Welcome to Vibrationdata Matlab Page

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

Additional Shock Analysis	Matlab Scripts
SRS Matlab Script (Kelly-Richman & Smallwood)	srs.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.	arbit.m
Tripartite Shock Response Spectra Plots	srs_tripartite.m
Mean filter method for removing saturation with optimization.	mean_filter_saturation.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 octaves.m PSD_octave.m
Multi-function signal processing script for time histories	signal_functions.m signal_function_extract.m signal_functon_stats.m
Integrate time history via the trapezoidal rule.	integrate_th.m
Differentiate a time history.	differ.m
Calculate the standard deviation time history from an instantaneous time history	std_dev_th.m
Power Spectral Density	PSD.m FFT_core.m psd.pdf spectral.pdf Shock_and_Vibration_Signal_Analysis.pdf
Conversion of a power spectral density to various octave formats	PSDoct.m octaves.m
Fourier transform	fourier.m progressbar.m
Inverse Fourier transform	invfourier.m
One-sided, Full-amplitude FFT. Includes spectrogram.	full_FFT.m fft.pdf
Inverse FFT	inverseFFT.m
Waterfall FFT	waterfall_FFT.m M57.pdf
Zoom FFT of a time series.	zoomFFT.m zoomFFT_plot.m zoom_fft.pdf zoomFFT_example.pdf d9p5.txt
Generation of time history signals: 1. sine 2. damped sine 3. sine sweep 4. white noise	generate.m sweep.m white.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
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

Filtering	Matlab Scripts
Butterworth Sixth Order Filter, Transfer Function	BH.m filter.pdf REFILT.pdf
Bessel Filter, Transfer Function	Bessel_H.htm
Butterworth Sixth Order Filter	Butterworth_filter.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

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 sdof_ran_engine.m interpolate_PSD.m calculate_PSD_slopes.m
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
SRS plotting function	SRS_plot.m
Synthesis of a Time History to Satisfy a Power Spectral Density	psd_syn.m psd_syn_data_entry.m progressbar.m Alternate method: psd_syn_sine.m
Multiply or divide one frequency response function by another.	real_div.m real_mult.m real_mult_intlog.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	Householder_tridiagonal.m
QR Householder Decomposition	QR_Householder.m
Eigenvalues via the QR Householder algorithm	QR_Householder_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 steps	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 single-degree-of-freedom system, ode45 numerical method.	free_ode45.m free_function.m
Free Vibration of a Single-degree-of-freedom System with Nonlinear Stiffness.	nonlin.pdf sdof_stiff2_ode45.m sdof_stiff2_free_function.m
Free vibration of a pendulum, ode45 numerical method. This program solves the nonlinear equation of motion such that large angular displacements are allowed.	pendulum_free_ode45.m pendulum_free_function.m
Vibration of a single-degree-of-freedom system subjected to sinusoidal base excitation, ode45 numerical method.	sinebase_ode45.m sinebase_function.m bode_transfer_function.m
Vibration of a single-degree-of-freedom system subjected to sinusoidal force excitation, ode45 numerical method.	sineforce_ode45.m sineforce_function.m bode_transfer_function.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
Newmark-Beta method for integration of a two-degree-of-freedom system	Newmark.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

Acoustics	Matlab Scripts
Far field radiation rattern of a circular piston in an infinite baffle.	piston_radiation_pattern.m
Sound Pressure Level from a time history.	SPL.m
Noise from a subsonic gas jet	jet_mixing_noise.m
Franken method for a cylindrical structure subjected to a sound pressure field	Franken.m
Liftoff acoustics of a rocket vehicle	liftoff_matlab.zip
Overall dB level from SPL or similar function	dB_rms.m
Transmission loss through a single partition	single_partition.m
Transmission loss through three media	transmission_three_media.m
Driving Point Impedance	dp_impedance.m dp_plot.m
Modal Density, Bending Modes, Flat Plate	modal_density.m
Vibration Response of a Thin Cylindrical Shell to External Acoustic Pressure via Statistical Energy Analysis	SEA_cylinder.m SEA_plot.m progressbar.m SEA_cylindrical_shell.pdf
Fill factor for a payload fairing	fill_factor.m octaves.m
Doppler shift	doppler.m Newsletter with Doppler shift article:   June 2003

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

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
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

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