Finite element modelling of beams with arbitrary active constrained layer damping treatments

TLDR: In this article, a generic analytical formulation that can describe these hybrid couplings in an accurate and consistent way was developed, which considers a partial layerwise theory, with an arbitrary number of layers, both viscoelastic and piezoelectric, attached to both surfaces of the beam.

Abstract: This paper concerns arbitrary active constrained layer damping (ACLD) treatments applied to beams. In order to suppress vibration, hybrid active-passive treatments composed of piezoelectric and viscoelastic layers are mounted on the substrate beam structure. These treatments combine the high capacity of passive viscoelastic materials to dissipate vibrational energy at high frequencies with the active capacity of piezoelectric materials at low frequencies. The aim of this research is the development of a generic analytical formulation that can describe these hybrid couplings in an accurate and consistent way. The analytical formulation considers a partial layerwise theory, with an arbitrary number of layers, both viscoelastic and piezoelectric, attached to both surfaces of the beam. A fully coupled electro-mechanical theory for modelling the piezoelectric layers is considered. The equations of motion, electric charge equilibrium and boundary conditions are presented. A one-dimensional finite element (FE) model is developed, with the nodal degrees of freedom being the axial and transverse displacements and the rotation of the centreline of the host beam, the rotations of the individual layers and the electric potentials of each piezoelectric layer. The damping behavior of the viscoelastic layers is modeled by the complex modulus approach. Three frequency response functions were measured experimentally and evaluated numerically: acceleration per unit force, acceleration per unit voltage into the piezoelectric actuator and induced voltage per unit force. The numerical results are presented and compared with experimental results to validate the FE model.