,
effects
under
both
deformable
non-deformable
conditions.
presented
solution
capable
of
determining
rigid
accomplished
specifying
stiffness
values,
thereby
obviating
necessity
additional
recalculations.
In
order
verify
results
compare
them
with
existing
literature,
free
clamped
solved
numerically
changing
problem.
formulation
frequency;
length
scale
warping,
field,
medium
included.
addition,
since
modeled
springs,
resulting
quite
general
can
be
used
solve
different
types
problems.
Zeitschrift für Naturforschung A,
Journal Year:
2025,
Volume and Issue:
unknown
Published: April 7, 2025
Abstract
This
study
considers
the
buckling
problem
of
beams
resting
on
a
nonlocal
foundation.
A
foundation
is
modeled
with
two
different
spring
structures
extending
under
and
along
length
beam
shear
layer
between
these
springs.
investigates
using
method
based
Fourier
sine
series
Stokes’
transformation.
Thus,
an
analytical
solution
by
transverse
springs
at
both
boundaries
presented.
can
solve
arbitrary,
i.e.,
rigid
non-rigid,
since
it
includes
stiffnesses
positioned
as
bearings
ends
The
be
set
arbitrarily
effects
numerous
boundary
conditions,
whether
or
deformable,
studied.
After
derivation
formulation,
parameters
critical
loads
foundations
are
investigated
through
numerical
examples.
International Journal Of Engineering & Applied Sciences,
Journal Year:
2025,
Volume and Issue:
17(1), P. 1 - 16
Published: May 1, 2025
This
study
investigates
the
bending
response
of
perforated
nanobeams
resting
on
Winkler-Pasternak
elastic
foundation
(WPEF),
using
Eringen's
theory
nonlocal
elasticity
(ENET).
The
analysis
examines
how
various
parameters
affect
mechanical
nanobeam,
including
parameter,
parameters,
filling
ratio,
and
number
holes.
Results
indicate
that
an
increase
in
parameter
produces
larger
transverse
displacements
compared
to
classical
beam
theory,
while
stiffness
decreases
due
nanoscale
effects.
significantly
influence
behavior,
with
Pasternak
model
proving
more
effective
than
Winkler
(WEF)
reducing
displacement.
Analysis
hole
properties
reveals
higher
ratios
stiffness,
holes
nanobeam
stiffness.
These
findings
are
crucial
for
optimizing
design
nanoelectromechanical
systems
other
nanostructured
devices
where
behavior
affects
performance.
Journal of Vibration Engineering & Technologies,
Journal Year:
2024,
Volume and Issue:
12(4), P. 6847 - 6863
Published: March 13, 2024
Abstract
Objective
The
purpose
of
this
work
is
to
investigate
the
size-dependent
free
vibrations
carbon
nanotube-reinforced
nanowires/nanobeams
with
movable
ends.
For
purpose,
two
end
conditions
are
considered
for
different
nanotube
distributions.
size
effect
addressed
modified
couple
stress
theory,
which
includes
a
material
length
scale
parameter.
Methods
In
study,
solution
approach
based
on
Fourier
sine
series
and
Stokes'
transformation
used.
With
help
approach,
both
rigid
can
be
investigated.
Firstly,
equation
sets
consisting
infinite
parameters
derived.
Then,
eigenvalue
problems
obtained
vibration
nanowires/nanobeams.
eigenvalues
these
give
frequencies
Conclusions
in
study
used
examine
conditions.
accuracy
proven
by
various
comparison
studies.
analyses
carried
out
nanowire/nanobeam
reinforced
nanotubes,
including
rotary
inertia
effect.
When
nanowire/nanobeams
nanotubes
examined,
it
understood
that
parameter,
distribution,
volume
fraction,
rotational
lateral
spring
cause
significant
changes
vibration.
Engineering Science and Technology an International Journal,
Journal Year:
2024,
Volume and Issue:
56, P. 101787 - 101787
Published: Aug. 1, 2024
The
development
of
perforation
technology
has
increased
the
use
perforated
structures
in
many
engineering
fields,
from
nano/micro
to
macro
scales.
This
paper
proposes
a
solution
method
analyze
free
vibration
characteristics
Rayleigh
beams
with
both
deformable
and
rigid
boundary
conditions
equal
square
holes
along
their
vertical
axes,
modeled
using
elastic
collapse
springs
at
beam
ends.
Using
Beam
Theory
an
eigenvalue-based
methodology
Stokes
transform
Fourier
series,
research
investigates
effects
parameters
such
as
number
holes,
filling
ratio,
deformability
on
dynamics.
challenges
associated
achieving
actual
applications
make
it
essential
examine
impact
beams.
Key
findings
indicate
that
perforations
stiffness
significantly
influence
vibrational
characteristics,
which
can
be
utilized
optimize
design
application
various
fields.
Particularly
noteworthy
is
effect
symmetrical
or
asymmetrical
variation
placed
ends
behavior.
These
results
contribute
deeper
understanding
dynamic
behavior
provide
practical
insights
for
structural
design.
