Research Article
A Multimode Approach to Geometrically Nonlinear Free and Forced Vibrations of Multistepped Beams
Table 5
The convergence test of the normalized first nonlinear modes with different numbers of basic functions in the forced vibration case.
| | | | | | | | Residual |
| | 0.536 | 1 | 0.2580741 | 0.258094 | 0.258076 | 0.2580746 | 1.738E−05 | | 1.724E−05 | 2.135E−06 | 4.5023E−07 | 1.135 | 1.3 | 0.556627 | 0.55690 | 0.556679 | 0.556639 | 2.302E−04 | | 2.265E−04 | 3.934E−05 | 1.201E−06 | 1.46 | 1.5 | 0.729168 | 0.72978 | 0.7292869 | 0.7291965 | 5.09E−04 | | 5.010E−04 | 9.033E−05 | 2.826E−05 | 1.9 | 1.8 | 0.96722 | 0.9686168 | 0.9675064 | 0.967296 | 1.132E−03 | | 1.11E−03 | 2.10E−04 | 6.7609E−05 |
| | 0.673 | 1 | 0.325504 | 0.32554426 | 0.3255096 | 0.325505 | 3.489E−05 | | 3.46E−05 | 4.321E−06 | 9.229E−07 | 1.184 | 1.3 | 0.5820689 | 0.58237815 | 0.5821253 | 0.58208203 | 2.568E−04 | | 2527E−04 | 4.333E−05 | 1.308E−05 | 1.496 | 1.5 | 0.745124 | 0.7457758 | 0.7452482 | 0.745153 | 5.367E−04 | | 5.275E−04 | 9.460E−05 | 2.947E−05 | 1.921 | 1.8 | 0.976748 | 0.978167 | 0.977032 | 0.9768179 | 1.157E−03 | | 1.13E−03 | 2.143E−04 | 6.891E−05 |
| | 0.843 | 1 | 0.4107732 | 0.4108534 | 0.4107839 | 0.4107751 | 7.01E−05 | | 6.952E−05 | 8.795E−06 | 1.913E−07 | 1.266 | 1.3 | 0.625555 | 0.625923 | 0.625621 | 0.625570 | 3.071E−04 | | 30251E−04 | 5/087E−05 | 1.511E−05 | 1.549 | 1.5 | 0.774468 | 0.775181 | 0.774603 | 0.774500 | 5.886–04 | | 5.787E−04 | 1.028E−04 | 3.179E−05 | 1.953 | 1.8 | 0.995041 | 0.996520 | 0.995335 | 0.995112 | 1.207E−03 | | 1.184E−03 | 2.229E−04 | 7.14E−05 |
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