State-Space Method for Systems with Dashpot Damping

two_dof_system_dashpots

Structural dynamics systems can be represented in terms of mass, damping and stiffness matrices.  Each of these matrices may be coupled depending on the model complexity, degrees-of-freedom, etc.   The mass and stiffness matrices in the assembled equation of motion may be uncoupled using the normal modes for the undamped system.  This approach gives real natural frequencies and real mode shapes.

Damping effects can be included in forced response analyses by implicitly assuming that the damping matrix can be diagonalized into modal damping coefficients by the undamped modes.   But systems with dashpots in general have damping matrices which cannot be uncoupled in this manner.

The state-space method is useful for modal and forced response analysis of systems with discrete dashpot damping.  This approach yields complex natural frequencies and mode shapes, with real and imaginary components.

Here is a paper:

Two-Degree-of-Freedom System, State-Space Method:   two_dof_state_space_revC.pdf

More later…

– Tom Irvine

Damping Identification from Shock Data via Wavelet Responses

three_shocks

Structural system & component damping can measured via modal testing with applied force excitation.  One excitation method is an impulse hammer test.  Another method is a  small shaker attached to structure via a stinger rod.

Damping can also be measured by mounting the test unit on a shaker table and applying base excitation.

There is a need to estimate component damping from pyrotechnic or pyrotechnic simulation shock tests where the source energy measurements are incomplete or unavailable.  This need may arise because modal and shaker table test data is unavailable.  Furthermore, damping is nonlinear and may be higher for a pyrotechnic shock event than for a modal or shaker table test

A source shock waveform can be modeled by a series of wavelets per Ferebee R , Irvine T, Clayton J, Alldredge D,  An Alternative Method Of Specifying Shock Test Criteria,  NASA/TM-2008-215253.   This method was original develop to characterize space shuttle solid rocket booster water impact shock.  This method can be extended for natural frequency and damping measurement for shock data.

The Wavelet Response Curve-fit Methodology is appropriate for mid and far field shock measurements where modal responses appear in the accelerometer time history data.

The method is implement via the following steps:

  • Assume a series of wavelet as the base input
  • Calculate the response of one or more SDOF systems to the assumed wavelet series
  • Subtract the resulting response signal from the measured accelerometer data and calculate error
  • The goal is to repeat this process thousands of times where the to minimize the residual error
  • Each of the following parameter are varied randomly with convergence
  • For each base input wavelet: frequency, amplitude, number of half-sines, delay
  • For each SDOF oscillator response: natural frequency, damping

The method yields natural frequency and damping estimates for the response acceleration.  It also gives an estimate of the assumed base input source shock.

The method is demonstrated in the following slides.

Slides:  shock_wavelet_damping_revC.pptx

Matlab scripts & sample shock data: Vibrationdata Signal Analysis Package

avionics_shock_data.mat

* * *

Reference Papers:

An Alternative Method Of Specifying Shock Test Criteria:
NASA/TM-2008-215253 & PowerPoint slide overview

 

* * *

– Tom Irvine

Damping References

pdtrans

Structural damping depends on materials, joints, boundary conditions, friction, acoustic radiation, etc.  Damping may be nonlinear, increasing as the excitation and response levels rise. The damping for a given structure or component must be measured!  

But here is some empirical background data…

Papers

Damping Properties of Materials

Damping Cross-Reference

Damping Values in Aerospace Structures and Components

Free Vibration with Coulomb Damping

Damping Identification Rev A

Related Blog Posts

Honeycomb Sandwich Panels

Vibroacoustics/Statistical Energy Analysis  – empirical formulas for loss factors

Wire Rope Cable Damping

Tall Building Natural Frequencies and Damping

Piezoelectric Shunt Damping

Nonlinear Modeling of Bolted Interfaces & Joints

Convert Modal Damping to a Damping Coefficient Matrix

Vibration Absorbers & Tuned Mass Dampers

Half-Power Bandwidth Method

Isolation

Isolator Photo Gallery

Avionics Box Isolation

Transmissibility of a Three-Parameter Isolation System

Webinar 43 – Two-degree-of-freedom System, Two-stage Isolation

– Tom Irvine

Engineering Status Reports

For the past eight years, I have written a required monthly status report to another organization for my NASA contractor work. I have written my accomplishments and planned work in short, concise sentences, usually in numbered list format.

