This paper is concerned with the analysis of the effectiveness of triangular shaped smart constrained layer damping (SCLD) treatment in attenuating geometrically nonlinear transient vibrations of laminated composite beams. The SCLD treatment is comprised of an advanced vertically reinforced 1–3 piezoelectric composite (PZC) as the constraining layer and an isotropic viscoelastic layer as the constrained layer, which is modeled using a two-dimensional fractional order derivative (FOD) model with Grünwald definition of the FODs. A nonlinear meshfree model of the smart composite beam is developed for analyzing its nonlinear transient response within the framework of a layerwise shear and normal deformation theory considering von Kármán type geometric nonlinearity. Cantilever type composite beams having different lamination sequences integrated with regular rectangular/triangular type of SCLD treatments are considered for presenting the numerical results. For comparison purpose, a geometrical constraint has been imposed such that both the rectangular and triangular shaped SCLD treatments will cover the equal area on the top surface of the beam. The numerical analyses demonstrate the effectiveness of the triangular shaped SCLD patches over the rectangular SCLD treatment in controlling the nonlinear vibration of laminated composite beams. The two-dimensional FOD model of the viscoelastic material has been efficiently implemented for the active damping analysis of smart composite beam.