Table 14 Variation of the First Three Modal Frequencies for a SS (2D-FGM) Beam with Changes in \(\chi\) and \(\gamma\), \(n_x = 3\), \(n_y = 4\), \(\eta = 100\), and \(n = 2\).

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

Frequencies for Different Modes under (SS) Boundary Condition

\(\gamma\)

\(\chi\)

0.2

0.3

0.5

0.8

0.9

Mode 1

0.0

7.7193

8.2097

9.9405

11.666

11.782

0.2

6.8712

7.4461

9.5287

11.559

11.686

0.3

6.3957

7.0263

9.3319

11.548

11.682

0.4

5.8780

6.5778

9.1472

11.578

11.719

0.5

5.3105

6.0989

8.9816

11.662

11.812

0.6

4.6848

5.5906

8.8434

11.818

11.978

0.7

3.9940

5.0611

8.7406

12.070

12.242

0.8

3.2435

4.5384

8.6679

12.446

12.634

Mode 2

0.0

30.514

30.800

31.062

31.409

31.513

0.2

28.618

28.945

29.274

29.663

29.771

0.3

27.566

27.918

28.292

28.707

28.817

0.4

26.424

26.805

27.237

27.681

27.793

0.5

25.167

25.582

26.091

26.568

26.682

0.6

23.756

24.213

24.829

25.342

25.459

0.7

22.127

22.636

23.411

23.963

24.082

0.8

20.147

20.725

21.764

22.354

22.474

Mode 3

0.0

68.359

68.419

68.549

68.691

68.754

0.2

63.530

63.599

63.777

63.962

64.028

0.3

61.082

61.156

61.368

61.583

61.651

0.4

58.617

58.696

58.955

59.208

59.277

0.5

56.149

56.234

56.558

56.863

56.932

0.6

53.705

53.796

54.214

54.591

54.661

0.7

51.347

51.444

52.007

52.489

52.558

0.8

49.221

49.323

50.130

50.780

50.845

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