Research Article
Analytic Solution for Nonlinear Multimode Beam Vibration Using a Modified Harmonic Balance Approach and Vieta’s Substitution
Table 1
(a) Convergence study for various excitation magnitudes,
. (b) Convergence study for various excitation frequencies,
= 7.5.
(a) |
| Normalized overall amplitude | = 1 | 7.5 | 15 | 25 |
| Zero level solution | 99.92 | 101.00 | 101.93 | 102.69 | 1st level solution | 100.00 | 100.03 | 100.13 | 100.32 | 2nd level solution | 100.00 | 100.00 | 100.00 | 100.00 |
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|
(b) |
| Normalized overall amplitude | | | | |
| Zero level solution | 99.79 | 100.44 | 96.43 | 79.43 | 1st level solution | 100.03 | 100.03 | 100.00 | 100.00 | 2nd level solution | 100.00 | 100.00 | 100.00 | 100.00 |
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