Active Control of Multiferroic Composite Shells Using 1-3 Piezoelectric Composites

This article deals with the analysis of active constrained layer damping (ACLD) of smart multiferroic or magnetoelectro-elastic doubly curved shells. The kinematics of deformations of the multiferroic doubly curved shell is described by a layer-wise shear deformation theory. A three-dimensional finite element model of multiferroic shells has been developed taking into account the electro-elastic and magneto-elastic couplings. A simple velocity feedback control law is employed to incorporate the active damping. Influence of layer stacking sequence and boundary conditions on the response of the multiferroic doubly curved shell has been studied. In addition, for the different orientation of the fibers of the constraining layer, the performance of the ACLD treatment has been studied. Keywords—Active constrained layer damping, doubly curved shells, magneto-electro-elastic, multiferroic composite, smart structures. I.INTRODUCTION TRUCTURES integrated with piezoelectric sensors and actuators possess self-sensing, self-monitoring, and diagnosing capabilities are commonly known as smart structures. It is evident from the open literature that the piezoelectric materials are the best smart materials for the active control of high-performance light weight flexible structures [1]-[4]. In order to achieve better performance from the piezoelectric materials of low control authority, they are being used as the constraining layer of the ACLD treatment rather than directly bonded to the substrates. Furthermore, the ACLD treatment can also be used as passive constrained layer damping (PCLD) by deactivating the applied control voltages [5]. Thus, the ACLD treatment has been established as an efficient smartness element providing both passive and active damping simultaneously when under operation [6]-[10]. A unique and interesting class of multiphase composites such as multiferroic or magnetoelectroelastic (MEE) composite consisting of ferroelectric/piezoelectric (BaTiO3) and ferromagnetic/ piezomagnetic (CoFe2O4) phases has attracted the interest of researchers over the last few years on account of promising properties of multiferroic composite materials. Multiphase composite structures made of ferroelectric and ferromagnetic layers are subjected to the actions of electro-elastic, magneto-elastic, and electromagnetic coupled fields, which are absent in the individual constituents. The unique property of MEE materials is that they have the ability to covert energy among magnetic, S. C. Kattimani is with the National Institute of Technology Karnataka, Surathkal-575025, India (phone: +91 824 2473661; +91 9481413661; e-mail: sck@ nitk.ac.in). electric and mechanical energies [11]-[16]. These interesting properties attracted the researchers to use the multiferroic materials in the fields of sensors, actuators, transducers, space structures, sonar applications. Most recently, Xin and Hu [17] studied the free vibration of simply supported multilayered MEE plates using the discrete singular convolution algorithm and state space approach. Gou et al. [18] investigated the static deformation of anisotropic four layered MEE plates under surface loading based on the modified couple-stress theory. Liu et al. [19] determined the high order solutions for MEE plates with non-uniform materials. Zhou and Zhu [20] used the third order shear deformation theory to study the vibration and bending analysis of multiferroic plates. Further, nonlinear analysis of MEE plates has attracted the interest of researchers considerably. Chen and Yu [21] developed the geometrically nonlinear multiphysics plate model and analyzed the MEE laminated composites by applying the variational asymptotic method. Shooshtari and Razavi [22] used thin plate theory to investigate a nonlinear free and forced vibration of transversely isotropic rectangular MEE thin plate. Farajpour et al. [23] investigated the nonlinear free vibration of size dependent MEE nanoplates subjected to external electric and magnetic potentials by considering the geometrical nonlinearity. Since the MEE shell can be a promising smart composite structure and is composed of smart materials, the necessity of using the additional means of smart damping such as the ACLD treatment for the active control of the multiferroic/MEE shell must be investigated. However, to the authors’ best knowledge, the research concerning the control of multiferroic shell is not yet reported. In this paper, threedimensional analysis of the ACLD of the multiferroic doubly curved shells integrated with the patches of the ACLD treatment has been carried out by the finite element method to investigate the active control vibrations. The effects of various parameters such as the effect of coupling coefficients, boundary conditions, aspect ratio and the variation of the piezoelectric fiber orientation angle in the 1-3 PZC constraining layer on the response of the multiferroic doubly curved shells have been thoroughly investigated. II.PROBLEM DESCRIPTION A schematic diagram of a multiferroic doubly curved shell with the ACLD patch at the center of the top surface of the shell is illustrated in Fig. 1 [5]. It may be noted that the results are also obtained by placing two patches of same volume at the edges of the top surface of the shell. The middle layer of the multiferroic shell is made of ferromagnetic Active Control of Multiferroic Composite Shells Using 1-3 Piezoelectric Composites