A clamped-free beam with partial active constrained layer damping (ACLD) treatment is modelled by using the finite element method. The Golla-Hughes-McTavish (GEM) method is employed to account for the frequency-dependent characteristic of the viscoelastic material (VEM). As the resultant finite element model contains too many degrees of freedom due to the introduction of dissipative coordinates, a model reduction is performed to bring the system back to its original size. Finally, optimal output feedback gains are designed based on the reduced models. Numerical simulations are performed to study the effect of different ACLD treatment configurations, with various element numbers, spacing and locations, on the damping performance of a flexible beam. Results are presented for damping ratios of the first two vibration modes. It is found that to enhance the second mode damping, without deteriorating the first mode damping, splitting a single ACLD element into two and placing them at appropriate positions of the beam could be a possible solution.