Finite element modeling of sandwich structures with viscoelastic core

The present study emerges from the need for reduction of noise and vibrations in almost all industrial fields and the need for an accurate and reliable low-cost numerical model capable of predicting the vibro-acoustic response of structures containing viscoelastic materials. Indeed, the use of steel/viscoelastic/steel sandwich panels has motivated the development of accurate prediction methods for their vibration and acoustic indicators. Moreover, such theories may support the development of new damping materials while prioritizing strategies for low cost and weight and maintaining component rigidity and feasibility.A new sandwich finite element is presented for the specific case of unsymmetrical three-layered damped sandwich beam with internal viscoelastic damping. The model is based on a discrete displacement approach and accounts for the curvature effect. The element uses C° continuous linear and cubic polynomials to interpolate the in-plane and transverse displacement fields, respectively. The rotational influence of the transversal shearing in the core on the skins' behaviours ensures displacement consistency over the interfaces between the viscoelastic core and the elastic skins, resulting in accurate representations of the physics. To take the frequency dependence into account, viscoelastic models such as ADF, GHM and MSE models are implemented. The element is extended to the vibration of unsymmetrical damped sandwich plates. Two efficient finite element sandwich plates are developed refined rectangular and triangular elements having four and three-corner nodes, respectively. Each node of both elements contains seven degrees of freedom. To allow for analysis with arbitrary orientation in three-dimensional space, two drilling degrees of freedom are added. A formulation with nine degrees of freedom per node is thus employed. The present sandwich element is easy to interface with classical elements. The element is fully validated through both experimental tests and classical 3D FE modeling to prove its accuracy and computational efficiency. The tests consist of various configurations of sandwich panels in a coupled and uncoupled plate-cavity system. A parametric study is finally presented to highlight the effects of skin and core properties on the vibration and radiation of such structures under both airborne and structure-borne excitations. Finally, to illustrate practical use of the element, NVH simulations were conducted on laminated steel panels with added sound packages and compared to steel panels.