This
manuscript
employs
a
surface
stress-driven
nonlocal
model
to
explore
the
combined
effects
of
long-range
interaction
and
energy
on
higher
vibration
modes
functionally
graded
nanobeams.
The
nanobeam
theory,
based
Bernoulli-Euler
kinematics,
incorporates
such
as
elasticity,
residual
stresses,
density,
rotary
inertia.
Hamilton's
principle
is
applied
derive
governing
equation
with
size-dependent
considerations.
main
outcomes
parametric
investigation,
considering
four
different
kinematic
boundary
conditions
(Cantilever,
Simply-Supported,
Clamped-Pinned,
Doubly-Clamped)
while
varying
parameter
material
gradient
index,
are
presented
discussed.
Additionally,
normalized
natural
frequencies
for
second,
third,
fourth
fifth
vibrations
provided
analyzed
each
case
under
study.
results
underscore
model's
effectiveness
in
capturing
overall
dynamic
behavior
nanobeams,
offering
cost-effective
approach
designing
optimizing
nano-scaled
structures.
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 of Advanced Materials and Structures,
Journal Year:
2023,
Volume and Issue:
unknown, P. 1 - 9
Published: Dec. 7, 2023
A
surface
stress-driven
nonlocal
model
is
employed
in
this
manuscript
to
study
the
coupled
effects
of
long-range
interaction
and
energy
on
free
vibrations
nano-beams
made
metal-ceramic
functionally
graded
material.
The
nanobeam
theory
formulated
based
Bernoulli-Euler
kinematics
include
elasticity,
residual
stresses,
density
rotary
inertia.
Hamilton's
principle
applied
derive
size-dependent
governing
equation.
main
results
a
parametric
investigation,
carried
out
considering
four
different
kinematic
boundary
conditions,
i.e.
Cantilever,
Simply-Supported,
Clamped-Pinned
Doubly-Clamped,
are
also
presented
discussed,
varying
parameter
material
gradient
index.
show
how
proposed
able
capture
overall
dynamic
behavior
nanobeams
provides
cost-effective
method
for
design
optimization
nano-scaled
structures.
Nanomaterials,
Journal Year:
2024,
Volume and Issue:
14(4), P. 350 - 350
Published: Feb. 12, 2024
This
paper
employs
a
surface
stress-driven
nonlocal
theory
to
investigate
the
synergistic
impact
of
long-range
interaction
and
energy
on
higher
vibration
modes
Bernoulli–Euler
nanobeams
made
functionally
graded
material.
It
takes
into
account
effects
such
as
modulus
elasticity,
residual
stresses,
density,
rotary
inertia.
The
governing
equation
is
derived
through
application
Hamilton’s
principle.
novelty
this
work
lies
in
its
pioneering
approach
studying
higher-order
vibrations,
carefully
considering
combination
interactions
materials
well-posed
mathematical
model
elasticity.
study
conducts
parametric
investigation,
examining
parameter
material
gradient
index
for
four
static
schemes:
Cantilever,
Simply-Supported,
Clamped-Pinned
Clamped-Clamped
nanobeams.
outcomes
are
presented
discussed,
highlighting
normalized
natural
frequencies
second
fifth
each
case
under
study.
In
particular,
illustrates
central
role
dynamic
response
nanobeams,
emphasizing
importance
them.
Furthermore,
analysis
reveals
that
influenced
by
combined
parameter,
index,
shapes
cross-sections
considered,
well
scheme
analyzed.
Mechanics of Advanced Materials and Structures,
Journal Year:
2024,
Volume and Issue:
unknown, P. 1 - 15
Published: Feb. 12, 2024
Despite
several
theoretical
investigations
on
the
torsional
dynamic
behavior
of
non-circular
micro/nanorods,
right
triangle
cross-section
is
still
unevaluated.
Therefore,
Timoshenko-Gere
theory
in
conjunction
with
nonlocal
strain
gradient
developed
for
modeling
scale-dependent
microscale
rods.
Various
anisotropic
materials,
i.e.
hexagonal,
trigonal,
triclinic,
and
monoclinic
materials
are
regarded
as
constituent
material
The
shear
stress
function
shape
according
to
calculated
function,
warping
obtained.
governing
equation
microrods
obtained
help
energy
approach
solved
using
an
analytical
method
by
regarding
two
different
boundary
conditions.
accuracy
proposed
model
validated
recent
similar
investigations.
Because
lack
mechanical
research
microrods,
methodology
was
equilateral
nanowire
reported
literature.
Eventually,
various
remarkable
variants'
effects
change
frequency
assessed
comprehensively.
It
found
that
hexagonal
triclinic
have
largest
smallest
values
frequency.
Also,
parameter,
b/h
ratio
play
a
decreasing
role
length
scale
parameters
mode
number
plays
increasing
role.
