Condensed finite element scheme for symmetric multi-layer structures including dilatational motion

Abstract

Condensed models act as useful tools to reduce the computational time in the finite element simulations by describing the dynamic behaviour of the multi-layer structure with only one equivalent homogeneous layer. Many condensed plate models in the literature assume constant velocity through the thickness which allows only anti-symmetric motions like bending and shear, but do not include symmetric motions like dilatational or compressional behaviour. The recently developed condensed model by Marchetti et al. (2021) overcomes this setback by including the symmetric motion through three dynamic intrinsic parameters of the multi-layer structure: a dynamic bending stiffness and two dynamic mass densities. This paper presents a finite element scheme to compute vibro-acoustic quantities from the condensed layer with these three dynamic parameters. It is further showed that the proposed scheme has high computational gain over the conventional full three-dimensional finite element approach.