I was then notified by this organization that the writing rules had been changed substantially. The new rules prohibited bullet or numerical list format. Personal pronouns could no longer be used. The sentences must be varied to avoid beginning each with the subject. The writing had to be in paragraph format with three sentences per paragraph, and on and on. There were so many new rules that I did not even read all of them. I wondered if perhaps an English literature major had been given an administrative role and was projecting his or her frustrations by imposing Byzantine writing style rules upon myself and others in this technical community.

So I submitted the following status report, with slight edit changes to avoid disclosing any proprietary information. I refer to myself in third person as the “greybeard.”

The organization responded by instructing me to return to my previous, concise writing style for the status reports, exempting me from the new rules.

And I really did give a presentation to NASA engineers that included a slide about monkeys SLaMS_SCLV201_keynote_revA.ppt

– Tom Irvine

* * *

Significant Accomplishments:

Dynamics Engineering: A Call to Serve! Enlightened were the apprentices as the greybeard mentored them with this presentation at the SLaMS Early Career Community webinar meeting, March 27, calling upon them to share their knowledge and become themselves teachers of the rising generation, underscored with Seneca the Younger’s proverb Docendo discimus – Latin “by teaching, we learn.” Reciprocal altruism of Vervet monkeys! Blind Faults underneath the Los Angeles Basin! Dragons to be launched on towering SpaceX boosters powered by Merlin engines! Thus was the eclectic tutelage of that day.

The raw, ominous Zeus-like power of pyrotechnic shock pulses cutting through rocket joint metal, propagating through modules and threatening sensitive electronic parts mounted on circuit boards – such has been the forlorn of many a NASA engineer. To which challenge did the greybeard prepare shock, structural dynamics, fatigue and statistical energy analysis software and training materials as tools for discerning the energy’s spectral content.

Work Planned:

Gathered will be engineers at the NESC Joint GN&C TDT and L&D TDT F2F Meeting at MSFC – week of April 16, 2018, bringing opportunities of collaboration for the greybeard and his esteemed colleagues. New ideas will arise upon which the greybeard will muse, research and present new papers and methodologies, knowing that if he sees farther than others– it is because he stands on the shoulders of giants.

The response of mechanical components bending and flexing in multi-modes driven by the surging oscillations of pyrotechnic shock waves, the stresses pulling molecules apart, potentially inducing cracks which threaten both component and launch vehicle, for which the greybeard is preparing a presentation for the Aerospace Spacecraft and Launch Vehicle Dynamic Environments Workshop, El Segundo, CA, June 26-28, 2018 – this and more are the planned endeavors for the month of April.

Deliverables:

Matlab scripts, the tools for synthesizing acceleration time histories across a series of wavelets, the greybeard’s quest to numerically replicate the damage potential of powerful undulations which could break launch vehicle components and structure, will be conveyed to NASA engineers. Tutorials and slides with examples using the scripts will be provided, enabling these ladies and gentlemen to perform calculations of their own in service of America’s space program.

* * *

Here is the bullet version, with no literary allusions.

Significant Accomplishments:

1. Gave presentation “Dynamics Engineering: A Call to Serve!” to the NASA SLaMS Early Career Community via webinar meeting, March 27. Presentation included references to reciprocal altruism of Vervet monkeys and blind faults underneath the Los Angeles basin.
2. Writing avionics component FEA shock analysis software and tutorials for NASTRAN implementation.

