In this page, the following two condensed models are discussed:
$\bullet$ Sigmoid model - applicable to three-layer structure of isotropic layers:
(see Arasan U., Marchetti F., Chevillotte F., Jaouen L., Chronopoulos D. and Gourdon E., 2021, "A simple equivalent plate model for dynamic bending stiffness of three-layer sandwich panels with shearing core", Journal of Sound and Vibration, 500, p. 116025. published version or preprint version)
$\bullet$ New condensed model - applicable to symmetric multilayers:
(see Marchetti F., Arasan U., Chevillotte F. and Ege K., 2021, "On the condensation of thick symmetric multilayer panels including dilatational motion", Journal of Sound and Vibration, 502, p. 116078. published version or preprint version)
Plot: $D_\text{eq}$$\eta_\text{eq}$$k_\text{eq}$TL
Show condensed model:
Sigmoid model parameters:
$D_\mathrm{low}=$ N m; $D_\mathrm{high}=$ N m
$f_T=$ Hz; $R=$
$\bullet$ $D_\text{low}$ is mainly controlled by the skin properties and core thickness
$\bullet$ Young's modulus of the core $(E_c)$ influences the transition frequnecy $(f_T)$ strongly than other properties
$\bullet$ If the core is too soft (or has low value of Young's modulus $(E_c)$), the new condensed model shows good correspondance with the TMM (in TL computations),
whereas the Sigmoid model shows good correspondance only at mass-law region
$\bullet$ If $E_c$ is increased, then the sigmoid model shows good correspondance with the new condensed model as well as with the TMM. This is because
the anti-symmetric motions (such as bending, shear) controlls the motion of the structure as the core becomes harder, for which the Sigmoid model is sufficent