Research Article
Free Transverse Vibration Analysis of Axially Functionally Graded Tapered Euler-Bernoulli Beams through Spline Finite Point Method
Table 3
Nondimensional transverse natural frequencies
for tapered homogenous beam; boundary condition: C-F.
| | | , | | | | | | | | | |
| | 0.2 | SFPM | 3.6083 | 20.6212 | 56.1954 | 3.8551 | 21.0569 | 56.6335 | | Reference [4] | 3.6083 | 20.621 | 56.1923 | 3.8551 | 21.0567 |
56.6303 | | FEM | 3.6113 | 20.5759 | 55.8008 | 3.8580 | 21.0108 | 56.2356 |
| | 0.4 | SFPM | 3.7371 | 19.114 | 50.3567 | 4.31878 | 20.0501 | 51.3378 | | Reference [4] | 3.7371 | 19.1138 | 50.3537 | 4.3188 | 20.05 | 51.3346 | | FEM | 3.7398 | 19.0857 | 50.0932 | 4.3213 | 20.0187 | 51.0670 |
| | 0.6 | SFPM | 3.93428 | 17.488 | 44.0279 | 5.00904 | 19.0651 | 45.7417 | | Reference [4] | 3.9343 | 17.4879 | 44.0248 | 5.009 | 19.0649 | 45.7384 | | FEM | 3.9366 | 17.4717 | 43.8706 | 5.0110 | 19.0463 | 45.5747 |
| | 0.8 | SFPM | 4.2925 | 15.7429 | 36.8881 | 6.19639 | 18.3858 | 39.8376 | | Reference [4] | 4.2925 | 15.7427 | 36.8852 | 6.1964 | 18.3855 | 39.8339 | | FEM | 4.2946 | 15.7366 | 36.8135 | 6.1978 | 18.3751 | 39.7517 |
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