readme.m
MATLAB PROGRAMS FOR "VIBRATION SIMULATION USING MATLAB AND ANSYS"
All the M-files which are listed in the book are available on this site. The
ANSYS-related files and some non-listed utility M-files are available for download
from the author's website, www.hatchcon.con.
Downloading or accessing the M-files constitutes your agreement with the following:
The M-files ("Files") are dedicated to the public domain and may be copied, used,
modified and distributed freely,provided, however, that the following
limitations shall apply to all copies and derivatives of the same and that
the user shall indemnify, defend and hold the author, Michael R. Hatch ("Author")
harmless from and against any and all liabilities arising out of or relating to
the copying, use, modification or distribution of the same.
Author shall not be liable for technical, editorial, or other errors or
omissions which may be contained in, or the negligent preparation of, the Files
or the results of their use. Author shall not be liable for incidental,
consequential, compensatory or exemplary damages resulting from such technical,
editorial, or other errors.
Author hereby disclaims any express or implied warranty, including but not
limited to, the warranty of merchantability or fitness for particular
purpose with regard to the contents, information, results or instructions
contained in the Files.
Author does not guarantee the usefulness of the results of any analysis
performed in accordance with the procedures and theories contained or
reflected in the Files. Confirming the usefulness of all the solutions, and
their accuracy, is the responsibility of the licensee or user.
Examples, solutions, theories, results, methods, and references to other
documents are provided by way of guidance and explanation only, and are not
guaranteed to provide the user with the most accurate, useful, or correct
analysis for any particular problem.
These M-files are User Contributed Routines which are being distributed by The MathWorks,
upon request, on an "as is" basis. A User Contributed Routine is not a product of The
MathWorks, Inc, and The MathWorks assumes no responsibility for any errors that may exist
in these routines.
Downloading:
This document lists all the MATLAB and ANSYS codes used in each chapter, along with a short
description of the purpose of each. This is the same information as in Appendix 1 of the
book.
Matlab files were created using Matlab Version 5.3.1.29215a and Simulink Version 3.0.1.
ANSYS files were created using ANSYS 5.6.1.
MATLAB codes have the suffix ".m" and the ANSYS codes have the suffix ".inp." Additional
output files from previous runs are stored as ".grp" or other suffixes and will be used
from time to time.
Coding format: All the MATLAB code available from downloading and shown in the book
starts over one tab, allowing comment lines to stand out. The code also includes
a lot of blank lines for readability (my apologies to tight "c" code programmers).
In most MATLAB code, critical definitions and calculations are only a few lines of code,
while plotting and annotating are the bulk of the space. For this reason, some code
listings in the book do not show all the plotting commands.
ANSYS eigenvalue/eigenvector results are converted to MATLAB input form using the
following MATLAB extraction codes:
ext56ux.m extracts the ANSYS UX degree of freedom
ext56uy.m extracts the ANSYS UY degree of freedom
ext56uz.m extracts the ANSYS UZ degree of freedom
ext56uxuy.m extracts the ANSYS UX and UY degrees of freedom
ext56uxuz.m extracts the ANSYS UX and UZ degrees of freedom
ext56uyuz.m extracts the ANSYS UY and UZ degrees of freedom
ext56uxuyuz.m extracts the ANSYS UX, UY and UZ degrees of freedom
The codes above all call a supporting MATLAB code ext56chk.m. All the codes should be
installed in the same directory as the ANSYS output code which is to be extracted or
should be installed in a directory which is in the MATLAB path. To use the extraction
code, rename the ANSYS eigenvector output file to have a ".eig" extension and
open MATLAB in the same directory. MATLAB will then open a window showing all the ".eig"
files in the directory. Double-click on the file to extract and MATLAB will output a
file with the "ext56xx.mat" name. If several files are to be extracted in the same
directory, rename the "ext56xx.mat" name to a unique name with the ".mat" extension.
