Stability of Homogeneous Smart Beams based on the First Order Shear Deformation Theory Located on a Continuous Elastic Foundation

Abstract

1 Abstract—This paper studies stability of homogeneous beams with piezoelectric layers subjected to axial load that is simply supported at both ends lies on a continuous elastic foundation. The displacement field of beam is assumed based on first order shear deformation beam theory. Applying the Hamilton's principle, the governing equation is established. The influences of applied voltage, dimensionless geometrical parameter and foundation coefficient on the stability of beam are presented. To investigate the accuracy of the present analysis, a compression study is carried out with a known data. Keywords—Stability, Homogeneous beam- Piezoelectric layer. I. INTRODUCTION HE applications of the smart materials have drawn attention in aerospace engineering, civil engineering, mechanical and even bio-engineering. The analysis of a coupled piezoelectric structure has recently been keenly researched because piezoelectric materials are more extensively used either as actuators or sensors. Examples include the analytical modelling and behaviour of a beam with surface-bonded or embedded piezoelectric sensors and actuators (1-3), and the use of piezoelectric materials in composite laminates and for vibration control (4). The use of finite element method in the analysis of piezoelectric coupled structures has been studied (5-8). Crawley and de Luis (9) developed the analytical model for the static and dynamic response of a beam structure with segmented piezoelectric actuators either bonded or embedded in a laminated composite. LaPeter and Cudney (10) proposed an analytic model for the segmented piezoelectric actuators bonded on a beam or a plate, and found the equivalent forcing functions of the actuators. The piezoelectric bimorph column structures were used as sensing elements. Dobrucki and Pruchnicki (11) presented an analysis theory of an axisymmetric piezoelectric bimorph. They also described a sensing theory for using the axisymmetric piezoelectric bimorph. Chandrashekhara and Bhatia (12) developed a finite element model for the active buckling control of laminated composite plates with surface bonded or embedded piezoelectric sensors that are either continuous or segmented. The dynamic buckling behavior of the laminated plate subjected to a linearly increasing compression load is investigated in their work. Chase and Bhashyam (13) derived optimal design equations to actively stabilize laminated plates loaded in excess of the critical buckling load using a large number of sensors and actuators. To the author's knowledge, there is no analytical solution available in the open literatures for stability of homogeneous beams with piezoelectric layers subjected to axial load that is simply supported at both ends lies on a continuous elastic foundation. In the present work, stability of homogeneous beams with piezoelectric layers subjected to axial load that is simply supported at both ends lies on a continuous elastic foundation studied. Appling the Hamilton's principle, the equilibrium equations of beam are derived and solved. The effects of applied voltage, dimensionless geometrical parameter and foundation coefficient on the critical buckling load of beam are presented. To investigate the accuracy of the present analysis, a compression study is carried out with a known data.