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Power-spectral-density

...

(PSD)

...

analysis

...

is

...

a

...

type

...

of

...

frequency-domain

...

analysis

...

in

...

which

...

a

...

structure

...

is

...

subjected

...

to

...

a

...

probabilistic

...

spectrum

...

of

...

harmonic

...

loading

...

to

...

obtain

...

probabilistic

...

distributions

...

for

...

dynamic

...

response

...

measures.

...

A

...

root-mean-square

...

(RMS)

...

formulation

...

translates

...

the

...

PSD

...

curve

...

for

...

each

...

response

...

quantity

...

into

...

a

...

single,

...

most

...

likely

...

value.

...

Because

...

PSD

...

curves

...

represent

...

the

...

continuous

...

probability

...

density

...

function

...

of

...

each

...

response

...

measure,

...

most

...

of

...

the

...

integrated

...

area

...

will

...

occur

...

near

...

the

...

resonant

...

frequencies

...

of

...

the

...

structure.

...

For

...

accuracy,

...

it

...

is

...

important

...

to

...

capture

...

response

...

at

...

frequency

...

steps

...

near

...

the

...

natural

...

modes

...

of

...

the

...

structure.

...

Harmonic

...

loading,

...

characterized

...

by

...

sine

...

and

...

cosine

...

functions,

...

may

...

have

...

various

...

components

...

at

...

different

...

phase

...

angles.

...

Either

...

hysteretic

...

or

...

viscous

...

damping

...

may

...

be

...

specified,

...

though

...

hysteretic

...

(displacement-based)

...

is

...

most

...

common

...

for

...

frequency-domain

...

applications.

...

The

...

frequency-dependent

...

behaviors

...

assigned

...

to

...

links

...

and

...

supports

...

are

...

applied

...

during

...

PSD

...

analysis.

...

More

...

on

...

harmonic

...

loading,

...

hysteretic

...

damping,

...

and

...

an

...

example

...

may

...

be

...

found

...

in

...

the

...

CSI Analysis Reference Manual (Frequency-Domain

...

Analyses,

...

page

...

419).

...

Steady-state

...

analysis

...

is

...

another

...

type

...

of

...

frequency-domain

...

analysis

...

in

...

which

...

a

...

structure

...

is

...

subjected

...

to

...

a

...

given

...

set

...

of

...

one

...

or

...

more

...

harmonic

...

load

...

patterns.

...

Response

...

is

...

then

...

calculated

...

in

...

a

...

deterministic

...

manner

...

for

...

each

...

frequency

...

of

...

vibration.

Additional notes on PSD include:

  • Fatigue analysis is one application for which PSD analysis is useful.

  • Use a constant function to ensure that the magnitude of probable load is the same at all frequencies.

  • The shape of the power-spectral-density

...

  • input

...

  • function

...

  • is

...

  • dependent

...

  • upon

...

  • the

...

  • probability

...

  • of

...

  • loading

...

  • for

...

  • each

...

  • frequency,

...

  • and

...

  • the

...

  • variation

...

  • in

...

  • likely

...

  • load

...

  • magnitude

...

  • as

...

  • a

...

  • function

...

  • of

...

  • its

...

  • frequency.

...

Show if
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TO DO (review and possibly delete):

  • The Hz in the denominator indicates that the probability is a density which may be integrated over the frequency range to produce a single RMS value.

See Also

  • Tutorial by Tom Irvine, July 28, 2000 (PDF) - obtain the PSD function from random vibration time-history data using a bandpass filtering method

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