The ".mat" extracted MATLAB file contains the following information:
evr: the modal matrix, with rows consisting of degrees of freedom and each column
representing a mode. The numbering of degrees of freedom is the same as the ANSYS
listing, which is in ascending order of the selected node numbers. Where multiple
directions are extracted, for instance UX and UY degrees of freedom, the degrees of
freedom are listed in that order, first the UX degrees of freedom and then the UY
degrees of freedom. The extracted modal matrix is of size: (total dof) x (modes).
freqvec: a vector listing the eigenvalues (resonant frequencies), in hz values.
The size of the frequency vector is (modes) x (1).
node_numbers: a vector listing the node numbers for the extracted data, of size (dof) x (1).
The extracted data can then be loaded and used to develop state space models of the system.
Chapter 2: Transfer Function Analysis
sdofxfer.m: Calculates and plots magnitude and phase for a single degree of freedom
system over a range of damping values.
tdofpz3x3.m: Uses the "num/den" form of the transfer function, calculates and plots
all nine pole/zero combinations for the nine different transfer functions for tdof
model. It prompts for values of the two dampers, c1 and c2, where the default (hitting
the "enter" key) values are set to zero to match the hand calculated values in (2.82).
The "transfer function" forms of the transfer functions are then converted to
"zpk - zero/pole/gain" form to enable graphical construction of frequency response
in the next chapter.
tdofpz3x3_rlocus.m: Plots pole and zero values for z11 transfer function for a range
of damping values.
Chapter 3: Frequency Response Analysis
tdofxfer.m: Plots tdof model poles and zeros in complex plane, user choice of damping
values. Uses several different model descriptions and frequency response calculating
techniques. The model is described in polynomial, transfer function and zpk forms.
Magnitude and phase versus frequency are calculated using a scalar frequency "for loop,"
vector frequency, automatic bode plotting and bode with magnitude and frequency outputs.
Chapter 4: Zeros in SISO Mechanical Systems
ndof_numzeros.m: Calculates and plots poles/zeros and transfer functions for user
selected input/output locations on a "n" dof series spring/mass model. Shows that
poles of "constrained" structures to left and right of input/output degrees of freedom
are the zeros of the unconstrained structure.
cantfem.inp: ANSYS code for resonant frequencies of cantilever and tip driving point
transfer function. Used to identify zero locations to compare with poles of
"constrained" system in cantzero.inp.
cantzero.inp: ANSYS code for resonant frequencies of cantilever with simple
support at tip. Used to identify poles of "constrained" structure.
cantzero.m: Uses eigenvalues and eigenvectors from cantfem.inp and cantzero.inp
to plot overlay of zeros of cantilever with poles of tip supported cantilever,
showing the correspondence. Calls cantzero_freq.m, cantfem_magphs.m.
Chapter 5: State Space Analysis
tdof_non_prop_damped.m: This code is used to develop an understanding of the
results of MATLAB's eigenvalue analysis and complex modes.
Chapter 6: State Space: Frequency Response, Time Domain
tdofss.m: Calculates and plots the four distinct frequency responses for the
tdof model.
tdof_ss_time_ode45_slnk.m: Solves for time domain response of tdof problem
using MATLAB's ODE45 solver, a Runga-Kutta method of solving differential
equations, as well as, MATLAB's Simulink block-diagram simulation tool.
tdof_ss_time_slnk_plot.m: Plots results from tdof_ss_time_ode45_slnk.m.
tdofssfun.m: Function code called by tdof_ss_time_ode45_slnk.m, contains
state equations.
tdofss_simulink.mdl: Simulink model called by tdof_ss_time_ode45_slnk.m,
defines state equations.
Chapter 8: Frequency Response: Modal Form
tdof_modal_xfer.m: Calculates and plots the four distinct frequency responses
and the individual modal contributions.
threedof.inp: ANSYS code that builds the undamped tdof model, calculates
eigenvalues and eigenvectors, outputs the frequency listing and eigenvectors,
plots the mode shapes. Calculates and plots all three transfer functions for
a force applied to mass 1.
