The present invention relates to a bearing support for a rotating engine such as a gas turbine engine, with a rotating shaft supported by at least one bearing and a frame, capable of running at least two different running speeds, characterised in that it comprises at least two mechanical supporting structures with different stiffnesses combined so as to support the bearing at one of these stiffnesses.The invention has the advantage that the use of mechanical structures avoids the presence of any hydraulic equipment, since the stiffness forces thus introduced can directly oppose excitation forces generated by the unbalanced mass of the engine shaft.