Formulation of 36-noded piezoelectric spectral finite element scheme with active/passive layers coupled by Lagrange multipliers

Abstract

A novel spectral finite element formulation scheme is presented for modeling a plate structure with surface-mounted piezoelectric transducers. Surface-mounted piezoelectric transducers may asymmetrically distribute the mass in the thickness direction of the plate/panel structure, resulting in a coupled mass matrix in spectral element formulation. A new procedure is developed by equating the layer-wise kinematics of the element using undetermined Lagrange multipliers to achieve the diagonal mass matrix. To demonstrate the effectiveness of the element formulation scheme, a two-dimensional piezoelectric spectral element is constructed with 36 nodes and five active/passive layers (layers: transducer/bond/plate/bond/transducer). The performance of the developed element is illustrated by (a) simulation of Lamb wave propagation and estimation of its velocity, and (b) simulation of the effect of transducer size, its dynamics and shear lag on sensor’s response. The results presented highlight the importance of modeling the dynamics of transducers and understanding the effects on sensor response. The presented technique has relevance in the field of structural health monitoring, wherein it can be used to model and simulate aircraft panels with surface-mounted piezoelectric transducers.