Electromechanical Vibration Characteristics of Porous Bimorph and Unimorph Doubly Curved Panels

Abstract

The aim of this study is developing an analytical solution for the free vibration of piezoelectric bimorph and unimorph doubly curved panels with a porous substrate. The panel is assumed to be relatively thick, and the effects of its shear deformation are taken into account. Nonlinear models are considered to describe the variation of mechanical properties and of the electric potential within porous host and piezoelectric layers, respectively. Furthermore, short and open circuit electrical conditions are studied to predict the frequency response for sensing and actuation applications. Employing the first-order shear deformation theory (FSDT), in conjunction with the Hamilton’s variational principle and Maxwell’s equation allows deriving six highly coupled partial differential equations to describe the system dynamics under electromechanical coupling. After analytically solving those equations for simply supported panels, the system frequency response is investigated, for various values of design parameters such as porosity, electrical boundary conditions, and geometry. Moreover, some types of smart panels, including bimorphs and unimorphs layouts, are analyzed. The analysis confirms that the above-mentioned parameters play major roles in the natural frequency response of this system and must be carefully considered in the mechatronic design of this smart structure, although they allow to tailor the system behaviour to the selected application.

Keywords

• structural mechatronics
• electromechanical coupling
• analytical methods
• system dynamics
• porous material
• piezoelectric material
• doubly curved shells