Table 7 The first three dimensionless natural frequencies for the FGPM beam type “C”

Multilayered FGPM beam with simply supported boundary condition

 0

0.1158

0.4627

1.0388

 0.2

0.1134

0.4530

1.0169

 1

0.109

0.4380

0.9833

 2

0.1084

0.4330

0.9722

 10

0.1061

0.4237

0.9513

Multilayered FGPM beam with clamped-free boundary condition

 0

0.0413

0.2583

0.7218

 0.2

0.0404

0.2529

0.7066

 1

0.0391

0.2445

0.6832

 2

0.0386

0.2418

0.6755

 10

0.0378

0.2366

0.6610

Multilayered FGPM beam with clamped–clamped boundary condition

 0

0.2626

0.7227

1.4138

 0.2

0.2571

0.7075

1.3841

 1

0.2486

0.6842

1.3386

 2

0.2458

0.6765

1.3235

 10

0.2405

0.6619

1.2948