A FEM piezoelectric beam model for damping circuit analysis

A finite element, developed for straight generally layered smart beam, is used to investigate vibration damping capability of circuit elements. First, the electric state is analytically condensed to kinematical quantities and the mechanical model is then written for shear deformable Timoshenko’s beam including the effects of electro-elastic couplings stacking sequence. The contributions of the external electric loads on both the equivalent stiffness properties and the equivalent mechanical boundary conditions are also taken into account. The finite element is formulated by using Hermite shape functions, which depend on parameters representative of the staking sequence through the equivalent electro-elastic stiffness coefficients. It is found that the electric boundary conditions are transferred to the FEM representation as nodal work-equivalent axial forces and bending moments. The State Space representation is then invoked for the assembled smart beam FEM model to favour its implementation in block diagram environment for multidomain simulation. The damping capability of some circuitry arrangements are analysed to show the versatility of the proposed model.