Work Planned:

1. Preparation of structural dynamics & statistical energy analysis software & webinars.
2. Prepare presentation for the Aerospace Spacecraft and Launch Vehicle Dynamic Environments Workshop, El Segundo, CA, June 26-28, 2018. Presentation title is Avionics Component FEA Shock Analysis.
3. Participate in the NESC Joint GN&C TDT and L&D TDT F2F Meeting at MSFC.

Deliverables:

1. Webinar audio/visual presentation files.
2. Revised Matlab & Python GUI signal analysis packages with enhanced features.
3. Statistical energy analysis, structural dynamics, vibration fatigue software and tutorial papers.

Honeycomb Sandwich Panels

Honeycomb-Sandwich-Panels-Marketimg_20171107_170159_750x750

Honeycomb sandwich structures are designed to have a high stiffness-to-mass ratio.   The stiff, strong face sheets carry the bending loads, while the core resists shear loads.

The face sheets are typically made from aluminum or carbon fiber with epoxy resin.

The honeycomb core material is usually aluminum for aerospace applications.   Other core materials include Nomex aramid or Kevlar para-aramid fiber sheets saturated with a phenolic resin.  In addition, closed cell foams such as Rohacell are substituted for honeycomb in some sandwich panel designs.

* * * *

According to Klos, Robinson and Buehrle…

Panels constructed from face sheets laminated to a honeycomb core are being incorporated into the design of modern aircraft fuselage and trim treatments. The mechanical properties of these panels offer a distinct advantage in weight over other commonly used construction materials.

The strength to weight ratio of honeycomb composite panels is high in comparison to rib stiffened aluminum panels used in previous generations of aircraft. However, the high stiffness and low weight can result in supersonic wave propagation at relatively low frequencies, which adversely affects the acoustical performance at these frequencies.

Poor acoustical performance of these types of structures can increase the cabin noise levels to which the passengers and crew are exposed.

* * * *

Here are some references:

Natural Frequencies of a Honeycomb Sandwich Plate:  honeyG.pdf

Honeycomb Sandwich Panel Damping:  honeycomb_sandwich_damping.pdf

Honeycomb Sandwich Ring Mode Frequency:  honeycomb_sandwich_ring_frequency.pdf

Hexcel Honeycomb Sandwich technical information:  honeycomb_design.pdf

Sound Transmission through a Curved Honeycomb Composite Panel:  ST_curved_honeycomb_panel.pdf

More later…

– Tom Irvine

An Indirect Method for Converting a Shock Response Spectrum Specification to a New Q Value

  •  Aerospace pyrotechnic shock response spectrum (SRS) specifications are almost always given with an amplification factor Q=10
  • Corresponding time history waveforms for the base input acceleration are almost never given with the specifications
  • Users are allowed to synthesize their own waveforms to satisfy the SRS for analysis & test purposes
  • Some shock analysis methods use the SRS directly without time history synthesis, such as modal combination methods
  • The following method enables an SRS specification to be converted to a new Q value for engineering purposes

Slides:  150_SRS_specification_new_Q.pptx

Software: Matlab Vibrationdata GUI

– Tom Irvine

Nastran Modal Transient & Response Spectrum Analysis for Base Excitation

FEA_modal_blog

  • Shock and vibration analysis can be performed either in the frequency or time domain
  • The time domain method requires more computation time but is much better suited for transient and nonstationary excitation
  • Time domain methods are also better for rainflow fatigue cycle counting
  • Students should already have some familiarity with Femap & Nastran
  • They should also be able to perform SRS time history synthesis as shown in previous Vibrationdata units
  • NX Nastran is used as the solver, but the methods should work with other versions
  • Two units for direct shock response spectrum analysis is also included

* * * * * * *

Prerequisite Materials

Webinar Index

Structural Dynamics Webinars

Matlab Vibrationdata GUI

* * * * * * *

Main Presentations:

