In what follows, we will discuss the Modal Lumped Parameter Model of an ACLD System
Lumped parameter model of a simply supported beam of length ‘l’, having a two-layer ACLD
patch of length ‘la’ over it is shown in Fig. 13.2.
Figure 38.1: Modal lumped parameter of an ACLD system
Evidently, the beam is having three elements. The
host/base beam is considered as a SDOF spring-mass system, the viscoelastic layer as a complex spring
and the constraining layer as an additional spring – all of which are connected in series. Inertia
contribution of the viscoelastic and constraining layer can be neglected for this layers. The following additional
assumptions are present in this model:
- The externally applied force on the system and the excitation voltage applied by the active
constraining layer are harmonic and synchronous in nature – hence the model is valid only at
steady state of excitation.
- The strain on the surface of the host beam is uniform below the viscoelastic layer. This is
valid when the length of the ACLD patch is considerably smaller than the wavelengths of the
host beam.
- The host beam follows classical Euler-Bernoulli beam theory. The effect of shear deformation
etc. is neglected in this model.
- For the host beam only bending strain is considered; whereas, for the viscoelastic layer shear
strain and for the constraining layer extensional strain is considered.
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