Vibrationdata Matlab Page

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Tutorials

Power Spectral Density Calculation via Matlab: psd_mat.pdf
Guest tutorial submitted by Bob Light.

Classic Pulse Base Input Shock Analysis	Matlab Scripts
Response of a Single-degree-of-freedom System Subjected to a Half-sine Base Excitation	halfsine.m time_calc.m SDOF_base_animation_function.m sbase.pdf
Response of a Single-degree-of-freedom System Subjected to a Versed-sine Base Excitation	versed_sine.m versed_time_calc.m sbase_versed_sine.pdf
SDOF response to a terminal sawtooth base input.	terminal_sawtooth.m terminal_sawtooth_time_calc.m terminal_sawtooth.pdf
SDOF response to a wavelet base input.	sdof wavelet.m sbase_wavelet.pdf
SDOF response to combined sinusoidal force and base excitation.	sdof_force_accel.m sdof_force_accel.pdf
SDOF response to unit step force	unit_step_force.m force_unit_step.pdf
TWO-DOF response to applied force excitation.	two_dof_force_sine.m gencoord.pdf
TWO-DOF response to a wavelet base input.	twodof wavelet.m twodof_wavelet.pdf

Additional Shock Analysis Matlab Scripts

SRS Matlab Script (Kelly-Richman & Smallwood) srs.m

Supporting function:
enter_time_history.m

srs_intr.pdf

DS_SRS1.pdf

SRS via convolution srs_conv.m

Time history response of a single-degree-of-freedom system to an arbitrary acceleration base input via a digitial recursive filtering relationship. arbit.m

Supporting function:
enter_time_history.m

Tripartite Shock Response Spectra Plots srs_tripartite.m

Mean filter method for removing saturation with optimization. mean_filter_saturation.m

Supporting functions
enter_time_history.m
mr_SRS.m

SRS plotting function SRS_plot.m

Interpolate an SRS function. interp_SRS.m

Shock pulse effective duration per MIL-STD-810F shock_effective_duration.m

progressbar.m

Waveform reconstruction via wavelets. waveform_reconstruct.m

wgen.m

wavelet_reconstruction.pdf

Scale a wavelet table to match an SRS specification. wavelet_scale_SRS.m

wqsrs.m

werror.m

Time history from a wavelet table. th_from_wavelet_table.m

Fouier Transforms	Matlab Scripts
Fourier transform	fourier.m Supporting functions: enter_time_history.m progressbar.m
Inverse Fourier transform	invfourier.m
One-sided, Full-amplitude FFT. Includes spectrogram.	full_FFT.m Supporting function: enter_time_history.m fft.pdf
Waterfall FFT	waterfall_FFT.m Supporting function: enter_time_history.m solid_motor_oscillation.pdf
Zoom FFT of a time series.	zoomFFT.m zoomFFT_plot.m zoom_fft.pdf zoomFFT_example.pdf d9p5.txt
Interpolation of a time history via its Fourier transform	interp_fourier.m

Signal Processing Matlab Scripts

Time History, PSD, SRS & SPL Statistics & Plotting signal_stats.m

coordinates_ss.m

coordinates_ss_scale.m

octaves.m

PSD_octave.m

Multi-function signal processing script for time histories signal_functions.m

signal_function_extract.m

signal_function_stats.m

Integrate time history via the trapezoidal rule. integrate_th.m

fade.m

integrate_th_mf.m

Differentiate a time history. differ.m

Calculate the standard deviation time history from an instantaneous time history std_dev_th.m

Determine the natural frequency and damping of a transient waveform using time history synthesis sinefdam.m
sf_engine.m

Determine the natural frequency of a sinusoidal waveform using time history synthesis sinefind.m
sfa_engine.m

Extract Time History Segment extract.m

Track frequency and amplitude for a sine sweep sine_sweep_spectral.m

Auto-correlation of two signals.
The Matlab Signal toolbox is not required.
auto_correlation.m

progressbar.m

Cross-correlation of two signals.
The Matlab Signal toolbox is not required.
cross_correlation.m

