...
Modal
...
analysis
...
,
...
or
...
the
...
mode-superposition
...
method,
...
is
...
a
...
...
...
procedure
...
which
...
evaluates
...
and
...
superimposes
...
free-vibration
...
mode
...
shapes
...
to
...
characterize
...
displacement
...
patterns.
...
Mode
...
shapes
...
describe
...
the
...
configurations
...
into
...
which
...
a
...
structure
...
will
...
naturally
...
displace.
...
Typically,
...
lateral
...
displacement
...
patterns
...
are
...
of
...
primary
...
concern.
...
Mode
...
shapes
...
of
...
low-order
...
mathematical
...
expression
...
tend
...
to
...
provide
...
the
...
greatest
...
contribution
...
to
...
structural
...
response.
...
As
...
orders
...
increase,
...
mode
...
shapes
...
contribute
...
less,
...
and
...
are
...
predicted
...
less
...
reliably.
...
It
...
is
...
reasonable
...
to
...
truncate
...
analysis
...
when
...
the
...
number
...
of
...
mode
...
shapes
...
is
...
sufficient.
...
A
...
structure
...
with
...
N
...
degrees
...
of
...
freedom
...
will
...
have
...
N
...
corresponding
...
mode
...
shapes.
...
Each
...
mode
...
shape
...
is
...
an
...
independent
...
and
...
normalized
...
displacement
...
pattern
...
which
...
may
...
be
...
amplified
...
and
...
superimposed
...
to
...
create
...
a
...
resultant
...
displacement
...
pattern,
...
as
...
shown
...
in
...
Figure
...
1:
Figure 1 - Resultant displacement and modal components
Numerical evaluation proceeds by reducing the equations of motion (N simultaneous differential equations coupled by full mass and stiffness matrices) to a much smaller set of uncoupled second order differential equations (N independent normal-coordinate equations). The orthogonality of mode-shape relations enables this reduction.
Related Content
Articles
Child pages (Children Display) | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
|
Tutorials
Filter by label (Content by label) | ||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
|
Test Problems
Filter by label (Content by label) | ||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
|