Chapter 9: Transient Response: Modal Form
tdof_modal_time.m: Plots displacements versus time in principal and physical
coordinates.
Chapter 10: Modal Analysis: State Space Form
tdofss_eig.m: Solves for the eigenvalues and eigenvectors in the state
space form of the tdof system.
tdof_prop_damped.m: Calculates poles and zeros of proportionally damped
tdof system. Plots initial condition responses for modes 2 and 3 in
physical and principal coordinate systems.
Chapter 11: Frequency Response: Modal State Space Form
tdofss_modal_xfer_modes.m: Solves for and plots frequency responses for
individual modal contributions and overall responses. Has code for plotting
frequency responses in different forms.
Chapter 12: Time Domain: Modal State Space Form
tdofss_modal_time_ode45.m: Plots tdof transient responses for overall and
individual modal contributions. Calls the function files below, which
define the state space system and individual modes.
tdofssmodalfun.m, tdofssmodal1fun.m, tdofssmodal2fun.m, tdofssmodal3fun.m:
Function files called by tdofss_modal_time_ode45.m.
Chapter 14: Finite Elements: Dynamics
cant_2el_guyan.m: Solves for the eigenvalues and eigenvectors of a
two-element cantilever beam.
cantbeam_guyan.m: Solves for eigenvalues and eigenvectors of a cantilever
with user-defined dimensions, material properties, number of elements and
number of mode shapes to plot. Guyan Reduction is an option. A 10-element
beam is used as an example.
cantbeam.inp: ANSYS code solves for the eigenvalues and eigenvectors of
a 10 element cantilever, the same beam as the cantbeam_guyan.m example.
Chapter 15: SISO State Space MATLAB Model from ANSYS Model
cantbeam_ss.inp: ANSYS code for cantilever beam, allows the user to
change the number of elements and the eigenvalue extraction technique.
The two variables "num_elem" and "eigext" can be easily changed to see
their effects.
cantbeam_ss_freq.m: Compares theoretical frequencies for the first 16
modes for a cantilever beam with MATLAB finite element and ANSYS finite
element results.
cantbeam_ss_modred.m: Creates a MATLAB state space model using the
eigenvalue and eigenvector results from previous ANSYS runs. Modes are
ranked for importance and several reduction techniques are used.
Chapter 16: Ground Acceleration MATLAB Model from ANSYS Model
cantbeam_ss_spring_shkr.inp: ANSYS model of shaker mounted cantilever
with tip mass and tip spring to shaker. Outputs mode shape plot file
cantbeam16red.grp.
cantbeam_ss_tip_con.inp: ANSYS model of shaker mounted constrained tip
cantilever. Outputs mode shape file tipcon16red.grp.
cantbeam_shkr_modeshape.m: Plots mode shapes from ANSYS modal analysis
results for any of the tip spring models, with 2, 4, 8, 10, 12, 16, 32
and 64 beam elements.
cantbeam_ss_shkr_modred.m: Creates a MATLAB state space model using the
results from ANSYS model cantbeam_ss_spring_shkr.inp. Ranks modes, then
uses several reduction techniques to define smaller model.
Chapter 17: SISO Disk Drive Actuator Model
srun.inp: ANSYS model of suspension.
arun.inp: ANSYS model of actuator/suspension system.
act8.m: MATLAB code for dc and peak gain ranking and reduction of
actuator/suspension model. Output from program is used for some input
to balred.m in Chapter 18.
Chapter 18: Balanced Reduction
balred.m: MATLAB code for balanced reduction of actuator/suspension model
from act8.m.
Chapter 19: MIMO Two-Stage Actuator Model
arunpz.inp: ANSYS model of two-stage actuator/suspension system.
act8pz.m: MATLAB model of two-stage actuator/suspension system, balanced
reduction.
