PSI - Issue 12

A. Chiappa et al. / Procedia Structural Integrity 12 (2018) 353–369 Chiappa et al. / Structural Integrity Procedia 00 (2018) 000 – 000

360

8

a

b

c

Fig. 4. Results of the third set of simulations for the 2D bulk case: (a) COMSOL; (b) APDL; (c) FEMAP.

2.2. Guided waves propagation in a 2D domain

As reported in the introduction, the physics of UGW is definitely more complex than that of bulk waves. The velocities of UGW depend upon the geometry of the waveguide while several modes can be involved. Transmission of waves travelling in a thin plate of isotropic material, with stress-free boundaries under the assumption of plane strain is the classical problem of Lamb waves propagation. The well-known Rayleigh-Lamb solutions of Lamb waves can be found in Rose (2014):

    qh ph

tan tan

2 k pq

4

 

for the symmetric modes





2

2 q k 

2

(6)



 2

    qh ph

2 4 q k 2

2 k pq 

tan tan

 

for the anti-symmetric modes

where k is the wavenumber, 2h is the plate thickness.