HOMOGENIZATION OF A MODEL PROBLEM IN THE THEORY OF THIN MEMBRANE SHELLS

We consider a Douglis-Nirenberg elliptic system containing principal t erms of order zero so that the resolvent is not compact. That system i s a simplified model of the membrane system for thin shells. We solve the corresponding periodic homogenization problem. The essential spect rum does not pass to the homogenization limit. Consequently, the middl e frequency vibrations of the heterogeneous shells cannot be described in terms of the homogenized system.