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

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.

[1]  Carlos E. S. Cesnik,et al.  Local interaction simulation approach for modeling wave propagation in composite structures , 2013 .

[2]  Pier Paolo Delsanto,et al.  Connection Machine Simulation of Ultrasonic Wave Propagation: Two Dimensional Case , 1992 .

[3]  Klaus-Jürgen Bathe,et al.  A finite element method enriched for wave propagation problems , 2012 .

[4]  Gui-Rong Liu.  A combined finite element/strip element method for analyzing elastic wave scattering by cracks and inclusions in laminates , 2002 .

[5]  Marek Krawczuk,et al.  Spectral Finite Element Method , 2012 .

[6]  U Gabbert,et al.  Simulation of Lamb wave reflections at plate edges using the semi-analytical finite element method. , 2012, Ultrasonics.

[7]  R. S. Schechter,et al.  Connection Machine Simulation of the Ultrasonic Wave Propagation in Materials III: the 3-D case , 1997 .

[8]  Shaorong Xie,et al.  A review of non-contact micro- and nano-printing technologies , 2014 .

[9]  Srinivasan Gopalakrishnan,et al.  A spectrally formulated plate element for wave propagation analysis in anisotropic material , 2005 .

[10]  Samir Mustapha,et al.  Concise analysis of wave propagation using the spectral element method and identification of delamination in CF/EP composite beams , 2010 .

[11]  P. Delsanto,et al.  Connection machine simulation of ultrasonic wave propagation in materials. I: the one-dimensional case , 1997 .

[12]  Ivan Bartoli,et al.  The response of rectangular piezoelectric sensors to Rayleigh and Lamb ultrasonic waves , 2007 .

[13]  D. Roy Mahapatra,et al.  A spectral finite element model for analysis of axial–flexural–shear coupled wave propagation in laminated composite beams , 2003 .

[14]  V. Giurgiutiu.  Tuned Lamb Wave Excitation and Detection with Piezoelectric Wafer Active Sensors for Structural Health Monitoring , 2005 .

[15]  Carlos E. S. Cesnik,et al.  Finite-dimensional piezoelectric transducer modeling for guided wave based structural health monitoring , 2005 .

[16]  Bc Lee,et al.  Lamb wave propagation modelling for damage detection: II. Damage monitoring strategy , 2007 .

[17]  Keith Worden,et al.  New trends in vibration based structural health monitoring , 2011 .

[18]  Marek Krawczuk,et al.  Wave propagation modelling in 1D structures using spectral finite elements , 2007 .

[19]  Chee Kiong Soh,et al.  Electromechanical Impedance Modeling for Adhesively Bonded Piezo-Transducers , 2004 .

[20]  Jan Drewes Achenbach,et al.  Strip Element Method to Analyze Wave Scattering by Cracks in Anisotropic Laminated Plates , 1995 .

[21]  Marek Krawczuk,et al.  ANALYSIS OF LONGITUDINAL WAVE PROPAGATION IN A CRACKED ROD BY THE SPECTRAL ELEMENT METHOD , 2002 .

[22]  Marek Krawczuk,et al.  Modelling of wave propagation in composite plates using the time domain spectral element method , 2007 .

[23]  J. Sirohi,et al.  Fundamental Understanding of Piezoelectric Strain Sensors , 1999, Smart Structures.

[24]  Carlos E. S. Cesnik,et al.  Review of guided-wave structural health monitoring , 2007 .

[25]  Bc Lee,et al.  Lamb wave propagation modelling for damage detection: I. Two-dimensional analysis , 2007 .

[26]  Zhengjia He,et al.  Modeling of wave propagation in one-dimension structures using B-spline wavelet on interval finite element , 2012 .