Further Studies of the Dynamic Response of a Simply Supported Beam Excited by a Pair of Out-of-Phase Piezoelectric Actuators

Abstract

The response of a simply supported beam excited by a pair of out-of-phase piezoelectric actuators perfectly bonded to the beam surface, is modelled analytically and measured experimentally. The analytical model follows the approach of Pan et al. (1992) and corrects errors in that work. Other analytical models are reviewed and it is shown that two equivalent force transfer mechanisms, either two counteracting uniform surface strain distributions or two counteracting uniform moment distributions, can be used in the models to describe the beam response at resonance, for in this condition, the free edge condition of the piezoelectric actuator does not affect the strain field. The analysis shows that this current model agrees with other modelling approaches, but experiments show that away from resonance, significant differences in the beam response are found due to the influence of the free edge condition of the piezoelectric actuator. However, none of the previously published papers nor the model discussed in this paper account for the force transfer mechanism due to the free edge of the piezoelectric actuator. The modelling technique postulated in this paper however will readily lend itself to be used when a more accurate extensional strain model is available.

<title>Frequency response of beams with passively constrained damping layers and piezoactuators</title>

“…We calculate the frequency response function via two methods: (1) progressive wave method (Pines and von Flotow, 1990;Rivory, Hansen and Pan, 1994), and (2) assumed modes method. This is done primarily to establish notation and to provide a baseline beam with no viscoelastic core.…”

Optimal shape control of functionally graded smart plates using genetic algorithms

“…Most of the effort, however, has been directed towards the vibration control of structures. Examples of these include the exact analytical solution provided by Rivory et al (1994) for the dynamic response of a simply-supported beam excited by a pair of out of phase piezoelectric actuators, Chen et al (1996) for laminated cylindrical shells with piezoelectric layers, Reddy (1999) for Navier solution of laminated composite plates with integrated sensors and actuators. Various finite element models have been proposed by Allik and Hughes (1970), Tzou and Tseng (1990), Lammering (1991), Hwang et al (1993), Heyliger et al (1996), Chandrasekharaiah (1998), Liew et al (2001Liew et al ( , 2003 and He et al (2001) for dynamic analysis and control of more complicated structures, such as laminate beams, plates and shells with piezoelectric patches and functionally graded plates and shells subjected to thermal loading.…”

Dynamics and topology optimization of piezoelectric fans

“…Piezoelectric resonators are used as actuators (Pan et al [4], Rivory et al [5], Tiersten [6], Seeley and Chattopadhyay [7], Seshu & Naganathan [8]) and sensors (Lee and Saravanos [9], Aldraihem and Kheir [10], Main et al [11]) for a wide variety of applications including piezoelectric fans, optical beam choppers, ultrasonic motors, microelectromechanical density sensors, and resonating viscometers. For these applications, little seems to be known about an optimal actuator-beam configuration including patch location, actuator patch-to-beam length ratio, and patch-to-beam thickness ratio.…”

“…Analytical, experimental and computational investigations of the dynamic response of such structures are presented in Rivory et al [5], Tiersten [6], Barboni et al [17], Main et al [11], Lobontiu et al [18], Shen [19], Pan and Hansen [20], Abramovich [21], Crawley and de Luis [22], and Strambi et al [23]. Rivory et al [24] and Tiersten [6] present an analytical dynamical model.…”