arXiv:1401.1691v2.-- et al. ; Recent years have witnessed the boom of cavity optomechanics, which exploits the confinement and coupling of optical and mechanical waves at the nanoscale. Among their physical implementations, optomechanical (OM) crystals built on semiconductor slabs enable the integration and manipulation of multiple OM elements in a single chip and provide gigahertz phonons suitable for coherent phonon manipulation. Different demonstrations of coupling of infrared photons and gigahertz phonons in cavities created by inserting defects on OM crystals have been performed. However, the considered structures do not show a complete phononic bandgap, which should enable longer lifetimes, as acoustic leakage is minimized. Here we demonstrate the excitation of acoustic modes in a one-dimensional OM crystal properly designed to display a full phononic bandgap for acoustic modes at 4 GHz. The modes inside the complete bandgap are designed to have high-mechanical Q-factors, limit clamping losses and be invariant to fabrication imperfections. ; This work was supported by the European Commission Seventh Framework Programs (FP7) under the FET-Open project TAILPHOX N 233883. J.G.-B., D.N.-U., E.C., F.A. and C.M.S.-T. acknowledge financial support from the Spanish projects ACPHIN (ref. FIS2009-10150) and TAPHOR (MAT2012-31392). J.G.-B. and D.P. acknowledges funding from the Spanish government through the Juan de la Cierva programme, D.N.- U. acknowledges funding from the Catalan government through the Beatriu de Pinos programme. ; Peer Reviewed