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Haar Wavelets

I am currently learning about Haar wavelets.

Here is a brief introduction: Haar_wavelet.pdf

Here is a Matlab GUI package:  Haar_wavelet_main.zip

Haar_wavelet_main.m  is the main script.

The remaining scripts are supporting functions.

I can understand how these wavelet are useful for transmitting communication signals.  I am still trying to determine whether they are really useful for shock and vibration analysis.

Haar wavelets can be used for filtering, but the traditional Bessel and Butterworth filters seem to be more appropriate for shock and vibration.

More later…

- Tom Irvine

Avionics components are subjected to acceptance random vibration tests to verify their parts and workmanship prior to flight. This is particularly important for circuit boards which have piece parts with vulnerable solder joints and lead wires. The acceptance test levels usually envelope the maximum expected flight environment as well. The acceptance test may thus serve two purposes.

A number of somewhat similar random vibration power spectral densities curves have been specified in historical references as “minimum workmanship” levels, as show in the figures in workmanship_psds.pdf

These levels typically apply to components whose mass does not exceed 23 kg (50 lbm).

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References

MIL-STD-1540B

MIL-STD-1540C

AEROSPACE REPORT NO. TR-2004(8583)-1 REV. A

NAVMAT-P9492

NASA_CxP_70036.pdf

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- Tom Irvine

Shock Fatigue

1. Determine whether a given PSD can cover an SRS Specification

2. Derive an Optimized PSD which will cover an SRS

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Aerospace Pyrotechnic-type SRS tests are almost always more difficult to configure and control in the test lab and are thus more expensive than shaker table PSD tests.

Some lower and even mid-level SRS specifications may not have the true damage potential to justify shock testing.

The purpose of this webinar is to demonstrate a shock and vibration comparison method based on the fatigue damage spectrum (FDS).

The comparison results can be used with other considerations to determine whether the random vibration test covers the shock requirement.

A related method is also demonstrated for deriving an optimized PSD to envelop an SRS.

These methods are found to be effective comparison and derivation tools within a framework of assumptions.

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PowerPoint Slides:

webinar_40_shock_fatigue.pptx

Audio/Visual Slides:

Shock_Fatigue.wmv

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Matlab script: Vibrationdata Signal Analysis Package

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See also:

Using Random Vibration Testing to Cover Shock Requirements

Fatigue Damage Spectrum

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Thank you,
Tom Irvine

Linear Algebra

I have been reviewing linear algebra recently.

Here is Matlab GUI package: vibrationdata_linear_algebra.zip

vibrationdata_linear_algebra.m is the main script.
The remaining scripts are supporting functions.

* * *

Currently installed functions include:

Two vectors:

Euclidean inner product (dot product)
Cross product

One Array:

Determinant
Gram-Schmidt Orthogonalization
Triangular Decomposition LU
Cholesky Decomposition LL’
Inverse
Pseudo Inverse
Eigenvalues & Vectors

Solve: Ax=b

More later…

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- Tom Irvine

Certain electronic components must be designed and tested to withstand sine-on-random environments.

The following can be done for test or analysis purposes:

1. Synthesize a time history to satisfy a sine-on-random specification

2. Convert a sine-on-random specification to an equivalent PSD, with the sine tones replaced by narrow bands

Methods for both of these options are presented in this Webinar.

* * *

PowerPoint Slides:

webinar_39_sine_on_random.pptx

Audio/Visual File:

Sine_on_random.wmv

* * *

Matlab script: Vibrationdata Signal Analysis Package

* * *

See also:

Fatigue Damage Spectrum

* * *

Thank you,
Tom Irvine

The front end of a typical rocket vehicle contains avionics and a payload, enclosed by a cylindrical skin. Rocket vehicles are subjected to intense acoustic loading during liftoff. The external acoustic pressure causes the skin surfaces to vibrate. The skin sections are also excited by structural-borne vibration transmitted directly from the engine or motor. Nevertheless, the acoustic field is usually the dominant excitation source.

The references present an empirical method for calculating the vibration response of a cylindrical skin to an external acoustic pressure field. This method is based on data collected by Franken from studies of Jupiter and Titan 1 acoustic and radial skin vibration data collected during static firings.

The external acoustic pressure field may be due either to liftoff or to aerodynamic buffeting thereafter.

* * *

References:

Vibration Response of a Cylindrical Skin to Acoustic Pressure via the Franken Method: Franken.pdf

Peter Franken, Methods of Space Vehicle Noise Prediction, WADC Technical Report 58-343, Volume II: Franken_acoustics.pdf

* * *

The scripts for performing this calculation are given at:
Vibrationdata Signal Analysis Package

>> vibrationdata > Acoustics & Vibroacoustics > Vibroacoustics

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- Tom Irvine

Avionics components in aircraft and launch vehicles may be mounted to surfaces which are exposed to high intensity acoustic excitation. The external acoustic pressure field causes the panel and shell surfaces to vibrate. This vibration then becomes a base input to any component mounted on the internal side. Components must be designed and tested accordingly.

The component vibration input levels can be derived via analysis and testing for a given sound pressure level.

Acoustic testing of the structure can be performed in a reverberant chamber or using a direct field method. There is some difficultly in testing, however, because the simulated acoustic field in the lab facility may be different in terms of spatial correlation and incidence than that of the flight environment even if the sound pressure level can be otherwise replicated.

The vibroacoustic analysis techniques include finite element and boundary element methods, as well as statistical energy analysis. These are powerful tools, but they require numerous assumptions regarding external acoustic pressure field type, coupling loss factors, modal density, impedance, radiation efficiency, critical and coincident frequencies, distinguishing between acoustically fast and slow modes, etc.

As an alternative, simple empirical methods exist for deriving the structural vibration level corresponding to a given sound pressure level. Two examples are the Franken and Spann techniques. These methods may be most appropriate in the early design stage before hardware becomes available for lab testing and before more sophisticated analysis can be performed.

The Spann method provides a reasonable estimate of the acoustically excited component vibration environments when only the areas exposed to the acoustic environment and mass are known.

Spann_vibroacoustic_method.pdf

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The scripts for performing this calculation are given at:
Vibrationdata Signal Analysis Package

>> vibrationdata > Acoustics & Vibroacoustics > Vibroacoustics

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- Tom Irvine

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