The concept of “mechanical impedance,” a quantity equivalent to Biot's Dynamic Modulus (reference i), has been utilised since 1939 by the de Havilland Aircraft Company as a standard method of treatment of vibration problems inengine airscrew systems, the method being applied principally to torsionalvibrations. In this work the effect of damping forces was neglected, on theassumption that the resonant frequencies of a system are not affected appreciablyby such forces so long as they remain of small magnitude.

The desire to justify this assumption by theoretical reasoning, and to evolve a method of attack for problems in which the damping forces are too large to be neglected, led to the application of the concept of mechanical impedance to damped systems.

The stresses in annular frames of constant flexural stiffness, as they occur in thin-walled shells are determined, assuming a finite depth of frame cross-section. The calculations are carried out for the fundamental load cases and the results presented in the form of diagrams.