Formulas for Structural Dynamics: Tables, Graphs and Solutions

| First and second eigenfunctions | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| First Span | |||||||||
| | X 1 | X ? 1 | X ? 1 | X ? ? 1 | X 2 | X ? 2 | X ? 2 | X ? ? 2 | |
| 0 | 0 | 3.142 | 0 | ?31.02 | 0 | 4.038 | 0 | ?58.89 | 1 |
| 0.05 | 0.1565 | 3.103 | ?1.545 | ?30.64 | 0.2007 | 3.965 | ?2.925 | ?57.70 | 0.95 |
| 0.1 | 0.3091 | 2.988 | ?3.051 | ?29.50 | 0.3941 | 3.748 | ?5.731 | ?54.15 | 0.90 |
| 0.15 | 0.4540 | 2.799 | ?4.482 | ?27.64 | 0.5732 | 3.396 | ?8.303 | ?48.38 | 0.85 |
| 0.2 | 0.5879 | 2.542 | ?5.803 | ?25.09 | 0.7316 | 2.923 | ?10.54 | ?40.60 | 0.80 |
| 0.25 | 0.7072 | 2.222 | ?6.981 | ?21.93 | 0.8638 | 2.349 | ?12.33 | ?31.09 | 0.75 |
| 0.3 | 0.8091 | 1.846 | ?7.989 | ?18.23 | 0.9652 | 1.698 | ?13.62 | ?20.18 | 0.70 |
| 0.35 | 0.8911 | 1.426 | ?8.797 | ?14.08 | 1.0330 | 0.9967 | ?14.34 | ?8.268 | 0.65 |
| 0.4 | 0.9511 | 0.9704 | ?9.388 | ?9.58 | 1.0650 | 0.2748 | ?14.44 | 4.237 | 0.60 |
| 0.45 | 0.9877 | 0.4909 | ?9.751 | ?4.847 | 1.0600 | ?0.4366 | ?13.91 | 16.91 | 0.55 |
| 0.5 | 1 | 0 | ?9.872 | 0 | 1.0220 | ?1.106 | ?12.75 | 29.32 | 0.50 |
| 0.55 | 0.9877 | ?0.4909 | ?9.751 | 4.847 | 0.9511 | ?1.702 | ?10.99 | 41.08 | 0.45 |
| 0.6 | 0.9511 | ?0.9704 | ?9.388 | 9.580 | 0.8532 | ?2.195 | ?8.66 | 51.38 | 0.40 |
| 0.65 | 0.8911 | ?1.426 | ?8.797 | 14.08 | 0.7337 | ?2.559 | ?5.827 | 61.28 | 0.35 |
| 0.7 | 0.8091 | ?1.846 | ?7.989 | 18.23 | 0.5998 | ?2.770 | ?2.558 | 69.22 | 0.30 |
| 0.75 | 0.7072 | ?2.222 | ?6.981 | 21.93 |