In the present paper, the active-passive hybrid vibration control performance due to Enhanced Smart Constrained Layer Damping (ESCLD) treatment as proposed by Liao and Wang on plate like structures has been considered. This treatment consists of a viscoelastic layer constrained between a smart piezoelectric layer and the base structure being controlled. Also, the smart constraining layer is clamped to the base structure. This type of damping treatment has got both active and passive component of damping. The passive damping is through cyclic shearing of viscoelastic constrained layer which is further enhanced by activating the smart piezoelectric constraining layer and the active component of the damping is through the transfer of control moments from the piezoelectric layer to the base structure through the viscoelastic layer and also bypassed through the clamps. A plate finite element has been formulated using first order shear deformation theory, including the effect of transverse shear and rotary inertia. The effect of the viscoelastic shear layer and piezoelectric constraining layer on the mass and stiffness has been included in the model. The viscoelastic shear layer is modeled usig Golla-Hughes-McTavish (GHM) method, which is a time domain approach. The clamps (edge elements) are modeled as equivalent springs connecting the smart piezoelectric constraining layer with the structure to be controlled. LQR optimal control strategy is used to obtain optimal control gains. The effect of the viscoelastic material properties (shear modulus and loss factor) on the hybrid vibration control performance is studied for both SCLD (without edge elements) and ESCLD systems.