a three dimensional structure showing lateral-torsional dynamic modes 12 15 % number of joints and number of members % joint x y z r 1 0 0 0 0 2 72 0 0 0 3 144 0 0 0 4 144 36 0 0 5 144 72 0 0 6 72 72 0 0 7 0 72 0 0 8 0 36 0 0 9 0 0 -120 0 10 144 0 -120 0 11 72 72 -120 0 12 72 36 0 0 % m j1 j2 Ax Asy Asz Jxx Iyy Izz E G p 1 1 2 1100 800 800 1000 500 500 999000 11100 0 2 2 3 1100 800 800 1000 500 500 999000 11100 0 3 3 4 1100 800 800 1000 500 500 999000 11100 0 4 4 5 1100 800 800 1000 500 500 999000 11100 0 5 5 6 1100 800 800 1000 500 500 999000 11100 0 6 6 7 1100 800 800 1000 500 500 999000 11100 0 7 7 8 1100 800 800 1000 500 500 999000 11100 0 8 8 1 1100 800 800 1000 500 500 999000 11100 0 9 9 1 1100 800 800 001 110 110 29000 11100 0 10 10 3 1100 800 800 001 110 110 29000 11100 0 11 11 6 1100 800 800 001 110 110 29000 11100 0 12 12 2 1100 800 800 1000 500 500 999000 11100 0 13 12 4 1100 800 800 1000 500 500 999000 11100 0 14 12 6 1100 800 800 1000 500 500 999000 11100 0 15 12 8 1100 800 800 1000 500 500 999000 11100 0 1 % 1: include shear deformation 1 % 1: include geometric stiffness /tmp/exE-msh % mesh data file name exE.plt % plot file name 20.0 % exaggerate mesh deformations 1 % 1: stiffness analysis, 0: data check only 1 % number of loaded joints % J Fx Fy Fz Mxx Myy Mzz 3 0 1 -10 0 0 0 0 % number of distributed loads 0 % number of internal concentrated loads 0 % number of members with temperature loads 3 % number of joints with reactions % J x y z xx yy zz 1= fixed, 0=free 9 1 1 1 1 1 1 10 1 1 1 1 1 1 11 1 1 1 1 1 1 0 % number of joints with support settlements 4 % number of desired dynamic modes of vibration 1 % 1: subspace Jacobi 2: Stodola 0 % 0: consistent mass ... 1: lumped mass matrix /tmp/exE-m % mode shape data file 1e-5 % mode shape tolerance 1.0 % shift value ... for unrestrained structures 1 7.32e-19 0 % bar numbers, density, and extra mass 2 7.32e-19 0 3 7.32e-19 0 4 7.32e-19 0 5 7.32e-19 0 6 7.32e-19 0 7 7.32e-19 0 8 7.32e-19 0 9 7.32e-19 0 10 7.32e-19 0 11 7.32e-19 0 12 7.32e-19 0 13 7.32e-19 0 14 7.32e-19 0 15 7.32e-19 0 1 % number of joints with extra mass or inertia % j M Ixx Iyy Izz - joints and concentrated mass and inertia 12 3.388 0 0 839.37 4 % number of modes to animate 1 2 3 4 % modes to animate 0 % don't pan during animation 2 % Condensation Method: 0= none 1= static 2= Guyan 3= Dynamic 1 % number of condensed joints 12 1 1 0 0 0 1 % joint number, 1: condense dof, 0: don't 1 2 3 % modes to match for dynamic condensation ________________________________________________________________________________ FRAME3DD