Abstract—In modern engineering, weight optimization has a priority during the design of structures. However, optimizing the weight can result in lower stiffness and less internal damping, causing the structure to become excessively prone to vibration. To overcome this problem, active or smart materials are implemented. The coupled electromechanical properties of smart materials, used in the form of piezoelectric ceramics in this work, make these materials well-suited for being implemented as distributed sensors and actuators to control the structural response. The smart structure proposed in this paper is composed of a cantilevered steel beam, an adhesive or bonding layer, and a piezoelectric actuator. The static deflection of the structure is derived as function of the piezoelectric voltage, and the outcome is compared to theoretical and experimental results from literature. The relation between the voltage and the piezoelectric moment at both ends of the actuator is also investigated and a reduced finite element model of the smart structure is created and verified. Finally, a linear controller is implemented and its ability to attenuate the vibration due to the first natural frequency is demonstrated. Keywords—Active linear control, Lyapunov stability theorem, piezoelectricity, smart structure, static deflection. I. INTRODUCTION smart structure is a structure that can sense external disturbances or oscillations and respond to that with active control in real time to maintain the requested requirements. Smart structures consist of highly distributed active devices which are primarily sensors and actuators either embedded or attached to an existing passive structure. As for sensors, mechanically induced deformations can be determined by measuring the induced electrical potential, whereas deformation or strains can be controlled through the introduction of an appropriate electric potential in actuator applications [1]. Recent innovations in piezoelectric materials and developments in control theory have made it possible to control the dynamics of these structures, and have led to an extensive amount of research activity in this field [2]. The work presented in this paper can be classified into three parts. In the first part, the electromechanical behavior of the smart structure is statically investigated, and the relation between deflection and applied voltage is derived. In the second part, the piezoactuator is modeled and the relationship N. H. Ghareeb is with the Mechanical Engineering Department of the Australian College of Kuwait, Mishrif, Kuwait (phone: +965-2537-6111, Ext: 4292; fax: +965-2537-6222; e-mail: n.ghareeb@ack.edu.kw). S. M. Soleimani is with the Civil Engineering Department of the Australian College of Kuwait, Mishrif, Kuwait (e-mail: s.soleimani@ack.edu.kw). M. S. Gaith is with the Mechanical Engineering Department of the Australian College of Kuwait, Mishrif, Kuwait (e-mail: m.gaith@ack.edu.kw). between the applied voltage and moment at its ends is investigated. The structural analytical model is then produced by using the finite element (FE) method, and the number of elements and nodes of the FE model is reduced by using the super element (SE) technique. Finally, a linear active controller based on the Lyapunov stability theorem is implemented, and the ability of the controller to attenuate the vibration of the smart structure once excited with its first eigenfrequency is demonstrated. II. THEORETICAL ANALYSIS A. Modeling of Static Deflection of the Smart Structure As previously mentioned, the smart structure used in this work is composed of a cantilevered steel beam, a bonding layer (adhesive) and a piezoelectric actuator. A similar work with only two layers of the smart beam is presented in [3]. A schematic of the cross section with the piezoelectric patch is shown in Fig. 1. The curvature δ″ can be expressed as [4]: b na t Z EI M      ' ' (1) where, E is the Young’s modulus, I is the moment of inertia, M is the bending moment, t b is the thickness of the steel beam, Z na is the distance to the neutral axis, and  is the strain. Using the constitutive piezoelectric equation for strain without the stress component gives [5]: p t V d d 2 31 31     (2) where d 31 is the piezoelectric strain coupling coefficient, ξ is the electric field component, V is the voltage, and t p is the thickness of the piezoelectric layer. Fig. 1 A schematic of the cross section of the smart structure Modeling, Analysis and Control of a Smart Composite Structure Nader H. Ghareeb, Mohamed S. Gaith, Sayed M. Soleimani A World Academy of Science, Engineering and Technology International Journal of Materials and Metallurgical Engineering Vol:10, No:8, 2016 994 International Scholarly and Scientific Research & Innovation 10(8) 2016 ISNI:0000000091950263 Open Science Index, Materials and Metallurgical Engineering Vol:10, No:8, 2016 publications.waset.org/10005047/pdf