Symmetry transitions of compressively prestressed long membranes under pressure

Abstract

This paper reports on the mechanical response of long postbuckled membranes to differential pressure. In the absence of pressure, membranes with Poisson's ratio /spl nu/=0.25 and prestrain /spl epsiv//sub 0/ more compressive than the critical value -17.3 t/sup 2//a/sup 2/, with the membrane thickness t and width a, show a meander-shaped postbuckling profile. With increasing pressure load, the structures undergo a second-order transition to a ripple-shaped profile at a critical pressure p/sub cr1/(/spl epsiv//sub 0/), and to a ripple-free profile at a higher critical pressure p/sub cr2/(/spl epsiv//sub 0/). At each transition, the structures gain additional symmetries. These phenomena were experimentally studied on micromachined PECVD silicon nitride thin film membranes. A variational calculus approach enabled p/sub cr1/(/spl epsiv//sub 0/), p/sub cr2/(/spl epsiv//sub 0/), /spl epsiv//sub 0,cr2/, and the symmetry contributions to the membrane profiles to be computed. Based on the numerical results, the prestrain and elastic modulus of a PECVD silicon nitride thin film were extracted as /spl epsiv//sub 0/=-1.78/spl times/10/sup -3/ and E=160 GPa, respectively.