Finite element formulation for composite plates with piezoceramic layers for optimal vibration control applications

A finite element (FE) formulation for piezoceramic laminated structures is derived, which includes plate elements that are developed using shear deformation (Mindlin plate) theory for each layer of the composite plate. In order to ensure shear continuity at the interface, a constraining matrix is introduced that defines the displacement field for each individual layer. The proposed model is applicable to both thick and thin plates where electromechanical coupling is present due to the piezoelectric effect. A combination of four-node Lagrange bilinear and eight-node serendipity quadratic elements are used for deriving the matrices and vectors necessary for approximating the solution. Electromechanical coupling terms model the orthotropic piezoelectric properties (g(31) = g(32)), and there is an orthotropic formulation for the mechanical properties of each plate layer. The proposed FE model is compared to FE models based on thin plate theory with isotropic piezoelectric actuation (g(31) = g(32)) and isotropic material properties. Modeling accuracy is evaluated by comparison with experimental measurements. A passive control application is presented that is based on shunting one of the piezoceramic patches with a LR (inductor and resistor) circuit; a linear quadratic regulator is added to the shunt to enable active control. An optimization study for hybrid control is presented where all of the control parameters, including active feedback gain, passive shunt inductance and resistance, are optimized numerically; the response of the structure to an impulse disturbance is simulated for both controlled and uncontrolled cases.