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TutorialsPower Spectral Density
Calculation via Matlab: psd_mat.pdf

Classic Pulse Base Input Shock Analysis 
Matlab Scripts 
Response of a
Singledegreeoffreedom System Subjected to a Halfsine Base Excitation

halfsine.m

Response of a
Singledegreeoffreedom System Subjected to a Versedsine Base
Excitation

versed_sine.m

SDOF response to a terminal sawtooth base input. 
terminal_sawtooth.m

SDOF response to a wavelet base input. 
sdof wavelet.m 
SDOF response to combined sinusoidal force and base excitation. 

SDOF response to unit step force  
TWODOF response to applied force excitation.  gencoord.pdf 
TWODOF response to a wavelet base input. 
twodof wavelet.mtwodof_wavelet.pdf 
Additional Shock Analysis  Matlab Scripts 
SRS Matlab Script (KellyRichman & Smallwood) 
srs.m
Supporting functions: srs_coefficients.m enter_time_history.m find_max.m fix_size.m srs_intr.pdf DS_SRS1.pdf 
SRS via convolution  srs_conv.m 
Time history response of a singledegreeoffreedom system to an arbitrary acceleration base input via a digitial recursive filtering relationship. 
arbit.m Supporting function: srs_coefficients_avd.m plot_peak_histogram.m plot_TH.m plot_histogram.m enter_time_history.m 
Tripartite Shock Response Spectra Plot  srs_tripartite.zip 
This
script demonstrates how an SRS can be calculated from a time history
using an FFT as an intermediate step. 
srs_from_fft.m Supporting functions: sdof_base_accel_transfer.m enter_time_history.m full_FFT_core.m fix_size.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 MILSTD810F 
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 
SRS amplitude conversion utility  srs_rel_disp.m 
Fouier Transforms 
Matlab Scripts 
Fourier transform 
fourier.mSupporting functions:find_max.m

Inverse Fourier transform 
invfourier.m 
Onesided, Fullamplitude FFT 
full_FFT.mSupporting function:full_FFT_core.mfix_size.mfind_max.m enter_time_history.m

Waterfall FFT 
waterfall_FFT.mSupporting
function:

Zoom FFT of a time series. 
zoomFFT.m

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
Supporting functions: differentiate_function.m plot_histogram.m coordinates_ss.m coordinates_ss_scale.m octaves.m PSD_octave.m plot_peak_histogram.m signal_stats_TH.m signal_stats_SRS.m signal_stats_SPL.m signal_stats_PSD.m 
Multifunction 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.zip 
This script corrects an acceleration signal so that its corresponding velocity and displacement time histories are stable and oscillate about the zero baseline  disp_correction.m enter_time_history.m velox_correction_d.m Butterworth_filter_function.m differentiate_function.m integrate_function.m half_cosine_fade.m cubic_spline_function.m fix_size.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 
Find phase angle between two signals for sine sweep excitation  sine_sweep_spectral_phase.m 
Autocorrelation
of two signals. The Matlab Signal toolbox is not required. 

Crosscorrelation
of two signals. The Matlab Signal toolbox is not required. 

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 curvefitting method. It is precise but may take a "long" computational time. 
remove_noise_frequency.m sfa_engine_60.m 
Cubic spline 
cubic_spline.m 
Relative displacement between two displacement time histories  relative_displacement.m 
Signal Generation 
Matlab Scripts 
Generation of time
history
signals:
2=cosine 3=damped sine 4=sine sweep 5=white noise 6=terminal sawtooth pulse 7=halfsine pulse 8=versed sine pulse 9=wavelet 
generate.mSupporting
functions:
Butterworth_LP_filter_function.m
filter_coefficients.m

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.

Supporting
functions: plot_histogram.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 
Bessel Filter, Transfer Function 
Bessel_H.m 
Butterworth Sixth Order Filter 
Butterworth_filter.mSupporting functions:enter_time_history.m filter_coefficients.mapply_filter.m 
Bessel Filter via Fourier transform 
fourier_filter_Bessel.mBessel_Transfer.m 
Butterworth Sixth Order Filter via Fourier transform 
fourier_filter.mButterworth_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 
Structural Dynamics: Beams & Rods 
Matlab Scripts 
Natural Frequencies and
Mode Shapes of a Beam
via the Finite Element
Method, with two degreesoffreedom per node.

beam.m

Natural Frequencies and Mode Shapes of a Beam via the Finite Element Method with six degreesoffreedom per node. The beam elements may be in a threedimensional frame.