Aliasing frequency calculator aliasing.m

Remove pure tone noise from a signal. Can be used to remove 60 Hz and harmonic noise.
This method uses a time domain method curve-fitting method. It is precise but may take a "long" computational time. remove_noise_frequency.m

sfa_engine_60.m

Cubic spline
cubic_spline.m

Signal Generation	Matlab Scripts
Generation of time history signals: 1=sine 2=cosine 3=damped sine 4=sine sweep 5=white noise 6=terminal sawtooth pulse 7=half-sine pulse 8=versed sine pulse 9=wavelet	generate.m sweep.m white.m
Generate a white noise time history where the user specifies the standard deviation and kurtosis. The skewness is approximately zero.	white_kurtosis.m progressbar.m
Generate a white noise time history where the user specifies the standard deviation, skewness and kurtosis.	white_kurtosis_skewed.m progressbar.m
Generate a time history with kurtosis > 3. The corresponding histogram has a shape similar to a witch hat.	witch.m

Filtering	Matlab Scripts
Butterworth Sixth Order Filter, Transfer Function	BH.m filter.pdf REFILT.pdf
Bessel Filter, Transfer Function	Bessel_H.m
Butterworth Sixth Order Filter	Butterworth_filter.m Supporting functions: enter_time_history.m filter_coefficients.m apply_filter.m
Bessel Filter via Fourier transform	fourier_filter_Bessel.m Bessel_Transfer.m
Butterworth Sixth Order Filter via Fourier transform	fourier_filter.m Butterworth_Transfer.m
Mean filter of a time history	mean_filter.m

Sine Vibration	Matlab Scripts
Sine Vibration Response Spectrum (VRS)	sine_vrs.m
Time history response of an SDOF system to a sinusoidal base input	sine_base.m

Power Spectral Density	Matlab Scripts
Overall Level of a Power Spectral Density Function	psd_integ.m Functions: calculate_PSD_slopes.m APSD_VPSD.m APSD_DPSD.m psdinteg.pdf
PSD plotting function with full grid	PSD_plot.m calculate_PSD_slopes.m
Synthesis of a Time History to Satisfy a Power Spectral Density	psd_syn.m psd_syn_data_entry.m psd_syn_white.m progressbar.m Alternate method: psd_syn_sine.m Alternate method for displacement PSD: disp_psd_syn_sine.m dpsd_syn_data_entry.m
Power Spectral Density	PSD.m FFT_core.m psd.pdf spectral.pdf Shock_and_Vibration_Signal_Analysis.pd
Conversion of a power spectral density to various octave formats	PSDoct.m octaves.m
P95/50 Envelope for a set of PSD measurements	P9550.m P9550_values.m calculate_PSD_slopes.m
Normal tolerance intervals, upper limits	k_factor.m

Random Vibration Matlab Scripts

Miles Equation for Base Excitation Miles.m

Miles Equation for Applied force Miles_force.m

Vibration Response Spectra Matlab Script
VRS.m

Functions:
calculate_PSD_slopes.m interpolate_PSD.m
vrs_engine.m
AVRS_plot.m
vrs.pdf

Determine the response of a particular SDOF system to a power spectral density base input sdof_ran.m

