Aerofoils (22) of a gas turbine engine are provided with a coating (34) or filler (44) of viscoelastic material. As ice accretes on the aerofoils (22) during operation, the resulting aerodynamic stability imbalance induces vibration in the aerofoils (22). The viscoelastic material (34, 44) damps this vibration, and in so doing generates heat, which melts the ice away from the aerofoils (22). Heat-conducting members conduct the heat to regions of the component in which ice accretion is to be prevented. Alternative embodiments are described in which the pseudoelastic behavior of a shape memory alloy (56), or eddy currents arising from the rotor blades' rotation in an axisymmetric magnetic field, are used as sources of heat.