Waves in Random and Complex Media,
Journal Year:
2021,
Volume and Issue:
34(5), P. 4632 - 4657
Published: Nov. 10, 2021
In
producing
small-scale
structures,
having
nonuniform
geometrics
and
voids
as
the
generation
defect
is
inevitable
problem.
However,
in
mathematical
simulations,
researchers
have
been
more
attentive
to
perfect
uniform
structures
because
of
simple
modeling.
This
article
investigates
nonlinear
free
vibrational
behavior
truncated
conical
imperfect
functionally
graded
(FG)
micro-scale
tubes,
including
porosity,
various
cross-section
functions.
The
modified
couple
stress
theory
Euler-Bernoulli
beam
coupled
with
Von-Kármán
are
employed
based
on
Hamilton's
principles
derive
general
equation
motion
related
boundary
conditions.
assumed
basis
four
different
functions,
involving
section,
linear
convex
exponential
section.
temperature-dependent
materials
were
combined
by
ceramic
metal
phases
along
tube
radius
that
this
combination
made
a
tube.
Furthermore,
derived
equations
finally
solved
via
generalized
differential
quadrature
method
(GDQM)
numerical
approach
iteration
technique.
Since
thermal
fins,
fluid
flow
diffuser,
nozzle,
etc.,
designed
for
specific
purposes
non-uniform
cross-section,
presented
results
an
excellent
sight
developing
designing
macro/-
micro-electromechanical
systems
(MEMS).
Applied Mathematical Modelling,
Journal Year:
2024,
Volume and Issue:
131, P. 438 - 468
Published: April 9, 2024
Recent
advancements
in
fibre
placement
technologies
have
expanded
the
potential
applications
of
variable
stiffness
curved
composite
beams
industries
such
as
aerospace,
automotive,
and
naval
engineering.
Accurate
solution
techniques
for
examining
these
beams,
especially
those
composed
advanced
materials,
are
indispensable.
In
view
this
demand,
study
proposes
a
new
high-order
computational
tool
that
combines
higher-order
accuracy
emerging
inverse
differential
quadrature
method
(iDQM)
simple
kinematics
Timoshenko
beam
theory
efficient
accurate
prediction
static
behaviour
both
constant
structures.
This
novel
application
iDQM
to
analysis
is
leveraged
upon
its
excellent
mitigate
differentiation-induced
errors
by
using
so-called
indirect
approximation
strategy.
Simple
procedures
implementing
different
orders
models
presented
analyse
problems,
independently
benchmarked
against
closed-form
Navier's
solutions,
well
numerical
solutions
obtained
through
(DQM)
finite
element
(FEM),
demonstrating
spectral
accuracy.
Furthermore,
scheme
offers
outstanding
recovering
transverse
shear
stress,
achieving
superior
over
lower-order
FEM
approximating
derivatives.
Remarkably,
predictions
exhibit
satisfactory
agreement
with
Strong
Unified
Formulation,
98%
efficiency.
Finally,
convergence
reveal
up
three
improved
faster
rates
compared
DQM,
constituting
benchmark
analysis.
