The wealth of technological patterning technologies of deca-nanometer resolution brings opportunities to artificially modulate thermal transport properties. A promising example is given by the recent concepts of "thermocrystals" or "nanophononic crystals" that introduce regular nano-scale inclusions using a pitch scale in between the thermal phonons mean free path and the electron mean free path. In such structures, the lattice thermal conductivity is reduced down to two orders of magnitude with respect to its bulk value. Beyond the promise held by these materials to overcome the well-known "electron crystal-phonon glass" dilemma faced in thermoelectrics, the quantitative prediction of their thermal conductivity poses a challenge. This work paves the way toward understanding and designing silicon nanophononic membranes by means of molecular dynamics simulation. Several systems are studied in order to distinguish the shape contribution from bulk, ultra-thin membranes (8 to 15 nm), 2D phononic crystals, and finally 2D phononic membranes. After having discussed the equilibrium properties of these structures from 300K to 400 K, the Green-Kubo methodology is used to quantify the thermal conductivity. The results account for several experimental trends and models. It is confirmed that the thin-film geometry as well as the phononic structure act towards a reduction of the thermal conductivity. The further decrease in the phononic engineered membrane clearly demonstrates that both phenomena are cumulative. Finally, limitations of the model and further perspectives are discussed. (C) 2015 AIP Publishing LLC.