A smart composite-piezoelectric one-dimensional finite element model for vibration damping analysis

Abstract

A one-dimensional finite element method for generally layered smart beams is presented in this paper. The model implements the first-order shear deformation beam theory and is based on the preliminary analytical condensation of the electric state to the mechanical state. This allows us to establish an effective mechanical beam kinematically equivalent to the original smart beam including the effects of electro-elastic couplings. The contributions of the external electric loads are included in both the equivalent stiffness properties and the equivalent mechanical boundary conditions. Hermite shape functions, which depend on parameters representative of the staking sequence through the equivalent electro-elastic stiffness coefficients, are used to formulate the finite element method. The state space representation is then invoked for the assembled smart beam finite element model to favor its implementation in a block diagram environment for multi-domain simulation. Validation results and solutions for passive and active vibrations damping system are presented last.