文件列表:

vtoolbox3.5 (0, 2002-03-12)
vtoolbox3.5\beaminfo (848, 2002-03-12)
vtoolbox3.5\e8_2_1.con (502, 2002-03-12)
vtoolbox3.5\e8_2_1.exa (2552, 2002-03-12)
vtoolbox3.5\intro.txt (1428, 2002-03-12)
vtoolbox3.5\p8_12 (714, 2002-03-12)
vtoolbox3.5\p8_3_10.con (2390, 2002-03-12)
vtoolbox3.5\truss1.con (398, 2002-03-12)
vtoolbox3.5\truss1.eqn (258, 2002-03-12)
vtoolbox3.5\truss1.out (204, 2002-03-12)
vtoolbox3.5\TRUSS2 (574, 2002-03-12)
vtoolbox3.5\truss2.con (526, 2002-03-12)
vtoolbox3.5\truss2.eqn (2778, 2002-03-12)
vtoolbox3.5\truss2.out (1196, 2002-03-12)
vtoolbox3.5\vtb1 (0, 2002-03-12)
vtoolbox3.5\vtb10 (249, 2002-03-12)
vtoolbox3.5\vtb10_1 (3411, 2002-03-12)
vtoolbox3.5\vtb10_ex (114, 2002-03-12)
vtoolbox3.5\vtb1_1 (1817, 2002-03-12)
vtoolbox3.5\vtb2 (738, 2002-03-12)
vtoolbox3.5\vtb2_1 (1101, 2002-03-12)
vtoolbox3.5\vtb2_2 (1167, 2002-03-12)
vtoolbox3.5\vtb2_3 (707, 2002-03-12)
vtoolbox3.5\vtb2_4 (882, 2002-03-12)
vtoolbox3.5\vtb2_5 (1005, 2002-03-12)
vtoolbox3.5\vtb2_6 (2494, 2002-03-12)
vtoolbox3.5\vtb3 (213, 2002-03-12)
vtoolbox3.5\vtb3_1 (704, 2002-03-12)
vtoolbox3.5\vtb3_2 (693, 2002-03-12)
vtoolbox3.5\vtb3_3 (741, 2002-03-12)
vtoolbox3.5\vtb3_4 (664, 2002-03-12)
vtoolbox3.5\vtb4 (149, 2002-03-12)
vtoolbox3.5\vtb4_1 (973, 2002-03-12)
vtoolbox3.5\vtb4_2 (1432, 2002-03-12)
vtoolbox3.5\vtb5 (490, 2002-03-12)
vtoolbox3.5\vtb5_1 (770, 2002-03-12)
vtoolbox3.5\vtb5_2 (477, 2002-03-12)
vtoolbox3.5\vtb5_3 (1154, 2002-03-12)
... ...

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 (window) 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 Type: beam 3) Type clear. Enter the data interactively. Type: [x,f]=VTB8_2(node,ncon,zero,force) 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: [x,f]=VTB8_2(node,ncon,zero,force,conm) 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 problem. 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. REVISION HISTORY 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

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