Functions:
sdof_ran_engine.m
interpolate_PSD.m
calculate_PSD_slopes.m

Multiply or divide one frequency response function by another. real_div.m

real_mult.m

real_mult_intlog.m

calculate_PSD_slopes.m

Linear Algebra Decomposition	Script
Triangular Decomposition (LU)	triangular_decomp.m pivot.m
Cholesky Decomposition (LLT )	Cholesky.m
Spectral Decomposition (LDLT)	spectral_decomp.m
Lanczos Tridiagonalization	Lanczos_tridiagonal.m
Householder Tridiagonalization, Four versions The alternate method uses a more efficient method for the tridiagonalization. The mo version is optimized for Matlab via sparse matrices. The Hessenberg version uses Matlab's hess function.	Householder_tridiagonal.m Householder_tridiagonal_alt.m Householder_tridiagonal_mo.m Hessenberg_tridiagonal.m supporting functions Standard_Eigen.m progressbar.m
QR Householder Decomposition	QR_Householder.m
Eigenvalues via the QR Householder algorithm. Two versions. The mo version is optimized for Matlab via sparse matrices.	QR_Householder_eigen.m QR_Householder_eigen_mo.m
Generalized eigenvalue problem	eigenvalue.m Generalized_Eigen.m Standard_Eigen.m
Single Value Decomposition of a matrix. Matlab already has a built-in function to do this, but this script demonstrates the steps	SVD.m

Linear Algebra, Matrix Inverse	Matlab Scripts
pseudo inverse of a matrix using two methods: 1. SVD 2. Ben-Israel & Cohen iteration	pseudo_inverse.m
QR Householder Method	QR_Householder_inv.m

Linear Algebra and Eigenvalues Matlab Scripts

Eigenvalues via the QR Householder algorithm QR_Householder_eigen.m

This program converts the generalized eigenvalue problem to a standarized form. convert_eig.m

Modified Gram-Schmidt Orthogonalization modified_Gram_Schmidt.m

Simultaneous iteration example for the generalized eigenvalue problem. simultaneous_iteration.m

Subspace Iteration subspace_iteration.m

Sturm Sequence for the Generalized Eigenvalue Problem sturm_sequence.m
LDLT.m

Transfer Functions from Modes
transfer_from_modes.m

transfer_from_modes.pdf

This program calculates a power transmissibility function (G^2/G^2) for a given pair of degree-of-freedoms in a system based on the mode shapes, natural frequencies, and damping ratios. The transmissibility function is referenced to a force input node.

powertrans_from_modes.m

Mass Condensation (Guyan Reduction)
mass_condensation.m
Generalized_Eigen.m

Single Value Decomposition of a matrix. Matlab already has a built-in function to do this, but this script demonstrates the procedure SVD.m

Single Value Decomposition of a semi-definite, symmetric matrix SVD_semidefinite_sym.m

pseudo inverse of a matrix using two methods:
1. SVD
2. Ben-Israel & Cohen iteration pseudo_inverse.m

Structural Dynamics: Beams & Rods	Matlab Scripts
Natural Frequencies and Mode Shapes of a Beam via the Finite Element Method, with two degrees-of-freedom per node. This program also calculates the participation factors and effective modal mass values. It allows for the addition of a point mass.	beam.m Functions: beam_data_entry.m local_stiffness.m local_mass.m assembly.m plot_modes.m mass_condense.m Generalized_Eigen.m beam.pdf
Natural Frequencies and Mode Shapes of a Beam via the Finite Element Method with six degrees-of-freedom per node. The beam elements may be in a three-dimensional frame.	beam_3D.m Functions: beam_3D_mass_condensation.m Generalized_Eigen.m beam_3D_modeplot.m User Guide beam_3D_guide.pdf
Normal modes & base excitation of a Cantilever Beam	cantilever_beam.m
Normal modes & base excitation of a Fixed-Free Rod	fixed_free_rod.m
Natural Frequencies and Mode Shapes of a Rocket Vehicle. The user must input a mass density file and an stiffness file. The stiffness file must be in terms of EI. A future version of this program will allow for joint compliance and a branch for a payload.	rocket_bending.m Functions: rocket_bending_data_entry.m rocket_local_stiffness.m rocket_local_mass.m assembly.m plot_modes.m

Structural Dynamics: Plates	Matlab Scripts
Natural Frequencies of a Circular Plate, Simply-supported, Bessel Function Solution	circular_SS.m
Natural Frequencies of a Circular Plate	circular_plate.m polarplot3d.m parse_pv_pairs.m
The Fundamental Frequency of an Isolated Circular Plate	circular_elastic.m
Natural Frequencies of a Annular Plate	annular_plate.m
The Fundamental Frequency of an Isolated Annular Plate	annular_elastic.m
The Natural Frequency of a Rectangular Plate Point-Supported at Each Corner	plate_corners.m pfunction.m

