Effects of piezoelectric sensor/actuator debonding on vibration control of smart beams

Abstract

In vibration control of smart structures, piezoelectric sensors/actuators are usually bonded to the surface of a host structure. Debonding may occur between the piezoelectric sensors/actuators and the host structure, and it may decrease the control efficiency of vibration suppression or even lead to an unstable closed loop control system. This paper investigates the effect of the debonding on vibration control of beams with piezoelectric sensors and actuators. Presented is a novel model, which takes into account both flexural and longitudinal displacements of the host beam and piezoelectric layers as well as the peel and shear strains of the adhesive layer. Both collocated and non-collocated control schemes are used to study the effects of sensor or actuator debonding on active vibration control of smart beams.

Introduction

Vibration control of flexible structures by distributed piezoelectric sensors and actuators has been widely studied in the past decade and more dimensions are introduced to improve control of structural behavior (See e.g. Baz and Poh, 1988; Im and Atluri, 1989; Shi and Atluri, 1990; Lee and Moon, 1990; Tzou and Anderson, 1992; Chandrashekhara and Agarwal, 1993; Gu et al., 1994; Crawley, 1994; Sun et al., 1999; Chee et al., 1998; Sun and Tong, 2001a, Sun, 2001b). As one of the most widely used smart materials, piezoelectric materials are usually surface bonded on or embedded into the host structures as distributed sensors and actuators. In most of the previous studies, it is assumed that piezoelectric actuators and sensors are perfectly bonded to the host structures. However, debonding between the piezoelectric layers and the host structures may occur during its service life. For example, high peel stresses may be created around the periphery of an actuator layer. This is particularly true when single crystal layers are used as actuators due to its extremely high breakdown voltage. When a full range of an electric filed is applied to a single crystal layer, high peel stresses may be developed even for a very thin layer. As a result of debonding, dynamic characteristics of an open loop system, the sensing and actuating behaviors of a sensor and actuator may be changed, and the properties of a closed loop system may be affected severely or even destabilized. Therefore investigating the effects of partial debonding of the piezoelectric actuator/sensor patches on active control of smart structures is of significant importance in addressing damage tolerance issues of smart structures.

A significant amount of studies have been conducted on modeling of delamination of composite structures. Delamination detection of the composite structures by using perfectly bonded/embedded piezoelectric sensor layer and actuator layer structures has also attracted increasingly attention in recent years. However, there exists a relatively less literature on modeling and control of flexible structures with partially debonded piezoelectric sensors and actuators. Seeley and Chattopadhyay (1999) developed a finite element model for the structures including actuator debonding based on a refined high order theory (HOT). In this model, the displacement continuity in the interface between the debonded and non-debonded areas is imposed and implemented using a penalty approach. They also conducted experimental investigation on vibration control of a composite beam with debonded piezoelectric actuator (Seeley and Chattopadhyay, 1998), and found that the debonding length is a critical factor to the closed-loop control. For the static case, Wang and Meguid (2000) analytically examined the static effect of the partial debonding of the actuator from the host structures under plane strain assumption.

To better understand the effect of debonding of the piezoelectric sensor/actuator on closed-loop vibration control of a beam, an analytical model of the beam with piezoelectric sensor and actuator layer including debonding is presented in this paper. In this model, both longitudinal and transverse vibrations are considered using classical beam theory. Taking the displacements and their corresponding internal forces as the state variables, a numerical approach based on the multiple shooting method is employed to solve the equations, and the continuity of displacements and the internal forces at the interfaces between the debonded and non-debonded areas can be ensured. Using this model, examined are the debonding effects on closed-loop vibration control of smart beams using two kinds of control laws.