An improved mechanical seal assembly is provided for sealing rotating shafts with respect to their shaft housings, wherein the rotating shafts are subject to substantial axial vibrations. The mechanical seal assembly generally includes a rotating sealing ring fixed to the shaft, a non-rotating sealing ring adjacent to and in close contact with the rotating sealing ring for forming an annular seal about the shaft, and a mechanical diode element that applies a biasing force to the non-rotating sealing ring by means of hemispherical joint. The alignment of the mechanical diode with respect to the sealing rings is maintained by a series of linear bearings positioned axially along a desired length of the mechanical diode. Alternative embodiments include mechanical or hydraulic amplification components for amplifying axial displacement of the non-rotating sealing ring and transfering it to the mechanical diode.