  In this paper, we consider the one-dimensional isentropic compressible Euler
equations with linear damping $\beta(t,x)\rho u$ in a bounded domain, which can
be used to describe the process of compressible flows through a porous
medium.~And the model is imposed a dissipative subsonic time-periodic boundary
condition.~Our main results reveal that the time-periodic boundary can trigger
a unique subsonic time-periodic smooth solution which is stable under small
perturbations on initial data. Moreover, the time-periodic solution possesses
higher regularity and stability provided a higher regular boundary condition.