Structural Dynamics, Other Matlab Scripts

Free vibration of a single-degree-of-freedom system, exact method. free.m
free.pdf

Free vibration of a multi-degree-of-freedom system, exact method.
mdof_free.m

Generalized_Eigen.m
plot_legend.m
line_colors.m

Natural frequenices, mode shapes, participation factors and effective modal mass values of a two-degree-of-freedom system. two_dof.m

Natural frequenices and mode shapes of a three-degree-of-freedom system. three_dof.m

Natural frequenices and mode shapes of a multiple-degree-of-freedom system.
mdof.m
Generalized_Eigen.m

Natural frequenices and mode shapes of a multiple-degree-of-freedom system, reduced to a subset of dof per the user's input.
mdof_reduced.m
Generalized_Eigen.m

Mass Condensation (Guyan Reduction)
mass_condensation.m
Generalized_Eigen.m

Craig-Bampton Method mdof_CB.m

The Steady-State Frequency Response Function of a Multi-degree-of-freedom System Subjected to Harmonic Base Excitation two_dof_frf.m

The Steady-State Frequency Response Function of a Single-degree-of-freedom System Subjected to Harmonic Force Excitation sdof_force_frf.m

The Steady-State Frequency Response Function of a Multi-degree-of-freedom System Subjected to Harmonic Force Excitation two_dof_force_frf.m

two_dof_force_frf_alt.m

Natural Frequency of a Single-degree-of-freedom System ( GUI ) SDOF_freq.m
SDOF_freq.fig

Vibration Analysis of an Isolated Mass with Six-degrees-of-freedom six_dof_iso.m

Multi-degree-of-freedom system subjected to applied force, modal transient analysis

mdof_arb_force.m
progressbar.m
Generalized_Eigen.m

Multi-degree-of-freedom system subjected to applied force, modal transient analysis, reduced system
mdof_reduced_arb_force.m
progressbar.m

Matlab script for reduced system subjected to applied force, modal transient analysis, mass condensation mdof_masscon_arb_force.m

Assembly of mass and stiffness matrices with transformation matrix
mass_stiffness_assembly.m
Generalized_Eigen.m

Natural Frequencies of Spring Mass Systems in Series spring_mass_series.m
Generalized_Eigen.m

Torsional natural frequencies of a rod or shaft rod_torsional_fn.m

Three-dimensional coordinate transformation coordinate_transformation_3D.m

Roots of characteristic equations for structural dynamics vibration_roots.m

See also:

Matlab RK4 Page

Matlab_Newmark_Page

Matlab ode45 Page

Material Science	Matlab Scripts
Stress Corrosion Cracking: stress required to propagate a partial through-the-thickness crack-like discontinuity	stress_intensity.m

Animation Matlab Scripts

Animation of a single-degree-of-freedom system (spring mass system) subjected to sinusoidal base excitation with time history display. SDOF_base_animation.m

Animation of a single-degree-of-freedom system (spring mass system) subjected to sinusoidal base excitation. (old) SDOF_sine.m

Animation of seven SDOF systems subjected to common sinusoidal base excitation. SDOF_sine7.m

Plot Digitization	Matlab Scripts
Digitize SRS and PSD plots from image files, such as .jpg files.	loglog_digitize.m
Digitize log-linear plot.	loglin_digitize.m
Digitize SPL plot	digitize_SPL.m
Another digitization program.	digitize_plot.m

Additional Plot Utilities	Matlab Scripts
Surface Scatter Plot from matrix with three columns of data	surface_scatter_plot.m
Plot a large time history by taking only the max and min within successive intervals.	small_plot.m
Plot EasyPlot *.sav files in Matlab	EasyPlot_translator.m

Utilities Matlab Scripts

ASTM E 1049-85 (2005) Rainflow Counting Method rainflow.m

This progam sets up a coordinate table interactively for a PSD or SRS. coordinates.m

Convert Matlab data to ASCII text.
These programs use syntax similar to C/C++. data_convert.m

data_convert_21.m

Convert time in seconds to hours, min, sec format. hrminsec.m

Multi-format data input utility. data_input.m

Remove header lines from an external ASCII input file. header.m

UCI data conversion.

