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We report measurements of the production of prompt D$^0$, D$^+$, D$^{*+}$ andD$^+_{\rm s}$ mesons in Pb-Pb collisions at the centre-of-mass energy pernucleon-nucleon pair $\sqrt{s_{\rm NN}}=5.02$ TeV, in the centrality classes0-10%, 30-50% and 60-80%. The D-meson production yields are measured atmid-rapidity ($|y|<0.5$) as a function of transverse momentum ($p_{\rm T}$).The $p_{\rm T}$ intervals covered in central collisions are: $1<p_{\rm T}<50$Gev/$c$ for D$^0$, $2<p_{\rm T}<50$ GeV/$c$ for D$^+$, $3<p_{\rm T}<50$ GeV/$c$for D$^{*+}$, and $4<p_{\rm T}<16$ GeV/$c$ for D$^+_{\rm s}$ mesons. Thenuclear modification factors ($R_{\rm AA}$) for non-strange D mesons (D$^0$,D$^+$, D$^{*+}$) show minimum values of about 0.2 for $p_{\rm T}$ = 6-10GeV/$c$ in the most central collisions and are compatible within uncertaintieswith those measured at $\sqrt{s_{\rm NN}}=2.76$ TeV. For D$^+_{\rm s}$ mesons,the values of $R_{\rm AA}$ are larger than those of non-strange D mesons, butcompatible within uncertainties. In central collisions the average $R_{\rm AA}$of non-strange D mesons is compatible with that of charged particles for$p_{\rm T} > 8$ GeV/$c$, while it is larger at lower $p_{\rm T}$. The nuclearmodification factors for strange and non-strange D mesons are also compared totheoretical models with different implementations of in-medium energy loss.

Measurement of D$^0$, D$^+$, D$^{*+}$ and D$^+_{\rm s}$ production in Pb-Pb collisions at $\mathbf{\sqrt{s_{\rm NN}}}= 5.02$ TeV