A quasi-2D finite element formulation of active constrained-layer functionally graded beam

A functionally graded (FG) beam with an active constrained-layer damping (ACLD) treatment is modeled and analyzed. ACLD consists of a passive element, in the form of a viscoelastic layer bonded to the host structure, and an active constraining element which is represented by a piezoelectric fiber-reinforced composite (PFRC) laminate. It is assumed in the current formulation that the field variables are expressible as polynomials through the thickness of the beam and are cubically interpolated across the span. Hamilton's principle is used in the derivation of the equations of motion, which are solved using the Newmark time-integration method. The versatility of the formulation is demonstrated using different support mechanisms in the form of analysis of cantilevered, fixed-end partially-constrained and simply-supported beam cases. The effects of ply orientation in PFRC laminate and varying elastic modulus in the FG beam are also examined.