...
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:
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.