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vtb8read.txt
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Chapter 8 Vibration Toolbox Notes
The three main files of the chapter 8 toolbox are named
VTB_?.m. Together they form a simple finite element
code which includes a graphical preprocessor for
entering the model (VTB8_1), the main body of the
finite element code for solving the problem (VTB8_2),
and a graphical post processor for viewing the problem
solution (VTB8_3). Other files exist as examples and
are described in the 'EXAMPLES' section.
THE GRAPHIC PREPROCESSOR (VTB8_1):
The graphic preprocessor is a very simple
preprocessor which allows simple problems to be defined
graphically. Note that editing of previously entered
data is not possible with the graphic preprocessor. For
more complicated models, it is suggested that the user
create a script file which defines the model and use the
main body of the finite element code directly. In
machines without a graphic user interface (GUI)
the view will move between the graphic screen and the
command screen. Pressing return in the graphics screen
will bring the view back to the command screen unless
you are picking a node with a pointing device such as a
mouse or trackball. Make sure that you know the node
number(s) you want to select before returning to the
command window. On GUI systems, it should be possible
to position the command and graphics windows next to
each other such that both can be seen at the same time.
When selecting nodes, it is possible to enter either the
node number or use a mouse (or other pointing device).
When a node is selected it is represented by an 'x'
instead of an 'o'. When is is deselected by the
computer its representation will return to an 'o'.
THE MAIN BODY (VTB8_2):
The main body of the program solves the problem
defined by a '.con' file created by VTB8_1 or a script
file, or uses the data as defined directly in the
workspace.
Four methods exist for creating this data.
1) Use the program vtb8_1.
2) Type clear. Enter the data interactively.
Save a file with the file extension .con.
i.e. type: save beam1.con or use the menu command
"Save Workspace" if it exists on your platform.
Make sure to save the file in the directory you want
it and use the extension ".con".
Type: vtb8_2
Load vtb8_2 when prompted.
3) Type clear. Enter the data interactively.
Type: [x,f]=vtb8_2(node,ncon,zero,force)
This method does not allow you to save the
equations and is not recommended.
4) Create a script 'm' file including the definitions.
Add the line:
save filename.con
to the end of the file.
Execute the script file.
Type: vtb8_2
The variable definitions and configurations are given
below. All variables must be defined,
even if they are not used.
node=[x1 y1;x2 y2;...]
ncon=[node1 node2 E A I G Rho;...]
Where 'node1' and 'node2' are connected by an
element, 'E' is Young's modulus, 'A' is the
cross sectional area, 'I' is the moment of area,
'G' is the shear modulus and 'Rho' is the
density per unit length (set 'G' equal to zero
to ignore shear deformation).
zero=[node# dof#;...]
'dof#' is the degree of freedom at node 'node#'
to constrain or load.
'dof#' numbers [1 2 3] correspond to [x y theta]
force is the magnitude of the load.
force=[node# dof# force]
conm=[node# mass]
Where 'node#' is the node at which the mass of
magnitude 'mass' is located.
All rotations are positive counter clockwise.
THE GRAPHICS POST-PROCESSOR (VTB8_3):
The graphics postprocessor can be used view results
of both static and dynamic analysis. It can be run
without arguments and will prompt you for the name of
the project. All date created by VTB8_2 must be saved
in order to use the graphics postprocessor. The
undeformed object is drawn in blue using '*' at the
nodal points. The deformed shape is drawn in red using
'o' at the nodal points.
EXAMPLE FILES:
VTB8_e1.m is an example script file of a five element
aluminum beam clamped at the left end with five
elements. The cross section is 5 cm square. No shear
deformation is modeled. Extensional degrees of freedom
are included (not zeroed). The force vector is zero
since this is a dynamic analysis.
p8_3_10.con is a ten element model of problem 8.3
produced using the graphics preprocessor. It can
be loaded and run by typing VTB8_2('p8_3_10').
e8_2_1.con is example 8.2.1. It can be loaded and
run by typing VTB8_2('e8_2_1').
e8_2_1.EXA is a diary file containing the session for
creating e8_2_1.con with VTB8_1
FILE TYPES:
All files related to the same problem have the same
name but different extensions. This helps to keep
problem sets together.
Files ending in the extension '.con' are connectivity
files which describe the problem geometry, element
parameters, and loads. They are the output of VTB8_1
and the input to VTB8_2. The variables are defined in
the description of the file 'VTB8_2'.
Files ending in the extension '.out' are output files
containing either the displacements and forces for the
static solution or the natural frequencies and mode
shapes for the dynamic case.
Files ending in the extension '.eqn' contain the
equations of motion.
VARIABLE DESCRIPTIONS:
In all vectors and matrices containing information
about displacements/forces, the coordinates are
[x1;y1;theta1;x2;y2;theta2...]. Each column of a matrix
describes the mode shape corresponding to its index
number. The variables f and x can be found in '.out'
files while the remaining variables are stored in the
'.eqn' files.
f Static problem: Force vector acting on each
degree of freedom externally.
Dynamic problem: Natural frequencies of the
problem in rad/s.
x Static problem: Displacement vector.
Dynamic problem: Mode shape matrix.
f1 Static problem: Applied loads on unconstrained
degrees of freedom.
Dynamic problem: Diagonal matrix of natural
frequencies.
x1 Static problem: Displacement vector of
unconstrained degrees of freedom.
Dynamic problem: Mode shape matrix,
unconstrained degrees of freedom only.
k1 Stiffness matrix corresponding to unconstrained
degrees of freedom only.
m1 Mass matrix corresponding to unconstrained
degrees of freedom only.
p Vector listing unconstrained degrees of freedom
in f1, x1, m1, and k1. p=[1;3;6] would mean
that x1, theta2 and theta3 were the only
unconstrained degrees of freedom.
ACKNOWLEDGEMENTS
Thanks is given to Dr. Maurice Petyt for his patience
testing numerous 1.2 beta versions of this software.
REVISION HISTORY
1.2 Updated to work with version 4.0 of Matlab. Open and Save
dialog boxes added.
1.1 Fixed bug causing vtb8_2 to crash when concentrated
masses were used but concentrated inertias were not.
Minor documentation changes.
1.0 First release