Nanoelectromechanical systems (NEMS), utilizing localized mechanical vibrations, have found application in sensors(1,2), signal processors(3,4) and in the study of macroscopic quantum mechanics(5-7). The integration of multiple mechanical elements via electrical or optical means remains a challenge in the realization of NEMS circuits(8-13). Here, we develop a phonon waveguide using a one-dimensional array of suspended membranes that offers purely mechanical means to integrate isolated NEMS resonators. We demonstrate that the phonon waveguide can support and guide mechanical vibrations and that the periodic membrane arrangement also creates a phonon bandgap that enables control of the phonon propagation velocity. Furthermore, embedding a phonon cavity into the phonon waveguide allows mobile mechanical vibrations to be dynamically switched or transferred from the waveguide to the cavity, thereby illustrating the viability of waveguide-resonator coupling. These highly functional traits of the phonon waveguide architecture exhibit all the components necessary to permit the realization of all-phononic NEMS circuits.