Research Article

Free Transverse Vibration Analysis of Axially Functionally Graded Tapered Euler-Bernoulli Beams through Spline Finite Point Method

Table 9

Nondimensional fundamental natural transverse frequencies for axially FG beams with respect to the gradient index.

P-PC-CC-PC-F
Case  1Case  2Case  1Case  2Case  1Case  2Case  1Case  2

−10Reference [14]11.45329.935824.057624.794916.477517.29933.56564.1800
SFPM11.45609.936624.066024.806816.411117.30373.53404.1801

−3Reference [14]11.244310.366923.945624.937516.030717.87013.14214.8317
SFPM11.244310.366923.944624.936616.026217.87013.14104.8317

0Reference [14]10.866310.866324.375224.375215.873417.91472.92565.0156
SFPM10.866410.866424.375624.375615.873517.91482.92565.0156

3Reference [14]10.366911.244324.937523.945615.717117.88672.85444.8466
SFPM10.366911.244324.936623.944615.716917.88742.85454.8466

10Reference [14]9.935811.453224.794923.945615.493017.90503.04314.4629
SFPM9.936611.456024.806824.066015.495817.91553.04314.4629