  Using data samples collected with the BESIII detector operating at the BEPCII
storage ring, we measure the cross sections of the
$e^{+}e^{-}\rightarrow\pi^{+}\pi^{-}D^{+}D^{-}$ process at center-of-mass
energies from 4.190 to 4.946 GeV with a partial reconstruction method. Two
resonance structures are seen and the resonance parameters are determined from
a fit to the cross section line shape. The first resonance we observe has a
mass of (4373.1 $\pm$ 4.0 $\pm$ 2.2) MeV/$c^2$ and a width of (146.5 $\pm$ 7.4
$\pm$ 1.3) MeV, in agreement with those of the $Y(4390)$ state; the other
resonance has a mass of (4706 $\pm$ 11 $\pm$ 4) MeV/$c^2$, a width of (45 $\pm$
28 $\pm$ 9) MeV, and a statistical significance of $4.1$ standard deviations
($\sigma$). This is the first evidence for a vector state at this mass value.
The spin-$3$ $D$-wave charmonium state $X(3842)$ is searched for through the
$e^{+}e^{-}\rightarrow\pi^{+}\pi^{-}X(3842)\rightarrow\pi^{+}\pi^{-}D^{+}D^{-}$
process, and evidence with a significance of $4.2\sigma$ is found in the data
samples with center-of-mass energies from 4.600 to 4.700 GeV.
