Characterisation of membranes produced for use as micro-electro-mechanical systems using vibrational techniques can give a measure of their behaviour and suitability for operation in different environments. Two membranes are studied here: germanium (Ge) and cubic silicon carbide (3C-SiC) on a silicon (Si) substrate. When driven at higher displacements, the membranes exhibit self-protecting behaviour. The resonant vibration amplitude is limited to a maximum value of around 10 nm, through dissipation of energy via higher harmonic vibrations. This is observed for both materials, despite their different Young's moduli and defect densities.