Table 17 Variation of the First Three Modal Frequencies for a CF (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 CF Boundary Condition

\(\gamma\)

\(\chi\)

0.2

0.3

0.5

0.8

0.9

Mode 1

0.0

2.1057

2.1610

2.7471

5.1833

6.3565

0.2

1.9964

2.0434

2.5629

4.9843

6.2422

0.3

1.9212

1.9630

2.4361

4.8401

6.1483

0.4

1.8259

1.8616

2.2773

4.6592

6.0242

0.5

1.7026

1.7315

2.0775

4.4376

5.8673

0.6

1.5395

1.5607

1.8249

4.1748

5.6784

0.7

1.3179

1.3311

1.5048

3.8778

5.4654

0.8

1.0088

1.0146

1.0998

3.5671

5.2464

Mode 2

0.0

15.7970

15.9800

17.0030

17.8280

17.8470

0.2

14.2840

14.4820

15.7520

16.8930

16.9050

0.3

13.4980

13.7030

15.1340

16.4860

16.4970

0.4

12.6920

12.9060

14.5280

16.1410

16.1520

0.5

11.8700

12.0930

13.9430

15.8780

15.8910

0.6

11.0380

11.2710

13.3900

15.7250

15.7430

0.7

10.2130

10.4530

12.8770

15.7160

15.7430

0.8

9.4175

9.6605

12.3920

15.8880

15.9260

Mode 3

0.0

46.7020

46.8960

47.1350

47.3640

47.3760

0.2

43.5960

43.8180

44.1320

44.3920

44.4050

0.3

41.9270

42.1640

42.5320

42.8090

42.8230

0.4

40.1540

40.4080

40.8460

41.1420

41.1560

0.5

38.2490

38.5220

39.0530

39.3690

39.3840

0.6

36.1640

36.4600

37.1230

37.4580

37.4740

0.7

33.8260

34.1500

35.0110

35.3620

35.3780

0.8

31.0860

31.4470

32.6430

32.9950

33.0100

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