State vector approach of free-vibration analysis of magneto–electro-elastic hybrid laminated plates

In this paper, state variable formulation for free vibration of the laminated structures bonded and embedded actuators and sensors (piezoelectric and/or piezomagnetic) is established. The present mixed type formulation has the great advantage that the size of the system to be solved is independent of the number of layers and is of order three for free vibration of the laminate with bonded and embedded piezoelectric and/or piezomagnetic layers. Analytical solutions of 3D free vibration of simply supported piezoelectric and piezomagnetic composite plates have been presented. The transfer matrices for either closed circuit or open circuit piezoelectric and piezomagnetic layers are derived. The special case of elastic layer is also treated. The assembly procedure is described for the different electric and magnetic surface conditions. Numerical examples are analyzed to study the vibration characteristics of smart laminate plates with different stacking sequence and different span to thickness ratio.