  We propose a scheme for the generation of a robust stationary squeezed state
of a mechanical resonator in a quadratically coupled optomechanical system,
driven by a pulsed laser. The intracavity photon number presents periodic
intense peaks suddenly stiffening the effective harmonic potential felt by the
mechanical resonator. These "optical spring kicks" tend to squeeze the
resonator position, and due to the interplay with fluctuation-dissipation
processes one can generate a stationary state with more than 13 dB of squeezing
even starting from moderately "pre-cooled" initial thermal states.
