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The static deflection method can be used for estimating the fundamental frequency of a grounded dynamic system. A 1 G body load is applied to the system for this analysis.

The method can be used as a “ballpark” check for finite element models in conjunction with modal analysis.

Here is a tutorial paper.

The paper also demonstrates the use of the static deflection shape as the starting vector for the inverse power iteration method for obtaining a better estimate of the fundamental frequency.

Matlab script: inverse_power_iteration_manual.m

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- Tom Irvine

PowerPoint File:

Webinar_14_PSD_synthesis.pptx

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Matlab script: Vibrationdata Signal Analysis Package

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See also: Vibrationdata Webinars

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- Tom Irvine

Testing to Shock Response Spectrum (SRS) specifications is usually performed using complex oscillating waveforms.  This is also true for analytical simulation  in the time domain.

There are several reasons for this.

Complex oscillating pulses can typically meet both the positive and negative SRS for a given axis.
Complex oscillating pulses can be generated in the lab using a shaker table, impact method, or explosives as appropriate for the given specification.
The specification itself may have been derived from a complex oscillating pulse.

Nevertheless, there is an occasional need to generate a half-sine pulse for a given SRS specification.

Here is a set of Matlab scripts for accomplishing this:

halfsine_synth.zip

The main script is halfsine_synth.m.   The remaining scripts are supporting functions.

There are three disadvantages to using a half-sine pulse for test or analysis.

Over-testing will occur at certain natural frequencies.
The half-sine pulse has a one-sided input which causes a one-sided response for higher natural frequency oscillators.  Thus, the half-sine pulse must be applied in each direction of each axis.
Also, a pure half-sine pulse produces a net velocity change and a displacement “ski slope” effect.

The Matlab scripts have an optional wavelet reconstruction function to synthesize an approximate half-sine pulse with zero net velocity and zero net displacement while still meeting the SRS specification within reasonable tolerance bands.

- Tom Irvine

PowerPoint File:

Webinar_13_PSD_sdof_response.pptx

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Reference Paper:  Derivation of Miles Equation

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Matlab script: Vibrationdata Signal Analysis Package

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See also: Vibrationdata Webinars

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- Tom Irvine

PowerPoint File:

Webinar_12_PSD_data.pptx

Audio/Visual File:

PSD data.wmv

Data:

Taurus_auto.dat – Time(sec) & Accel(G)

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Matlab script: Vibrationdata Signal Analysis Package

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See also: Vibrationdata Webinars

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- Tom Irvine

Here is a signal analysis package GUI written using Tkinter: vibrationdata_gui_python.zip

It is compatible with Python versions 2.7 to 3.3, and hopefully future 3.x versions.

vibrationdata.py is the main script.

The remaining scripts are supporting functions.

These scripts demonstrate the use of multiple windows.

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The following signal analysis functions are currently available:

Statistics
Trend Removal & Scaling
Butterworth Filter
Bessel Filter
Fourier Transform
Fast Fourier Transform (FFT)
Waterfall FFT
Power Spectral Density (PSD)
SDOF Response to Base Input
Shock Response Spectrum (SRS)
Rainflow Cycle Counting
Differentiate Time History
Integrate Time History
Autocorrelation
Cross-correlation
Cepstrum & Auto Cepstrum
Sound Pressure Level (SPL)

The following PSD functions are also available:

Overall GRMS
SDOF Response to Base Input PSD
Vibration Response Spectrum (VRS)

The following miscellaneous functions are also available:

Sine Amplitude Conversion
SDOF Response: Peak Sigma for Random Base Input
SDOF Response to Classical Pulse Base Input

More will be added in future revisions…

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See also: Python Wiki

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- Tom Irvine

PowerPoint File:

Webinar_11_PSD.ppt

The sample PSD specification is taken from:  NAVMAT-P9492

Audio/Visual File:

PSD.wmv

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Reference Papers:

Integration of the Power Spectral Density Function

Statistical Degrees-of-Freedom

Power Spectral Density Units [ G^2 / Hz ]

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Matlab script: Vibrationdata Signal Analysis Package

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See also: Vibrationdata Webinars

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- Tom Irvine

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