Generates a series of two-columns files (time & amplitude) from a UCI input file.
The first column is time(sec).
The additional columns are amplitude. uci.m

Principal moment of interia from a rotational inertia matrix. principal_moi.m

Add dB values for SPLs & PSDs. add_dB.m

Calculate the arc length of a half-sine wave.
These scripts demonstrate the use of the quad function with variable coefficients. arclength_sine.m

arc_function.m

Calculate the roots of a cubic polynomial. cubic_poly_roots.m

Interpolation	Matlab Scripts
Interpolate or extrapolate given two reference coordinates. Linear, Semilog and log options are included.	interpolate_coordinates.m
Logarithmic interpolation of a function.	intlog.m
Interpolate log-linear function.	int_semilog.m

Calculate pi	Matlab Scripts
Calculate pi using a series expansion of cos(theta) and by applying the Newton-Raphson method. The goal is to find the root of cos(theta)=-1.	pi_nr.m
Calculate pi by determining the arclength of a quarter circle.	pi_arclength.m progressbar.m
Calculate pi by determining the area of a quarter circle. Simple grid point integration is used.	pi_gpi.m progressbar.m

Statistics	Matlab Scripts
Normal tolerance intervals, upper limits	k_factor.m
Integrate the noncentral t-distribution	noncentral_t_distribution.m
Integrate the noncentral t-distribution, table format	noncentral_t_distribution_table.m
Integrate the student t-distribution.	integrate_t_distribution.m t_distribution.m
Integrate the chi-square curve.	integrate_chi_square.m chi_function.m
Integrate the normal distribution curve.	integrate_normal_distribution.m

Finance	Matlab Scripts
Loan calculation script for principal and interest	loan.m

Additional Shock Analysis	Matlab Scripts
SRS Matlab Script (Kelly-Richman & Smallwood)	srs.m Supporting function: enter_time_history.m srs_intr.pdf DS_SRS1.pdf
SRS via convolution	srs_conv.m
Time history response of a single-degree-of-freedom system to an arbitrary acceleration base input via a digitial recursive filtering relationship.	arbit.m Supporting function: enter_time_history.m
Tripartite Shock Response Spectra Plots	srs_tripartite.m
Mean filter method for removing saturation with optimization.	mean_filter_saturation.m Supporting functions enter_time_history.m mr_SRS.m
SRS plotting function	SRS_plot.m
Interpolate an SRS function.	interp_SRS.m
Shock pulse effective duration per MIL-STD-810F	shock_effective_duration.m progressbar.m
Waveform reconstruction via wavelets.	waveform_reconstruct.m wgen.m wavelet_reconstruction.pdf
Scale a wavelet table to match an SRS specification.	wavelet_scale_SRS.m wqsrs.m werror.m
Time history from a wavelet table.	th_from_wavelet_table.m

Signal Processing	Matlab Scripts
Time History, PSD, SRS & SPL Statistics & Plotting	signal_stats.m coordinates_ss.m coordinates_ss_scale.m octaves.m PSD_octave.m
Multi-function signal processing script for time histories	signal_functions.m signal_function_extract.m signal_function_stats.m
Integrate time history via the trapezoidal rule.	integrate_th.m fade.m integrate_th_mf.m
Differentiate a time history.	differ.m
Calculate the standard deviation time history from an instantaneous time history	std_dev_th.m
Determine the natural frequency and damping of a transient waveform using time history synthesis	sinefdam.m sf_engine.m
Determine the natural frequency of a sinusoidal waveform using time history synthesis	sinefind.m sfa_engine.m
Extract Time History Segment	extract.m
Track frequency and amplitude for a sine sweep	sine_sweep_spectral.m
Auto-correlation of two signals. The Matlab Signal toolbox is not required.	auto_correlation.m progressbar.m
Cross-correlation of two signals. The Matlab Signal toolbox is not required.	cross_correlation.m
Aliasing frequency calculator	aliasing.m
Remove pure tone noise from a signal. Can be used to remove 60 Hz and harmonic noise. This method uses a time domain method curve-fitting method. It is precise but may take a "long" computational time.	remove_noise_frequency.m sfa_engine_60.m
Cubic spline	cubic_spline.m

