On Concentrated Masses and Stiffnesses in Structural Theories

Vibration of structures subjected to concentrated masses and stiffnesses is a popular topic of interest and significance in the mechanics community. Unfortunately, in vibration analysis of structures, the concentrated parameters such as masses, springs, and even supports are not permitted theoretically for some cases. In this paper, we prove that concentrated parameters are not admissible in vibration analysis for those structures whose static Green's functions have a singularity at the origin. The classes of structure include membranes, Mindlin plates and various theories of shells.