Finite element modelling of hybrid active–passive vibration damping of multilayer piezoelectric sandwich beams—part II: System analysis

Abstract

SUMMARYAn electromechanically coupled ÿnite element model has been presented in Part 1 of this paper in order to handle active-passive damped multilayer sandwich beams, consisting of a viscoelastic core sandwiched between layered piezoelectric faces. Its validation is achieved, in the present part, through modal analysis comparisons with numerical and experimental results found in the literature. After its validation, the new ÿnite element is applied to the constrained optimal control of a sandwich cantilever beam with viscoelastic core through a pair of attached piezoelectric actuators. The hybrid damping performance of this ÿve-layer conÿguration is studied under viscoelastic layer thickness and actuator length variations. It is shown that hybrid active-passive damping allows to increase damping of some selected modes while preventing instability of uncontrolled ones and that modal damping distribution can be optimized by proper choice of the viscoelastic material thickness.

A computational framework for the analysis of linear piezoelectric beams using hp-FEM

“…In the case of quadratic electric potential distribution, a diagonal electric permittivity tensor and piezoelectric component P 133 ¼ 0, which is the case for a major class of piezoceramics [31] and, specifically, the ones used in piezoelectric beam literature [6,10,5,1,3,8,9,21], the three differential Eq. (57) take the form,…”

“…Along the same lines, Koutsawa [23] attempts to solve the problem of static piezoelectric beams by using higher order displacement theories for beams. This paper aims to present a simple three-dimensional finite element framework for linear piezoelectric beams, derived from first principles, in order to bridge the gap between existing simplified lumped or distributed parameter models [1,6,[8][9][10]12,13] and the most sophisticated nonlinear warping beam models [19][20][21][22][23]. In the process, interesting new physical magnitudes, such as the coupled shear or the coupled bending/torsional moment introduced as a result of an electric displacement, will naturally arise.…”

“…Some approaches can be found in the literature in the form of simplified single degree of freedom systems or two-dimensional beams, which are often referred to as lumped parameter and distributed parameter models, respectively [1,6,[8][9][10][11]. In the lumped parameter model, the piezoelectric device is constructed via a mass-spring-damper system coupled with a capacitor and a resistor [12,6,13].…”

“…One of the main simplifying assumptions in almost all of these approaches is that of vanishing electric field in certain directions, depending on the orientation of polarisation [6,3,8,9,4,10]. In piezoelectric beam literature, these are normally referred to as different modes of coupling and are denoted by d ij ; i; j ¼ 1 .…”

Structural vibration control using extension and shear active-passive piezoelectric networks including sensitivity to electrical uncertainties

“…Nevertheless, few studies focus on the optimization of this coupling for given structure and piezoelectric material. In particular, it has been shown that piezoelectric actuators using their thickness-shear mode can be more effective than surface-mounted extension piezoelectric actuators for both active Raja, Prathap and Sinha, 2002;Baillargeon and Vel, 2005;Trindade and Benjeddou, 2006) and passive (Benjeddou and Ranger-Vieillard, 2004;Benjeddou, 2007;Trindade and Maio, 2008) vibration damping. One of the reasons for that is the thicknessshear electromechanical coupling coefficient k 15 that is normally twice the value of the extension one, k 31 , which may lead to a higher effective electromechanical coupling coefficient (Trindade and Benjeddou, 2009).…”