Random Vibration	Matlab Scripts
Miles Equation for Base Excitation	Miles.m
Miles Equation for Applied force	Miles_force.m
Vibration Response Spectra Matlab Script	VRS.m Functions: calculate_PSD_slopes.m interpolate_PSD.m vrs_engine.m AVRS_plot.m vrs.pdf
Determine the response of a particular SDOF system to a power spectral density base input	sdof_ran.m Functions: sdof_ran_engine.m interpolate_PSD.m calculate_PSD_slopes.m
Multiply or divide one frequency response function by another.	real_div.m real_mult.m real_mult_intlog.m calculate_PSD_slopes.m

Linear Algebra and Eigenvalues	Matlab Scripts
Eigenvalues via the QR Householder algorithm	QR_Householder_eigen.m
This program converts the generalized eigenvalue problem to a standarized form.	convert_eig.m
Modified Gram-Schmidt Orthogonalization	modified_Gram_Schmidt.m
Simultaneous iteration example for the generalized eigenvalue problem.	simultaneous_iteration.m
Subspace Iteration	subspace_iteration.m
Sturm Sequence for the Generalized Eigenvalue Problem	sturm_sequence.m LDLT.m
Transfer Functions from Modes	transfer_from_modes.m transfer_from_modes.pdf
This program calculates a power transmissibility function (G^2/G^2) for a given pair of degree-of-freedoms in a system based on the mode shapes, natural frequencies, and damping ratios. The transmissibility function is referenced to a force input node.	powertrans_from_modes.m
Mass Condensation (Guyan Reduction)	mass_condensation.m Generalized_Eigen.m
Single Value Decomposition of a matrix. Matlab already has a built-in function to do this, but this script demonstrates the procedure	SVD.m
Single Value Decomposition of a semi-definite, symmetric matrix	SVD_semidefinite_sym.m
pseudo inverse of a matrix using two methods: 1. SVD 2. Ben-Israel & Cohen iteration	pseudo_inverse.m

Structural Dynamics, Other	Matlab Scripts
Free vibration of a single-degree-of-freedom system, exact method.	free.m free.pdf
Free vibration of a multi-degree-of-freedom system, exact method.	mdof_free.m Generalized_Eigen.m plot_legend.m line_colors.m
Natural frequenices, mode shapes, participation factors and effective modal mass values of a two-degree-of-freedom system.	two_dof.m
Natural frequenices and mode shapes of a three-degree-of-freedom system.	three_dof.m
Natural frequenices and mode shapes of a multiple-degree-of-freedom system.	mdof.m Generalized_Eigen.m
Natural frequenices and mode shapes of a multiple-degree-of-freedom system, reduced to a subset of dof per the user's input.	mdof_reduced.m Generalized_Eigen.m
Mass Condensation (Guyan Reduction)	mass_condensation.m Generalized_Eigen.m
Craig-Bampton Method	mdof_CB.m
The Steady-State Frequency Response Function of a Multi-degree-of-freedom System Subjected to Harmonic Base Excitation	two_dof_frf.m
The Steady-State Frequency Response Function of a Single-degree-of-freedom System Subjected to Harmonic Force Excitation	sdof_force_frf.m
The Steady-State Frequency Response Function of a Multi-degree-of-freedom System Subjected to Harmonic Force Excitation	two_dof_force_frf.m two_dof_force_frf_alt.m
Natural Frequency of a Single-degree-of-freedom System ( GUI )	SDOF_freq.m SDOF_freq.fig
Vibration Analysis of an Isolated Mass with Six-degrees-of-freedom	six_dof_iso.m
Multi-degree-of-freedom system subjected to applied force, modal transient analysis	mdof_arb_force.m progressbar.m Generalized_Eigen.m
Multi-degree-of-freedom system subjected to applied force, modal transient analysis, reduced system	mdof_reduced_arb_force.m progressbar.m
Matlab script for reduced system subjected to applied force, modal transient analysis, mass condensation	mdof_masscon_arb_force.m
Assembly of mass and stiffness matrices with transformation matrix	mass_stiffness_assembly.m Generalized_Eigen.m
Natural Frequencies of Spring Mass Systems in Series	spring_mass_series.m Generalized_Eigen.m
Torsional natural frequencies of a rod or shaft	rod_torsional_fn.m
Three-dimensional coordinate transformation	coordinate_transformation_3D.m
Roots of characteristic equations for structural dynamics	vibration_roots.m
See also: Matlab RK4 Page Matlab_Newmark_Page Matlab ode45 Page

