  Screened modified gravity (SMG) is a kind of scalar-tensor theory with
screening mechanisms, which can suppress the fifth force in dense regions and
allow theories to evade the solar system and laboratory tests. In this paper,
we investigate how the screening mechanisms in SMG affect the gravitational
radiation damping effects, calculate in detail the rate of the energy loss due
to the emission of tensor and scalar gravitational radiations, and derive their
contributions to the change in the orbital period of the binary system. We find
that the scalar radiation depends on the screened parameters and the
propagation speed of scalar waves, and the scalar dipole radiation dominates
the orbital decay of the binary system. For strongly self-gravitating bodies,
all effects of scalar sector are strongly suppressed by the screening
mechanisms in SMG. By comparing our results to observations of binary system
PSR J1738+0333, we place the stringent constraints on the screening mechanisms
in SMG. As an application of these results, we focus on three specific models
of SMG (chameleon, symmetron, and dilaton), and derive the constraints on the
model parameters, respectively.
