About the partition impedance of plates, shells and membranes

The partition impedance of thin, undisturbed plates, shells and membranes is a useful concept in boundary value problems. It describes the effect of a thin partition in front of, between or behind layers of air and/or absorbers as a series impedance assuming that the vibration pattern of the plate or shell coincides with the pattern of the incident wave at its surface. This condition is satisfied for a large plate with no internal distortions such as fixations or stiffeners. The partition impedance is defined and handled in texts about structure-borne sound mostly with simplifications which make its application difficult in problems of air-borne sound absorption or transmission. It is shown that plates, membranes or shells can be considered for such boundary value problems like foils, generalised in the sense, that their surface mass density is modified by elastic effects. Further, a general scheme is described for the derivation of the partition impedance of shells.