Optomechanical systems combine extreme sensitivity and bandwidth in the control of mechanical motion, of interest for various applications. Integrated on a chip, actuated and detected all-optically by a single laser, they could disrupt sensing technologies. We introduce here a multiphysics model that describes their operation in the oscillating mode, under sinusoidal modulation of the laser, when both photothermal forces and radiation pressure/electrostriction are present, and when (non)linear absorption occurs in the device. The model is validated by systematic experiments on ultra-high frequency optomechanical disk resonators and leads to a quantitative assessment of the amplitude and phase of the demodulated output signal, which carries the sensing information.