Mechanics of Advanced Materials and Structures,
Journal Year:
2023,
Volume and Issue:
31(22), P. 5437 - 5453
Published: June 2, 2023
Integral
forms
of
Eringen's
nonlocal
theory
are
employed
to
model
nanoscale
constitutive
relations
without
possible
potential
paradoxes.
The
Timoshenko
beam
as
well
the
element-free
Galerkin
method
accepted
rotating
nanobeams
and
develop
numerical
solutions
critical
angular
velocities
for
nanobeams.
Optional
setting
angles
natural
defects
taken
into
account
in
buckling
analyses.
Important
design
parameters,
including
length-to-height
ratios,
ratios
hub
radii
lengths,
angles,
additional
supports
carefully
assessed
between
local
beams.
Symmetry,
Journal Year:
2024,
Volume and Issue:
16(11), P. 1467 - 1467
Published: Nov. 5, 2024
In
this
paper,
an
ancient
Babylonian
algorithm
for
calculating
the
square
root
of
2
is
unveiled,
and
potential
link
between
primitive
technique
Chinese
method
explored.
The
iteration
process
a
symmetrical
property,
whereby
approximate
converges
to
exact
one
through
harmonious
interactions
two
roots.
Subsequently,
extended
in
ingenious
manner
solve
algebraic
equations.
To
demonstrate
effectiveness
modified
algorithm,
transcendental
equation
that
arises
MEMS
systems
considered.
Furthermore,
established
adeptly
adapted
handle
differential
equations
fractal-fractional
Two
illustrative
examples
are
presented
consideration:
first
nonlinear
first-order
equation,
second
renowned
Duffing
equation.
results
age-old
approach
offers
novel
highly
effective
addressing
contemporary
problems
with
remarkable
ease,
presenting
promising
solution
diverse
range
modern
challenges.
Thermal Science,
Journal Year:
2024,
Volume and Issue:
28(3 Part A), P. 2153 - 2163
Published: Jan. 1, 2024
In
this
paper,
we
consider
a
combined
technique
for
fractal
modification
of
the
attachment
oscillator
arising
from
nanotechnology.
This
is
called
as
TSFT-GRHBM
by
coupling
two-scale
transformation
and
global
residue
harmonic
balance
method.
The
approximations
frequencies
are
given
without
linearization.
Numerical
results
provided
to
confirm
its
efficiency.
Communications in Theoretical Physics,
Journal Year:
2024,
Volume and Issue:
76(4), P. 045003 - 045003
Published: Feb. 2, 2024
Abstract
The
time-delayed
fractal
Van
der
Pol–Helmholtz–Duffing
(VPHD)
oscillator
is
the
subject
of
this
paper,
which
explores
its
mechanisms
and
highlights
stability
analysis.
While
technologies
are
currently
garnering
significant
attention,
focus
research
remains
crucially
relevant.
A
non-perturbative
approach
employed
to
refine
set
stage
for
system
under
scrutiny.
innovative
methodologies
introduced
yield
an
equivalent
linear
differential
equation,
mirroring
inherent
nonlinearities
system.
Notably,
incorporation
quadratic
nonlinearity
into
frequency
formula
represents
a
cutting-edge
advancement.
analytical
solution’s
validity
corroborated
using
numerical
approach.
Stability
conditions
ascertained
through
residual
Galerkin
method.
Intriguingly,
it
observed
that
delay
parameter,
in
context
system,
reverses
stabilizing
influence,
impacting
both
amplitude
delayed
velocity
position.
precision
underscored
by
close
alignment
with
results.
Furthermore,
study
reveals
characteristics
emulate
damping
behaviors.
Given
applicability
across
diverse
nonlinear
dynamical
systems,
emerges
as
promising
avenue
future
research.
