Electromechanical Coupling Characteristics of Functionally Graded Piezoelectric Ceramic Beam

Abstract

The tremendous attention of researchers has been attracted to the unusual properties of piezoelectric ceramic materials. A semi-analytical approach to estimate the electromechanical coupling characteristics of multilayered functionally graded piezoelectric ceramic beams with different boundary conditions is presented. The state space method is formulated to the electroelastic theory to derive the state equations for ceramic beams along the thickness direction. The mixed supported boundary conditions are represented by means of the displacement function and Fourier series expansions, respectively. A global propagator matrix is used to connect the field variables at the internal interface to those at the external interface for the whole structure. Governing equations of the models with geometrical nonlinearity are solved using the secant method. Numerical examples show the correctness of the proposed method by finite element model and the influence of the functional gradient index factors η, different boundary conditions, and loading voltage on the static behavior of piezoelectric ceramic beams. Our results show that the modified state space approach overcomes the disadvantage of the inability to address clamped supported and free boundary conditions. η possesses the ability to improve interfacial stress discontinuities.