Table 5 The first three dimensionless natural frequencies for the FGPM beam type “A”

Multilayered FGPM beam with simply supported boundary condition

 0

0.1179

0.4711

1.0576

 0.2

0.1156

0.4618

1.0368

 1

0.1121

0.4476

1.0048

 2

0.1108

0.4427

0.9940

 10

0.1085

0.4332

0.9726

Multilayered FGPM beam with clamped-free boundary condition

 0

0.0420

0.2630

0.7349

 0.2

0.0412

0.2578

0.7204

 1

0.0399

0.2499

0.6981

 2

0.0395

0.2472

0.6906

 10

0.0387

0.2419

0.6758

Multilayered FGPM beam with clamped–clamped boundary condition

 0

0.2673

0.7356

1.4380

 0.2

0.2621

0.7213

1.4097

 1

0.2540

0.6991

1.3661

 2

0.2513

0.6916

1.3514

 10

0.2459

0.6767

1.3224