Animation	Matlab Scripts
Animation of a single-degree-of-freedom system (spring mass system) subjected to sinusoidal base excitation with time history display.	SDOF_base_animation.m
Animation of a single-degree-of-freedom system (spring mass system) subjected to sinusoidal base excitation. (old)	SDOF_sine.m
Animation of seven SDOF systems subjected to common sinusoidal base excitation.	SDOF_sine7.m

Utilities	Matlab Scripts
ASTM E 1049-85 (2005) Rainflow Counting Method	rainflow.m
This progam sets up a coordinate table interactively for a PSD or SRS.	coordinates.m
Convert Matlab data to ASCII text. These programs use syntax similar to C/C++.	data_convert.m data_convert_21.m
Convert time in seconds to hours, min, sec format.	hrminsec.m
Multi-format data input utility.	data_input.m
Remove header lines from an external ASCII input file.	header.m
UCI data conversion. Generates a series of two-columns files (time & amplitude) from a UCI input file. The first column is time(sec). The additional columns are amplitude.	uci.m
Principal moment of interia from a rotational inertia matrix.	principal_moi.m
Add dB values for SPLs & PSDs.	add_dB.m
Calculate the arc length of a half-sine wave. These scripts demonstrate the use of the quad function with variable coefficients.	arclength_sine.m arc_function.m
Calculate the roots of a cubic polynomial.	cubic_poly_roots.m

Welcome to Vibrationdata Matlab Page

Dear Guest,

The subscription entitles the user to download all of the items on this page, as well as other Vibrationdata pages.

Thank you for your support.

Sincerely, Tom Irvine Email: tomirvine@aol.com

Tutorials

Power Spectral Density Calculation via Matlab: psd_mat.pdf Guest tutorial submitted by Bob Light.

Classic Pulse Base Input Shock Analysis

Matlab Scripts

Response of a Single-degree-of-freedom System Subjected to a Half-sine Base Excitation

Response of a Single-degree-of-freedom System Subjected to a Versed-sine Base Excitation

SDOF response to a terminal sawtooth base input.

SDOF response to a wavelet base input.

TWO-DOF response to a wavelet base input.

Fouier Transforms

Matlab Scripts

Fourier transform

Supporting functions: enter_time_history.m progressbar.m

Inverse Fourier transform

One-sided, Full-amplitude FFT. Includes spectrogram.

Supporting function: enter_time_history.m fft.pdf

Waterfall FFT

Supporting function: enter_time_history.m solid_motor_oscillation.pdf

Zoom FFT of a time series.

Interpolation of a time history via its Fourier transform

Cubic spline

Signal Generation

Matlab Scripts

Generation of time history signals: 1=sine 2=cosine 3=damped sine 4=sine sweep 5=white noise 6=terminal sawtooth pulse 7=half-sine pulse 8=versed sine pulse 9=wavelet

Generate a white noise time history where the user specifies the standard deviation and kurtosis. The skewness is approximately zero.

Generate a white noise time history where the user specifies the standard deviation, skewness and kurtosis.

