Finite element free vibration analysis of smart laminated composite beams and plates

The present paper deals with the development of a finite element method for the free vibration analysis of smart laminated composite beams and plates. The structure consists of a laminated composite substrate to which are surface bonded or embedded a set of piezoelectric layers, one of which is a sensor while the others are actuators. The analysis considers the linear piezoelectric constitutive relations and the first order shear deformation behaviour. An eight noded quadratic isoparametric piezoelectric element is developed to discretize the analysis domain, and the same shape functions are used to describe the electrical field, the charge density, the structural geometry as well as the structural displacements. Numerical results are obtained to study the effects of (1) stacking sequences of the composite laminae and piezoelectric layers, (2) geometric boundary conditions and (3) application of electrical voltages on the free vibration frequencies.