Functions: User Guide 
Normal modes & base excitation of a Cantilever Beam 
cantilever_beam.m 
Normal modes & base excitation of a FixedFree 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

Structural Dynamics: Plates 
Matlab Scripts 
Natural Frequencies of a Circular Plate, Simplysupported, Bessel Function Solution  circular_SS.m 
Natural Frequencies of a Circular Plate  
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 PointSupported at Each Corner 
plate_corners.mpfunction.m 
Structural Dynamics, Other  Matlab Scripts 
Free vibration of a singledegreeoffreedom system, exact method. 
free.m free.pdf 
Free vibration of a multidegreeoffreedom 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 twodegreeoffreedom system.  two_dof.m 
Natural frequenices and mode shapes of a threedegreeoffreedom system.  three_dof.m 
Natural frequenices and mode shapes of a multipledegreeoffreedom system.  
Natural frequenices and mode shapes of a multipledegreeoffreedom system, reduced to a subset of dof per the user's input.  
Mass Condensation (Guyan Reduction)  
CraigBampton Method  mdof_CB.m 
The SteadyState Frequency Response Function of a Multidegreeoffreedom System Subjected to Harmonic Base Excitation  two_dof_frf.m 
The SteadyState Frequency Response Function of a Singledegreeoffreedom System Subjected to Harmonic Force Excitation  sdof_force_frf.m 
The SteadyState Frequency Response Function of a Multidegreeoffreedom System Subjected to Harmonic Force Excitation 
two_dof_force_frf.mtwo_dof_force_frf_alt.m 
Natural Frequency of a Singledegreeoffreedom System ( GUI ) 
SDOF_freq.m SDOF_freq.fig 
Vibration Analysis of an Isolated Mass with Sixdegreesoffreedom  six_dof_iso.m 
Multidegreeoffreedom system subjected to applied force, modal transient analysis 

Multidegreeoffreedom system subjected to applied force, modal transient analysis, reduced system  
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  
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 
Threedimensional coordinate transformation  coordinate_transformation_3D.m 
Roots of characteristic equations for structural dynamics  vibration_roots.m 
See also: Matlab acoustics PageMatlab linear algebra PageMatlab_modal_transient_PageMatlab_Newmark_Page

Material Science 
Matlab Scripts 
Stress Corrosion Cracking: stress required to propagate a partial throughthethickness cracklike discontinuity 
stress_intensity.m 
Animation  Matlab Scripts 
Animation of a singledegreeoffreedom system (spring mass system) subjected to sinusoidal base excitation with time history display. 
SDOF_base_animation.m 
Animation of a singledegreeoffreedom 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 loglinear 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 104985 (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 
Multiformat data input utility.  data_input.m 
Remove header lines from an external ASCII input file.  header.m 
UCI data conversion. Generates a series of twocolumns 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
halfsine 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 loglinear function. 
int_semilog.m 
Math & Geometry 
Matlab Scripts 
Calculate pi using a
series expansion of

pi_nr.m 
Calculate pi by determining the arclength of a quarter circle. 
pi_arclength.mprogressbar.m 
Calculate pi by determining the area of a quarter circle. Simple grid point integration is used. 
pi_gpi.mprogressbar.m 
Calculate the area of a quadrilateral which may be irregular from its coordinates  quadrilateral_area.m 
Calculate the area of a triangle from its coordinates.  triangle_area.m 
Statistics 
Matlab Scripts 
Normal tolerance intervals, upper limits 
k_factor.m 
Integrate the noncentral tdistribution 
noncentral_t_distribution.m 
Integrate the noncentral tdistribution, table format 
noncentral_t_distribution_table.m 
Integrate the student tdistribution. 
integrate_t_distribution.m
t_distribution.m 
Integrate the chisquare curve. 

Integrate the normal distribution curve. 
integrate_normal_distribution.m 
Finance 
Matlab Scripts 
Loan calculation script for principal and interest 
loan.m 

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