Generate a time history with kurtosis > 3. The corresponding histogram has a shape similar to a witch hat.

Filtering

Matlab Scripts

Butterworth Sixth Order Filter, Transfer Function

Bessel Filter, Transfer Function

Butterworth Sixth Order Filter

Bessel Filter via Fourier transform

Mean filter of a time history

Sine Vibration

Matlab Scripts

Sine Vibration Response Spectrum (VRS)

Power Spectral Density

Matlab Scripts

Overall Level of a Power Spectral Density Function

psd_integ.m Functions: calculate_PSD_slopes.m APSD_VPSD.m APSD_DPSD.m psdinteg.pdf

PSD plotting function with full grid

Synthesis of a Time History to Satisfy a Power Spectral Density

Alternate method: psd_syn_sine.m

Power Spectral Density

Conversion of a power spectral density to various octave formats

P95/50 Envelope for a set of PSD measurements

Triangular Decomposition (LU)

Cholesky Decomposition (LLT )

Spectral Decomposition (LDLT)

Matlab Scripts

pseudo inverse of a matrix using two methods: 1. SVD 2. Ben-Israel & Cohen iteration

Structural Dynamics: Beams & Rods

Matlab Scripts

Natural Frequencies and Mode Shapes of a Beam via the Finite Element Method, with two degrees-of-freedom per node. This program also calculates the participation factors and effective modal mass values.

It allows for the addition of a point mass.

beam.m Functions: beam_data_entry.m local_stiffness.m local_mass.m assembly.m plot_modes.m mass_condense.m Generalized_Eigen.m

Normal modes & base excitation of a Cantilever Beam

Normal modes & base excitation of a Fixed-Free Rod

Natural Frequencies and Mode Shapes of a Rocket Vehicle. The user must input a mass density file and an stiffness file. The stiffness file must be in terms of EI.

A future version of this program will allow for joint compliance and a branch for a payload.

rocket_bending.m Functions: rocket_bending_data_entry.m rocket_local_stiffness.m rocket_local_mass.m assembly.m plot_modes.m

Structural Dynamics: Plates

Matlab Scripts

The Fundamental Frequency of an Isolated Circular Plate

The Fundamental Frequency of an Isolated Annular Plate

The Natural Frequency of a Rectangular Plate Point-Supported at Each Corner

Material Science

Matlab Scripts

Stress Corrosion Cracking: stress required to propagate a partial through-the-thickness crack-like discontinuity

Plot Digitization

Matlab Scripts

Digitize SRS and PSD plots from image files, such as .jpg files.

Digitize log-linear plot.

Digitize SPL plot

Sincerely, Tom Irvine
Email: tomirvine@aol.com

Power Spectral Density Calculation via Matlab: psd_mat.pdf
Guest tutorial submitted by Bob Light.

Supporting functions:
enter_time_history.m
progressbar.m

Supporting function: enter_time_history.m

fft.pdf

Supporting function:
enter_time_history.m

solid_motor_oscillation.pdf

Generation of time history signals:

1=sine
2=cosine
3=damped sine
4=sine sweep
5=white noise
6=terminal sawtooth pulse
7=half-sine pulse
8=versed sine pulse
9=wavelet

psd_integ.m

Functions:
calculate_PSD_slopes.m
APSD_VPSD.m
APSD_DPSD.m
psdinteg.pdf

Alternate method:
psd_syn_sine.m

pseudo inverse of a matrix using two methods:
1. SVD
2. Ben-Israel & Cohen iteration

Natural Frequencies and Mode Shapes of a Beam via the Finite Element Method, with two degrees-of-freedom per node.

This program also calculates the participation factors and effective modal mass values.

beam.m

Functions:

beam_data_entry.m
local_stiffness.m
local_mass.m
assembly.m
plot_modes.m
mass_condense.m
Generalized_Eigen.m

rocket_bending.m

Functions:

rocket_bending_data_entry.m
rocket_local_stiffness.m
rocket_local_mass.m
assembly.m
plot_modes.m