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We present measurements of the elliptic flow, $v_2$, as a function oftransverse momentum ($p_T$), pseudorapidity ($\eta$), and centrality in$d$$+$Au collisions at $\sqrt{s_{_{NN}}}=$200, 62.4, 39, and 19.6 GeV. Thebeam-energy scan of $d$$+$Au collisions provides a testing ground for the onsetof flow signatures in small collision systems. We measure a nonzero $v_2$signal at all four collision energies, which, at midrapidity and low $p_T$, isconsistent with predictions from viscous hydrodynamic models. Comparisons withcalculations from parton transport models (based on the {\sc ampt} Monte Carlogenerator) show good agreement with the data at midrapidity to forward($d$-going) rapidities and low $p_T$. At backward (Au-going) rapidities and$p_T>1.5$ GeV/$c$, the data diverges from {\sc ampt} calculations of $v_2$relative to the initial geometry, indicating the possible dominance ofnongeometry related correlations, referred to as nonflow. We also presentmeasurements of the charged-particle multiplicity ($dN_{\rm ch}/d\eta$) as afunction of $\eta$ in central $d$$+$Au collisions at the same energies. We findthat in $d$$+$Au collisions at $\sqrt{s_{_{NN}}}=$200 GeV the $v_2$ scales with$dN_{\rm ch}/d\eta$ over all $\eta$ in the PHENIX acceptance. At$\sqrt{s_{_{NN}}}=$62.4, and 39 GeV, $v_2$ scales with $dN_{\rm ch}/d\eta$ atmidrapidity and forward rapidity, but falls off at backward rapidity. Thisdeparture from the $dN_{\rm ch}/d\eta$ scaling may be a further indication ofnonflow effects dominating at backward rapidity.

Measurements of azimuthal anisotropy and charged-particle multiplicity in $d$$+$Au collisions at $\sqrt{s_{_{NN}}}=$200, 62.4, 39, and 19.6 GeV