smart technologies for safety engineering

Smart Technologies in Vibroacoustics 307
Figure 8.8 Dimensions of the system composed of a cell of the active elasto–poroelastic panel and
acoustic medium waveguide, and the finite element mesh of the 1/8-slice model (a different brick element
mesh was used for the full model of a system composed of the elastic plate and the 50 mm long acoustic
waveguide; see, for example, Figure 8.9(d) below)
the poroelastic layer is coupled to a fragment of acoustic medium (air waveguide), which is
subjected to an acoustic pressure excitation and transfers this excitation on to the panel. The
assembly of the panel, as well as the finite element mesh of a modeled fragment of the system
composed of the panel and the waveguide, are presented in Figure 8.8. Only a slice of the
whole assembly is modeled after giving proper consideration to all possible symmetries.
The in-plane dimensions of the cell of the panel are 80 mm × 80 mm and the total thickness
is 12.8 mm, where 0.8 mm is the thickness of the plate and 12 mm stands for the thickness of the
poroelastic layer (see Figure 8.8). The plate of the panel cell is simply-supported. The elastic
material of the plate is aluminum (Ee = 70 × 10 9 N/m 2 , νe = 0.33 and ϱe = 2700 kg/m 3 ) and
the poroelastic layer is made of a polyurethane foam with material properties given in Table 8.1
(foam A). The pores are filled with air. Table 8.2 gives all the necessary data for the air as the
interstitial fluid and thus completes the material data for the elastic foam with air in the pores.
The acoustic medium is a 80 mm × 80 mm × 38 mm waveguide of the air (the relevant material
properties are in the upper part of Table 8.2). In the cases examined below, where only the
aluminum plate or layer is analysed (i.e. with no poroelastic layer), the length of the acoustic
waveguide is augmented by the thickness of the poroelastic layer and amounts to 50 mm.
In the complete assembly of the panel, piezoelectric transducers (0.5 mm thick) are glued
to the upper surface of the elastic plate. They are through-thickness polarized so they stretch
significantly in their plane when a voltage is applied to the electrodes, in this way inducing
a bending deformation of the plate. The material of piezoelectric wafers is the transversely
isotropic PZT4 ceramic, with data presented in Table 8.3. The material constants are given
according to the contracted notation used in Section 8.4.3.