Dynamics of Structures with Piezoelectric Sensors and Actuators for Structural Health Monitoring

The dynamic analysis of structures with piezoelectric sensors and actuators is used in this paper to establish a method for crack detection in aerospace structures. Piezoelectric strips used as sensors and actuators are bonded on both sides of a thin structure which executes flexural oscillations. The differential voltage outputs of the piezoelectric sensors are used to detect the presence of cracks in the structure. The structural analysis uses a finite element formulation for the piezoelectric strips coupled with the structure and a nonlinear model for the cracks. This paper presents first the results of the dynamic analysis in the frequency domain of healthy and cracked plates undergoing forced flexural vibrations generated by a pair of piezoelectric actuators submitted to an oscillatory voltage excitation. The peaks in the differential voltage output obtained in the case of a cracked plate at several frequencies during the frequency sweep were found to be indicative measures for the presence of a crack in the structure. The results of the dynamic analysis in the time domain have also shown that this method has a good sensitivity in detecting cracks in the structures. Introduction Structural damage detection at the earliest possible stage is very important in the aerospace industry to prevent major failures and for this reason it has recently attracted a topical research interest. Many authors, such as Giurgiutiu & Rogers [1], Kwan et al. [2], Liu et al. [3], Rees et al. [4], Zagrai & Giurgiutiu [5] and others presented ingenious methods for crack detection in structures, many of them using piezoelectric sensors and actuators. Piezoelectric strip actuators bonded on both sides of a delta wing have also been used for the active control of the aeroelastic oscillations by two of the present authors and their graduate student [6]. Later, Yang et al. [7] and others studied the vibration control of beam structures using piezoelectric actuators. The aim of this paper is to present a method of detection of cracks in structures executing flexural oscillations by using piezoelectric sensors and actuators bonded to these structures. This work is a part of a cooperative effort to develop smart technologies for structural health monitoring of aerospace structures, which included the development of modeling tools simulating the effect of cracks on the dynamic behavior of structures at low and medium frequencies, and of several damage detection strategies based on modal analysis, time-frequency approach and flexural wave propagation analysis using piezoelectric sensors and actuators and shape-memory alloys [8-9]. Crack detection strategy The detection strategy used in this study is based on the observation that the strain changes caused by cracks in the structure are relatively small, and the resulting variations of the voltage output of the piezoelectric sensors (which are proportional to the strain changes) are difficult to be measured, especially when the sensor is not very close to the crack. For this reason, in this detection strategy two piezoelectric sensors are glued on the opposite sides of a bending structure and their voltage outputs are conveniently subtracted in order to eliminate the voltage corresponding to the same level of strain on both sides. If there is a crack, the strains on the two sides of the structure will be different, and hence the induced voltage generated in the piezoelectric strips will also be different. By conveniently measuring the voltage difference between the two piezoelectric strip sensors, the presence of cracks can be predicted. Key Engineering Materials Vol. 347 (2007) pp 493-498 online at http://www.scientific.net © (2007) Trans Tech Publications, Switzerland Online available since 2007/Sep/15 All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of the publisher: Trans Tech Publications Ltd, Switzerland, www.ttp.net. (ID: 130.203.133.34-16/04/08,10:07:55) The strain changes due to the presence of cracks were found to be small when the structure is subjected only to static loads, and thus the sensor sensitivity is restricted only to very small distances from the crack. For this reason, in the proposed approach, the thin structure executes flexural oscillations produced for example by piezoelectric actuators bonded on the opposite structure sides, which are submitted to oscillatory voltage excitations, or by unsteady aerodynamic loads acting on wing structures, which occur naturally in many flight evolutions of airplanes. During the cycle of the flexural oscillations, the crack is closed when there is a local compression, and then it opens during the extension portion of the cycle. Due to this nonlinear mechanical behavior of the crack, the differential strain changes measured by a pair of piezoelectric sensors bonded on the opposite sides of the structure are much larger than in the case of static loads, increasing thus substantially the sensitivity of this detection procedure. Finite element model used for structures with cracks and with bonded piezoelectric strips Piezoelectric materials are used to convert the mechanical displacement into an electrical field (voltage potential), in which case the piezoelectric material acts as a sensor, or vice versa when it acts as an actuator. Mathematically, piezoelectricity is described using the well known constitutive equations of the piezoelectric material [10], which define the interaction between the stress, strain, charge-displacement, and electric field in the form } ’ ] _} ’ ] _ } ’ E d T s S T E ? , } ’ ] _} ’ ] _} ’ E T d D T g ? , (1) where , , and } are the strain, stress, electric field and electric flux density vectors, respectively, and ] _, } ’ S } ’ T } ’ E ’ D E s ] _ d and ] _ T g are the compliance, piezoelectric coupling and dielectric matrices, and where the superscript T denotes the transposed matrix. Consider a thin piezoelectric strip of width and length ) (x bp 1 2 x x l p / ? , as shown in Fig. 1, which is bonded on the upper (or lower) surface of a beam (or plate) of height , and denote by the flexural displacement of the beam. The contact between the piezoelectric strips and the surface of the structure is assumed to be ideal. h 2 * t x w , + Figure 1. Piezoelectric strip bonded on a beam. If the electrical field is zero, the piezoelectric strip can be used as a sensor, in which case the output voltage out h can be expressed, if the strip width is constant, in the form [10] p b * + dx w x b h d E R t x x p p f out % | | ? h Ð ) ( 2 1 31 μ * + ] _ ) ( ' ) ( ' 1 2 31 x w x w b h d E R t p p f out % % / ? h , (2) where is the Young elasticity modulus of the piezoelectric material, is the piezoelectric constant, is an amplifier constant, and where p E 31 d f R * + ] _ 1 1 x x x w x w ? • • ? | and * + * + dt x w d x w 1 1 | ? | % . The dynamic analysis of the structure with piezoelectric strips is performed in this study using a finite element formulation (which is not presented here due to the space limitation). The numerical results presented further are obtained using the ANSYS finite element program [11]. In this study, the 8-node element SOLID5 is used to model the piezoelectric strips, and the three-dimensional element SOLID45 is used to model the structure. 494 Damage Assessment of Structures VII