version: 20080314 http://www.duke.edu/~hpgavin/frame/ GPL Copyright (C) 1992-2008, Henri P. Gavin FRAME3DD is distributed in the hope that it will be useful but with no warranty. For details see the GNU Public Licence: http://www.fsf.org/copyleft/gpl.html ________________________________________________________________________________ a three dimensional structure showing lateral-torsional dynamic modes Fri Mar 14 12:44:03 2008 ________________________________________________________________________________ JOINTS: 12 MEMBERS: 15 FIXED JOINTS: 3 PRESCRIBED DISPLACEMENTS: 0 JOINT LOADS: 1 UNIFORM MEMBER LOADS: 0 CONCENTRATED MEMBER LOADS: 0 For 2D problems, the Y-axis is vertical. For 3D problems, the Z-axis is vertical. ________________________________________________________________________________ J O I N T D A T A R E S T R A I N T S Joint X Y Z radius Fx Fy Fz Mx My Mz 1 0.000000 0.000000 0.000000 0.000 0 0 0 0 0 0 2 72.000000 0.000000 0.000000 0.000 0 0 0 0 0 0 3 144.000000 0.000000 0.000000 0.000 0 0 0 0 0 0 4 144.000000 36.000000 0.000000 0.000 0 0 0 0 0 0 5 144.000000 72.000000 0.000000 0.000 0 0 0 0 0 0 6 72.000000 72.000000 0.000000 0.000 0 0 0 0 0 0 7 0.000000 72.000000 0.000000 0.000 0 0 0 0 0 0 8 0.000000 36.000000 0.000000 0.000 0 0 0 0 0 0 9 0.000000 0.000000 -120.000000 0.000 1 1 1 1 1 1 10 144.000000 0.000000 -120.000000 0.000 1 1 1 1 1 1 11 72.000000 72.000000 -120.000000 0.000 1 1 1 1 1 1 12 72.000000 36.000000 0.000000 0.000 0 0 0 0 0 0 M E M B E R D A T A (local) Member J1 J2 Ax Asy Asz Jxx Iyy Izz E G roll 1 1 2 1100.0 800.0 800.0 1000.0 500.0 500.0 999000.0 11100.0 0 2 2 3 1100.0 800.0 800.0 1000.0 500.0 500.0 999000.0 11100.0 0 3 3 4 1100.0 800.0 800.0 1000.0 500.0 500.0 999000.0 11100.0 0 4 4 5 1100.0 800.0 800.0 1000.0 500.0 500.0 999000.0 11100.0 0 5 5 6 1100.0 800.0 800.0 1000.0 500.0 500.0 999000.0 11100.0 0 6 6 7 1100.0 800.0 800.0 1000.0 500.0 500.0 999000.0 11100.0 0 7 7 8 1100.0 800.0 800.0 1000.0 500.0 500.0 999000.0 11100.0 0 8 8 1 1100.0 800.0 800.0 1000.0 500.0 500.0 999000.0 11100.0 0 9 9 1 1100.0 800.0 800.0 1.0 110.0 110.0 29000.0 11100.0 0 10 10 3 1100.0 800.0 800.0 1.0 110.0 110.0 29000.0 11100.0 0 11 11 6 1100.0 800.0 800.0 1.0 110.0 110.0 29000.0 11100.0 0 12 12 2 1100.0 800.0 800.0 1000.0 500.0 500.0 999000.0 11100.0 0 13 12 4 1100.0 800.0 800.0 1000.0 500.0 500.0 999000.0 11100.0 0 14 12 6 1100.0 800.0 800.0 1000.0 500.0 500.0 999000.0 11100.0 0 15 12 8 1100.0 800.0 800.0 1000.0 500.0 500.0 999000.0 11100.0 0 Include shear deformations. Include geometric stiffness. J O I N T L O A D S + E