smart technologies for safety engineering

Smart Technologies in Vibroacoustics 315
(a) plate and total
displacements
Deformations and amplitude of vertical displacements:
(b) plate and solid
phase
(c) fluid phase and
acoustic medium
Figure 8.14 Passive reduction of vibroacoustic transmission ( f = 1610 Hz)
in the acoustic waveguide is almost 2.6 × 10 −6 m, whereas the maximal deflection of the elastic
plate is much less and reaches 8 × 10 −8 m. Notice also that the vibrations of the solid phase
of the poroelastic layer are in antiphase to the wave propagating in the fluid phase (or in the
air in the pores). The incident acoustic wave of this frequency is very poorly transmitted by
the panel: its energy is dissipated by the poroelastic layer.
8.10.5 Test of Active Behavior of the Panel
The purpose of the test of active behavior of the panel is to determine the voltage excitation
necessary for active reduction of vibroacoustic transmission and to check how it works by
performing the vibroacoustic analysis with control. Harmonic steady-state analysis will be
used for the test. However, since the problem is perfectly linear, the results obtained for
different frequencies can be superposed. In practice, transient or multifrequency vibrations
can be controlled by applying an appropriate signal to the piezoelectric actuator. Nevertheless,
single frequency signals may also be used to control some predominant spectral components
of vibrations.
Remember that the complete system considered here is composed of the active elasto–
poroelastic panel and the waveguide of the acoustic medium. A plane (harmonic) acoustic wave
propagates in the waveguide on to the poroelastic layer of the single-plate panel. The wave
may be attenuated by the dissipative poroelastic layer, and partially reflected and transmitted
through the panel. It has been shown in the previous section that for higher frequencies,
the passive reduction of vibroacoustic transmission by poroelastic material is sufficient: the
coupled resonance and the plate resonance around the higher eigenfrequency are well damped
(see Figure 8.13). Nevertheless, the resonance vibrations at the first eigenfrequency of the plate
are not attenuated and an active treatment must be applied with the use of the piezoelectric
actuator.