In 1989 he received his DSc in the same disciplines from the Moscow State University and the Higher Attestation Commission of the former USSR.

From 1993 Krylov worked in the UK, conducting research on ground vibrations generated by railway trains and by road vehicles.

[3][4] Krylov predicted the existence of localised elastic waves in immersed solid wedges and proposed to use them for wave-like aquatic propulsion of marine vessels.

He suggests using electric motors or shape-memory materials to emulate the propulsion of some fish, such as stingrays, a process less efficient but quieter than conventional propellers.

[5] He also investigated the method of damping structural vibrations based on the "acoustic black hole effect" for flexural waves propagating in plates of variable local thickness.