We consider Einstein’s equations coupled to the Euler equations in plane symmetry, with compact spatial slices and constant mean curvature time. We show that for a wide variety of equations of state and a large class of initial data, classical solutions break down in finite time. The key mathematical result is a new theorem on the breakdown of solutions of systems of balance laws. We also show ...

Plates reinforced by ribs or joists are common elements in lightweight building structures, as well as in other engineering structures. However, these structures are not well suited for the common simplified prediction models such as Statistical Energy Analysis (SEA) or the European calculation standard EN 12354. There are several reasons for this: One is that the overall vibration field is not...

A weighted sum of spatial gradients (WSSG) control metric for use in active structural acoustic control of finite ribbed plates was developed and compared to volume velocity. A finite element model was used to obtain the displacement field on the plate, and a finite difference derivative approach to obtaining the terms in WSSG was used. Previous results of ASAC on finite ribbed plates are minim...