Degeneration of a compound plate system to a membrane-plate system: A singularly perturbed transmission problem

Summary Asymptotic expansions are constructed for solutions of some singularly perturbed transmission problems arising in engineering mechanics. The physical problem is that of a plate under tension which consists of two materials, with one material of small flexural rigidity, , surrounded by the other. The problems of deflection due to lateral loading and natural frequencies of vibration are solved for small positive . The limit probelm, =0, is a membrane-plate system under tension.This research was initiated during a visit to Laboratorio di Analisi Numerica del C.N.R., Università di Pavia, and has been partially supported by NSF Grant 02 MCS-7902663.