Q U I V A L E N T J O I N T L O A D S (global) Joint Fx Fy Fz Mxx Myy Mzz 3 0.000 1.000 -10.000 0.000 0.000 0.000 E L A S T I C S T I F F N E S S A N A L Y S I S via L D L' decomposition J O I N T D I S P L A C E M E N T S (global) Joint X-dsp Y-dsp Z-dsp X-rot Y-rot Z-rot 1 0.006266 -0.002420 0.000002 0.000018 0.000000 0.000244 2 0.006266 0.015165 -0.000003 0.000000 0.000000 0.000244 3 0.006266 0.032759 -0.000036 -0.000021 0.000001 0.000244 4 -0.002526 0.032759 -0.000741 -0.000019 0.000011 0.000244 5 -0.011318 0.032759 -0.001400 -0.000018 0.000020 0.000244 6 -0.011318 0.015165 -0.000003 -0.000001 0.000018 0.000244 7 -0.011318 -0.002420 0.001300 0.000018 0.000018 0.000244 8 -0.002526 -0.002420 0.000655 0.000018 0.000009 0.000244 12 -0.002526 0.015165 0.000003 0.000000 0.000010 0.000244 M E M B E R E N D F O R C E S (local) Member Joint Nx Vy Vz Txx Myy Mzz 1 1 -0.140t 0.013 -0.224 2.770 10.831 0.069 1 2 0.140t -0.013 0.224 -2.770 5.291 0.837 2 2 -0.013t -0.092 -0.123 3.235 -2.331 -3.418 2 3 0.013t 0.092 0.123 -3.235 11.158 -3.211 3 3 0.213c 0.149 -0.543 -2.950 38.056 3.188 3 4 -0.213c -0.149 0.543 2.950 -18.498 2.184 4 4 0.092c 0.150 -0.359 -2.823 15.593 2.182 4 5 -0.092c -0.150 0.359 2.823 -2.676 3.202 5 5 0.150c -0.092 -0.359 2.676 2.823 -3.202 5 6 -0.150c 0.092 0.359 -2.676 23.010 -3.423 6 6 0.002c 0.013 0.008 2.860 -3.359 0.836 6 7 -0.002c -0.013 -0.008 -2.860 2.808 0.082 7 7 0.013c -0.002 0.008 -2.808 -2.860 -0.082 7 8 -0.013c 0.002 -0.008 2.808 2.585 0.027 8 8 0.017c -0.002 0.190 -2.557 -5.348 0.030 8 1 -0.017c 0.002 -0.190 2.557 -1.484 -0.092 9 9 -0.414t 0.029 0.138 -0.023 -8.300 2.251 9 1 0.414t -0.029 -0.138 0.023 -8.275 1.286 10 10 9.579c -0.695 0.137 -0.023 -8.264 -42.393 10 3 -9.579c 0.695 -0.137 0.023 -8.208 -41.291 11 11 0.834c -0.335 -0.275 -0.023 16.012 -20.110 11 6 -0.834c 0.335 0.275 0.023 16.986 -20.071 12 12 0.105c 0.127 0.101 -2.960 -3.183 2.002 12 2 -0.105c -0.127 -0.101 2.960 -0.465 2.581 13 12 -0.000t -0.121 0.184 2.905 -13.157 -4.360 13 4 0.000t 0.121 -0.184 -2.905 -0.127 -4.366 14 12 0.230c 0.127 -0.468 -2.664 -3.041 1.999 14 6 -0.230c -0.127 0.468 2.664 19.887 2.565 15 12 0.000c 0.004 0.182 2.763 -12.862 0.360 15 8 -0.000c -0.004 -0.182 -2.763 -0.251 -0.057 R E A C T I O N S (global) Joint Fx Fy Fz Mxx Myy Mzz 9 -0.138 0.029 -0.414 -2.251 -8.300 -0.023 10 -0.137 -0.695 9.579 42.393 -8.264 -0.023 11 0.275 -0.335 0.834 20.110 16.012 -0.023 R M S E Q U I L I B R I U M E R R O R: 2.864e-07 M O D A L A N A L Y S I S R E S U L T S Total Mass: 3.388000e+00 Structural Mass: 8.116416e-13 J O I N T M A S S E S (diagonal