Nastran Modal Transient Slides:  200_FEA_modal_transient_revJ.pptx

Nastran FEA Base Excitation via Response Spectrum:  201_FEA_response_spectrum_revE.pptx

Nastran FEA Base Excitation with Multiple Response Spectrum Inputs:  202_FEA_response_spectrum_multiple_revA.pptx

Nastran FEA Frequency Response Function for Base Input:  203_FEA_frf_revB.pptx

FEA PSD Response for Base Excitation using Femap, Nastran & Matlab:  204_FEA_psd.pptx

Avionics Component Shock Sensitivity & FEA Shock Analysis:  avionics_box_fea_shock.pptx

* * * * * * *

Nastran Files

Students should generate their own files, but here are several for reference:

square_plate_normal_modes.bdf

square_plate_modal_transient_seismic_mass.bdf

square_plate_response_spectrum.bdf

square_plate_response_spectrum_multiple.bdf

square_plate_response_frf.bdf

square_plate_psd.bdf

Nastran Acceleration Time History:  srs2000G_accel.nas

* * * * * * *

See also:    Vibrationdata Nastran

– Tom Irvine

Extract Mass & Stiffness Matrices from Nastran model

The punch file method may be used to extract the mass & stiffness matrices from Nastran models.  The format is awkward since zero terms are not stored.  Also the matrices are assumed to be symmetric, and the upper triangular portion above the diagonal is not stored.

Here is a paper from the Middle East Technical University which explains the format:  paper link.

The key is to apply the following command in the *.nas, *.dat, *.bdf or equivalent file:

PARAM,EXTOUT,DMIGPCH

Here is a sample file for a fixed-free beam, aluminum, 24 inch long, solid cylinder, 0.25 inch diameter, 24 elements:  beam_24e_diam_0p25_punch-000.nas

Its punch file output is:  beam_24e_diam_0p25_punch-000.pch

The fundamental frequency is 11.9 Hz.

If Femap is used, select the punch output with coupled mass.

Here is a C++ program which converts the punch file into full mass & stiffness matrices in ASCII text format:

mass_stiffness_punch.cpp

mass_stiffness_punch.exe

The mass & stiffness matrices can then be imported to Excel, Matlab or some other program.

* * *

Note:  the dimension of the extracted mass matrix will be less than that of the stiffness matrix for models with massless nodes.

Here is a workaround:

An Indirect Method for Extracting Nastran Full Mass Matrices for Models with Massless Nodes  extract_massless_node.pdf

– Tom Irvine

Cuba Sonic Attack Analysis

spectrogram_Cuba

A sound file from the attack on the U.S. Embassy in Cuba has now been made available on the Internet.  I did a spectral analysis of this file using my Matlab GUI scripts.  The sound source is still unknown.  The attacks have caused hearing, cognitive, visual, balance, sleep and other problems for embassy personnel.

Here is a quick look paper: Cuba_sonic_analysis.pdf

Here is the sound file: Cuba_sonic.mp3   Turn up the speaker volume to hear the sound.

– Tom Irvine

NASA SP-8072 Launch Vehicle Liftoff Acoustics

liftoff_acoustics

NASA SP-8072  Acoustics Loads Generate by the Propulsion System

The liftoff analysis has been added to the GUI package at:  Vibrationdata Matlab GUI

The function can be accessed via:

>> vibrationdata > Miscellaneous Functions I > Acoustics Vibroacoustics & SEA > acoustics > Launch Vehicle Liftoff Acoustics

Here is document which gives further details using an older C++ version: liftoff_notes.pdf

* * * * *

The aerodynamic flow-induced pressure during the transonic and maximum dynamic pressure phases can be calculated using the follow tools:

Prediction of Sound Pressure Levels on Rocket Vehicles During Ascent: flow.pdf

This function can be accessed via:

>> vibrationdata > Miscellaneous Functions I > Acoustics Vibroacoustics & SEA > acoustics > Launch Vehicle Aerodynamic Flow

– Tom Irvine