Interplay between optomechanics and the dynamical Casimir effect

We develop a model of quantum field confined within cavity with movable wall where the position is quantized. obtain full description dynamics both and confining depending on initial state whole system. Both reaction back-reaction wall, field, can be taken into account, as well external driving forces wall. The exactly reproduces resonant mode stimulation due to periodic motion mirror (dynamical Casimir effect), standard radiation pressure effects quantized wall(optomechanics). also accounts for interplay two scenarios. Finally, time evolution force shows between static dynamical effect.