Vibrationdata FEA Matlab GUI Package User Guide Revision A By Tom Irvine Email: tom@vibrationdata.com March 25, 2014 Introduction Matlab Script: vibrationdata_fea_preprocessor.zip vibrationdata_fea_preprocessor.m is the main script. The remaining scripts are supporting functions. The user is responsible for consistent units. The package allows for nodes and elements in a 3D space. There are three translational and three rotational degrees-of-freedom per node. The available elements are dof springs, point masses and rigid links. Additional elements will be included in future revisions, such as beams, plates, gap springs, etc. This package began as a preprocessor, but it will solve for the normal modes. Forced response and enforced acceleration will added in future revisions, both for frequency and time domain analyses. Static analysis and buckling are also on the to-do list. The scripts have some error-detection capability, but further checks are needed. The data may be input manually or through an input file as shown in the following example. Examples Examples are given in the appendices. 1
References 1. T. Irvine, Two-degree-of-freedom System Subjected to a Half-sine Pulse Force, Revision A, Vibrationdata, 2014. 2. T. Irvine, Sample Lateral Natural Frequency Calculations for a Space Vehicle/Dispenser Analysis, Vibrationdata, 2001. 3. T. Irvine, Assembly of Subsystem Matrices, Revision B, Vibrationdata, 2012. 2
APPENDIX A Example Consider the two-degree-of-freedom system in Figure A-1 with the mass and stiffness values shown in Table A-1. k 3 m2 x 2 k 2 m1 x 1 k 1 Figure A-1. Two-degree-of-freedom System, Springs & Masses Table A-1. Parameters Variable Value Unit m 1 3.0 lbf sec^2/in m 2 2.0 lbf sec^2/in k 1 400,000 lbf/in k 2 300,000 lbf/in k 3 100,000 lbf/in The equations of motion for this system are given in Reference 1. 3
The data could be added manually into the vibrationdata_fea_preprocessor script. Or it could be imported via a file. The input file could either be an ASCII text or Excel file. Here is the input file and its format. The row order is unimportant. Lower case must be used for the identifying text labels. Underscores must be used where there are two or more words in the label. Node 1 0 0 0 1 1 1 1 1 1 Node 2 1 0 0 0 1 1 1 1 1 Node 3 2 0 0 0 1 1 1 1 1 Node 4 3 0 0 1 1 1 1 1 1 point_mass 2 3 0 0 0 point_mass 3 2 0 0 0 dof_spring_property 1 400000 0 0 0 0 0 dof_spring_property 2 300000 0 0 0 0 0 dof_spring_property 3 100000 0 0 0 0 0 dof_spring_element 1 1 2 dof_spring_element 2 2 3 dof_spring_element 3 3 4 The node format is: node Node number X coord Y coord Z coord TX TY TZ RX RY RZ TX, TY & TZ are the translational constraints in the X, Y & Z-axes, respectively. RX, RY & RZ are the rotational constraints about the X, Y & Z-axes, respectively. A constraint value of 1 means fixed. A value of 0 indicates free. 4
The point_mass format is: point_mass Node number mass JX JY JZ JX, JY & JZ are the polar moments of inertia about the X, Y & Z-axes, respectively. The dof_spring_property format is: dof_spring_property Spring Property Number KX KY KZ K theta X K theta Y K theta Z KX, KY & KZ are the translational stiffness values in the X, Y & Z-axes, respectively. The dimension is [force/length]. K theta X, K theta Y & K theta Z are the rotational stiffness values about the X, Y & Z-axes, respectively. The dimension is [force/radian]. The stiffness values may be set to zero is the corresponding dofs are to be constrained. The axes are global. The dof_spring_element format is: dof_spring_element Spring Property Number Node 1 Node 2 5
Figure A-2. Two-degree-of-freedom System, Finite Element Model The blue lines are the dof springs. The red circles are point masses. The numbers are node numbers. The nodal coordinate spacing is somewhat arbitrary for this example since neither the stiffness nor point mass depends on length. 6
The normal modes results from vibrationdata_fea_preprocessor are: mass = 3 0 0 2 stiffness = 700000-300000 -300000 400000 Natural Frequencies n f(hz) 1 48.552 2 92.839 ModeShapes 0.3797-0.4349 0.5326 0.4651 7
APPENDIX B Example The three-degree-of-freedom system in Figure B-1 is taken from Reference 2. It is a real-world problem from a launch vehicle/dispenser analysis. This example will demonstrate the use of rigid link elements, although the analysis could have been performed without the links. x 2 x 3 m2 m3 k 2 k 3 m1 x 1 k 1 Figure B-1. Three-degree-of-freedom System, Springs & Masses Table B-1. Parameters Variable Value Unit m 1 379 kg m 2 2367 Kg m 3 2367 Kg k 1 1.48e+08 N/m k 2 1.10e+07 N/m 8
Here is the model file. node 1 0 0 0 1 1 1 1 1 1 node 2 1 0 0 0 1 1 1 1 1 node 3 2 0.5 0 0 1 1 1 1 1 node 4 2-0.5 0 0 1 1 1 1 1 node 5 3 0.5 0 0 1 1 1 1 1 node 6 3-0.5 0 0 1 1 1 1 1 point_mass 2 379 0 0 0 point_mass 5 2367 0 0 0 point_mass 6 2367 0 0 0 dof_spring_property 1 1.48E+08 0 0 0 0 0 0 dof_spring_property 2 11000000 0 0 0 0 0 0 dof_spring_element 1 1 2 0 0 0 0 0 dof_spring_element 2 3 5 0 0 0 0 0 dof_spring_element 2 4 6 rigid_link 2 3 1 0 0 0 0 0 rigid_link 2 4 1 0 0 0 0 0 The rigid_link format is: rigid_link Primary Node Secondary Node TX TY TZ RX RY RZ TX, TY & TZ are the translational links in the X, Y & Z-axes, respectively. RX, RY & RZ are the rotational links about the X, Y & Z-axes, respectively. A constraint value of 1 means connected. A value of 0 indicates disconnected. 9
Figure B-2. Three-degree-of-freedom System, Finite Element Model The blue lines are the dof springs. The black lines are rigid links. The red circles are point masses. The numbers are node numbers. Again, the nodal coordinate spacing is somewhat arbitrary for this example since neither the stiffness nor point mass depends on length. 10
The normal modes results from vibrationdata_fea_preprocessor are: mass = 379 0 0 0 2367 0 0 0 2367 stiffness = 170000000-11000000 -11000000-11000000 11000000 0-11000000 0 11000000 Natural Frequencies n f(hz) 1 10.116 2 10.85 3 106.66 ModeShapes = 0.0019 0.0000 0.0513 0.0145 0.0145-0.0005 0.0145-0.0145-0.0005 11