of the mass matrix) (global) Joint X-mass Y-mass Z-mass X-inrta Y-inrta Z-inrta 1 6.59934e-14 6.70916e-14 6.45263e-14 1.36297e-11 1.61272e-11 3.22536e-12 2 4.94285e-14 5.27413e-14 5.38578e-14 3.94678e-13 5.74037e-12 6.09113e-12 3 6.59934e-14 6.70916e-14 6.45263e-14 1.36297e-11 1.61272e-11 3.22536e-12 4 4.08825e-14 4.08642e-14 4.30972e-14 7.36651e-13 2.88336e-12 3.58488e-12 5 3.01037e-14 3.12018e-14 3.23183e-14 3.77110e-13 2.87458e-12 3.22533e-12 6 8.53182e-14 8.86310e-14 8.60658e-14 1.36473e-11 1.89929e-11 6.09116e-12 7 3.01037e-14 3.12018e-14 3.23183e-14 3.77110e-13 2.87458e-12 3.22533e-12 8 4.08825e-14 4.08642e-14 4.30972e-14 7.36651e-13 2.88336e-12 3.58488e-12 9 8.49534e+02 8.49534e+02 8.49534e+02 8.49534e+02 8.49534e+02 8.49534e+02 10 8.49534e+02 8.49534e+02 8.49534e+02 8.49534e+02 8.49534e+02 8.49534e+02 11 8.49534e+02 8.49534e+02 8.49534e+02 8.49534e+02 8.49534e+02 8.49534e+02 12 3.38800e+00 3.38800e+00 3.38800e+00 7.54219e-13 5.74915e-12 8.39370e+02 Use consistent mass matrix. N A T U R A L F R E Q U E N C I E S & M A S S N O R M A L I Z E D M O D E S H A P E S convergence tolerance: 1.000e-05 MODE 1: f= 0.688737 Hz, T= 1.451933 sec X- modal participation factor = 1.8393e+00 Y- modal participation factor = -1.2912e-02 Z- modal participation factor = -1.2184e-05 Joint X-dsp Y-dsp Z-dsp X-rot Y-rot Z-rot 1 4.966e-01 8.853e-02 5.338e-05 3.126e-04 3.471e-05 -1.285e-03 2 4.966e-01 -3.811e-03 -4.945e-06 3.363e-08 -1.353e-05 -1.284e-03 3 4.966e-01 -9.614e-02 -5.416e-05 -3.118e-04 3.451e-05 -1.285e-03 4 5.429e-01 -9.614e-02 -1.150e-02 -3.212e-04 1.600e-04 -1.284e-03 5 5.890e-01 -9.614e-02 -2.315e-02 -3.231e-04 3.113e-04 -1.281e-03 6 5.890e-01 -3.811e-03 7.794e-07 2.634e-07 3.398e-04 -1.282e-03 7 5.890e-01 8.853e-02 2.317e-02 3.233e-04 3.118e-04 -1.281e-03 8 5.429e-01 8.853e-02 1.152e-02 3.215e-04 1.605e-04 -1.284e-03 9 5.344e-25 1.052e-25 7.463e-29 -3.028e-24 1.544e-23 -1.634e-30 10 5.344e-25 -1.134e-25 -7.572e-29 3.264e-24 1.544e-23 -1.634e-30 11 6.246e-25 -4.102e-27 1.101e-30 1.185e-25 1.806e-23 -2.134e-30 12 5.429e-01 -3.811e-03 -3.596e-06 5.729e-08 1.597e-04 -1.283e-03 MODE 2: f= 0.702172 Hz, T= 1.424152 sec X- modal participation factor = 1.2929e-02 Y- modal participation factor = 1.8406e+00 Z- modal participation factor = 1.4962e-03 Joint X-dsp Y-dsp Z-dsp X-rot Y-rot Z-rot 1 3.976e-03 5.426e-01 5.654e-05 -5.340e-05 -1.001e-05 6.929e-06 2 3.975e-03 5.433e-01 5.546e-04 -2.575e-06 -1.086e-07 4.437e-06 3 3.975e-03 5.432e-01 5.576e-05 -5.952e-05 1.057e-05 1.924e-06 4 3.816e-03 5.432e-01 -1.321e-03 -2.559e-05 3.461e-05 3.382e-06 5 