Table 4 The fundamental frequency parameters of a (CS) beam on a variable foundation \(k_r^{2f*} = \eta (1 + \sin (\alpha x_r^*))\), analyzed for different values of \(\eta\), \(\chi\), and \(\alpha\).

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

\(\eta\)

\(\alpha\)

\(\chi = 0.1\)

\(\chi = 0.3\)

\(\chi = 0.5\)

\(\chi = 0.8\)

10

1

11.8304

11.8476

11.9900

12.3961

3

11.8304

11.8535

12.0486

12.5289

6

11.8304

11.8576

12.0118

12.1159

100

1

11.8312

11.9988

13.2767

16.6340

3

11.8314

12.0540

13.7435

17.5816

6

11.8316

12.0918

13.4395

14.3370

1000

1

11.8398

13.1581

19.5162

38.2187

3

11.8412

13.4814

20.6969

41.1130

6

11.8433

13.6745

19.6366

24.4428

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