Table 2 Comparison of the fundamental frequency parameters of a (SS) beam partially resting on a variable foundation, described by \(k_r^{2f*} = \eta (1 + \sin (\alpha x_r^*))\), for various values of \(\alpha\) and \(\chi\), with \(\eta = 100\).

From: A discrete model for analyzing the free vibrations of a non-uniform 2D-FGM beam under elastic foundations and different support conditions

\(\alpha\)

\(\chi = 0.3\)

\(\chi = 0.7\)

\(\chi = 0.4\)

24

Present Study

24

Present Study

Present Study

1

8.142

8.136

12.99

13.012

9.154

3

8.397

8.404

14.28

14.303

9.714

6

8.586

8.596

11.98

11.949

9.820