3.656e-03 5.432e-01 -2.017e-03 -1.733e-05 3.696e-05 1.961e-06 6 3.656e-03 5.433e-01 -1.122e-04 -3.567e-05 3.190e-06 4.454e-06 7 3.655e-03 5.426e-01 -1.573e-03 -1.120e-05 -3.093e-05 6.954e-06 8 3.816e-03 5.426e-01 -1.099e-03 -1.945e-05 -3.152e-05 5.496e-06 9 4.780e-27 6.065e-25 8.216e-29 -1.752e-23 1.377e-25 9.154e-33 10 4.113e-27 6.070e-25 8.102e-29 -1.754e-23 1.192e-25 2.542e-33 11 3.995e-27 6.078e-25 -1.629e-28 -1.756e-23 1.155e-25 1.990e-29 12 3.816e-03 5.433e-01 4.416e-04 -6.096e-06 1.540e-06 4.442e-06 MODE 3: f= 3.018204 Hz, T= 0.331323 sec X- modal participation factor = 6.8439e-02 Y- modal participation factor = -7.1749e-04 Z- modal participation factor = -3.0034e-06 Joint X-dsp Y-dsp Z-dsp X-rot Y-rot Z-rot 1 1.259e+00 -2.477e+00 3.652e-05 3.039e-03 9.892e-05 3.441e-02 2 1.259e+00 -2.118e-04 -2.353e-06 4.353e-08 -3.482e-05 3.439e-02 3 1.259e+00 2.477e+00 -3.667e-05 -3.039e-03 9.878e-05 3.441e-02 4 2.020e-02 2.477e+00 -1.065e-01 -2.888e-03 1.480e-03 3.440e-02 5 -1.219e+00 2.477e+00 -2.091e-01 -2.828e-03 2.909e-03 3.442e-02 6 -1.219e+00 -2.118e-04 1.426e-07 3.367e-08 2.856e-03 3.439e-02 7 -1.219e+00 -2.477e+00 2.091e-01 2.828e-03 2.909e-03 3.442e-02 8 2.020e-02 -2.477e+00 1.065e-01 2.888e-03 1.480e-03 3.440e-02 9 2.602e-23 -4.948e-23 9.806e-28 1.432e-21 7.517e-22 8.399e-28 10 2.602e-23 4.947e-23 -9.845e-28 -1.431e-21 7.517e-22 8.399e-28 11 -2.695e-23 -4.367e-27 -3.292e-30 1.261e-25 -7.766e-22 8.269e-28 12 2.020e-02 -2.118e-04 -8.865e-07 3.338e-08 1.477e-03 3.449e-02 MODE 4: f= 13.989185 Hz, T= 0.071484 sec X- modal participation factor = 1.7774e-06 Y- modal participation factor = -1.4963e-03 Z- modal participation factor = 1.8407e+00 Joint X-dsp Y-dsp Z-dsp X-rot Y-rot Z-rot 1 9.586e-07 -5.857e-04 1.335e-02 3.615e-03 -1.335e-02 1.017e-06 2 1.977e-06 -4.417e-04 6.807e-01 -2.056e-03 -2.312e-08 4.139e-08 3 2.995e-06 -5.795e-04 1.335e-02 3.616e-03 1.335e-02 -9.350e-07 4 5.277e-07 -5.794e-04 1.349e-01 2.548e-03 8.164e-03 -3.662e-07 5 -8.672e-07 -5.794e-04 1.973e-01 1.403e-03 -3.301e-03 -9.638e-07 6 -1.007e-06 -4.410e-04 2.680e-02 -1.590e-02 -3.560e-07 4.229e-08 7 -1.148e-06 -5.855e-04 1.972e-01 1.403e-03 3.300e-03 1.049e-06 8 5.210e-07 -5.856e-04 1.348e-01 2.547e-03 -8.165e-03 4.490e-07 9 1.715e-22 4.620e-23 7.700e-24 -1.279e-21 4.751e-21 5.335e-31 10 -1.715e-22 4.622e-23 7.699e-24 -1.280e-21 -4.751e-21 -4.903e-31 11 3.984e-27 -2.046e-22 1.545e-23 5.666e-21 1.138e-25 1.186e-31 12 5.246e-07 -4.416e-04 5.433e-01 -9.073e-03 -1.809e-07 4.418e-08 M A T R I X I T E R A T I O N S: 2 There are 4 modes below 13.989185 Hz. ... All 4 modes were found.