This paper presents a formulation for earthquake resistant design of o
ptimum hybrid isolation systems for sensitive equipment protection. Th
e hybrid system under consideration consists of laminated rubber beari
ngs, viscodampers and a set of actuators which, grounded on the main s
tructural system, deliver forces on the basement of the isolated subst
ructure mounted on the main structural system. An integrated design pr
ocedure for the passive and active components of the isolation system
is developed aiming at acceleration reduction under random excitation.
Linear models are used for the isolated structure, the main structura
l system and the isolation system. Fractional derivative Maxwell eleme
nts are used to model the mechanical behaviour of the viscodampers. Th
e active component of the isolation system applies forces proportional
to the absolute velocity of the isolated piece of equipment. Constrai
nts in the deformation capacity of the isolators as well as constraint
s in the capacity of the actuators are considered for the design of an
optimal hybrid isolation system. Simple numerical examples are develo
ped herein to illustrate the design procedure. The superiority of hybr
id systems over passive systems in reducing acceleration response is d
emonstrated.