  We study gravitational wave production during kinetic preheating after
inflation with a focus on scenarios that arise in $\alpha$-attractor models
where a scalar dilaton-like inflaton is kinetically coupled to a second scalar
field. We present high-resolution lattice simulations of three
$\alpha$-attractor models for a range of parameters to probe regions where
preheating is efficient. We find that preheating in these models can be
extremely violent, resulting in gravitational wave energy densities that can be
constrained by cosmic microwave background measurements of the effective number
of relativistic species, $N_{\rm eff}$
