Materials,
Journal Year:
2022,
Volume and Issue:
15(19), P. 6803 - 6803
Published: Sept. 30, 2022
An
efficient
eigenvalue
algorithm
is
developed
for
the
axial
vibration
analysis
of
embedded
short-fiber-reinforced
micro-/nano-composite
rods
under
arbitrary
boundary
conditions.
In
formulation,
nonlocal
elasticity
theory
used
to
capture
size
effect,
and
deformable
conditions
at
ends
are
simulated
using
two
elastic
springs
in
direction.
addition,
determine
reinforcing
effect
restrained
nano-/micro-rods,
a
new
system
linear
equations
with
concept
infinite
power
series
presented.
After
performing
mathematical
processes
known
as
Fourier
sine
series,
Stokes’
transformation
successive
integration,
we
finally
obtain
coefficient
matrix
terms
various
rigid
or
Some
accurate
solutions
free
frequencies
without
being
by
means
given
show
performance
present
method.
The
presence
spring
changes
corresponding
mode
shapes.
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.
Archive of Applied Mechanics,
Journal Year:
2024,
Volume and Issue:
94(5), P. 1291 - 1311
Published: April 4, 2024
Abstract
In
this
study,
Eringen’s
nonlocal
elasticity
theory
that
applies
the
small
size
effects
in
functionally
graded
porous
nanotubes
embedded
an
elastic
matrix
is
discussed.
The
material
properties
of
are
taken
into
account
to
vary
over
radius
direction
with
a
rule
mixture.
free
torsional
vibration
relation
according
theory,
via
Hamilton’s
principle,
obtained
and
eigenvalue
solution
constructed
for
response
presented
work.
analytical
model
validated
by
comparing
calculated
mathematical
results
homogeneous
rigid
non-rigid
boundary
conditions.
Special
attention
given
deformable
conditions,
porosity
coefficient,
grading
coefficient
also
influence
medium
on
frequencies.
paper,
it
has
been
proven
length,
medium,
spring
rigidities,
coefficients
frequency
nanotube
not
small.
ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik,
Journal Year:
2025,
Volume and Issue:
105(2)
Published: Feb. 1, 2025
Abstract
In
this
study,
the
torsional
vibration
of
a
functionally
graded
viscoelastic
nanotube
has
been
carried
out
under
boundary
conditions
employing
nonlocal
strain
gradient
theory.
First,
equation
motion
problem
established
using
Hamiltonian
principles
and
Kelvin–Voigt
model.
For
solution
problem,
derivatives
higher‐order
Fourier
series
obtained
with
help
Stokes'
transforms
have
utilized.
Thus,
an
eigenvalue
constructed
from
which
fundamental
frequencies
can
be
calculated.
The
results
presented
in
tables
graphs,
it
is
observed
that
damping
very
important
effect
on
vibration.
It
also
revealed
as
length
scale
parameters
k
(power‐law
exponent)
increase,
decreases
parameter
grows,
rises.
The Journal of Strain Analysis for Engineering Design,
Journal Year:
2023,
Volume and Issue:
58(8), P. 672 - 683
Published: April 19, 2023
A
novel
stability
model
is
analytically
reformulated
for
the
nano-sized
beam
resting
on
a
one-parameter
elastic
foundation.
The
solution
based
nonlocal
strain
gradient
elasticity
theory.
To
corporate
small
size
effects,
two
scale
parameters
are
introduced.
six-order
ordinary
differential
form
of
buckling
equation,
together
with
force
boundary
conditions,
utilized
to
examine
equation
in
terms
lateral
deflection.
infinite
linear
equations
discretized
help
Stokes’
transformation
and
Fourier
sine
series.
present
work
can
investigate
effects
spring
at
ends,
properties,
medium
parameter,
behavior
nanobeam.
predictions
proposed
analytical
deformable
conditions
agreement
those
available
scientific
literature
nanobeam
foundation
closed
solution.
presence
foundation,
nonlocal,
properties
change
loads
mode
shapes.
