Supplementary Material

Section 1 details the methodology for designing and manufacturing the devices used in this work. Section 2 presents a scheme of the experimental setup. Section 3 introduces the model that describes the self-pulsing mechanism that allows the driving of the optomechanical cavities to a mechanical lasing regime. In section 4, the differential equations describing the driving mechanism are solved numerically and results are compared with experimental measurements. Finally, Section 5 presents the numerical simulations of the whole system including both oscillators, the external modulation and a weak mechanical interaction between them