The increased emphasis placed on the design of “noiseless” machinery has led to the requirements of better evaluation of the magnetic attractive forces developed between rotor and stator of induction motors, better evaluation of stator response to such forces, and better evaluation of the sound waves radiated by the vibrating stator frame. This paper treats the crucial phase of the problem, determining the vibration characteristics of two concentric shells (stator core inside the stator frame) coupled by nonrigid ribs. The vibration theory of such coupled structures is developed and the theoretical results are compared with the experimental measurements obtained for a 30-hp, 3-phase, induction motor. The agreement is within 7 per cent. Parts 1 and 3 of the problem, determination of the airgap force waves and of the sound radiated, are discussed in separate papers.