Table 6 The first three dimensionless natural frequencies for the FGPM beam type "B"

Multilayered FGPM beam with simply supported boundary condition

 0

0.1201

0.4795

1.0760

 0.2

0.1177

0.4701

1.0550

 1

0.1141

0.4557

1.0225

 2

0.1129

0.4509

1.0118

 10

0.1107

0.4420

0.9919

Multilayered FGPM beam with clamped-free boundary condition

 0

0.0428

0.2677

0.7478

 0.2

0.0419

0.2625

0.7332

 1

0.0407

0.2544

0.7107

 2

0.0402

0.2518

0.7033

 10

0.0394

0.2468

0.6894

Multilayered FGPM beam with clamped–clamped boundary condition

 0

0.2721

0.7488

1.4638

 0.2

0.2668

0.7342

1.4352

 1

0.2586

0.7116

1.3912

 2

0.2559

0.7042

1.3767

 10

0.2509

0.6903

1.3494