A mathematical model for the instability of tube rows subjected to crossflow is examined. The theoretical model, based on the fluid-force data for a pitch-to-diameter ratio of 1.33, provides additional insight into the instability phenomenon. Tests are also conducted for three sets of tube rows. The effects of mass ratio, tube pitch, damping, detuning and finned tubes are investigated. Theoretical results and experimental data are in good agreement.

A procedure is described for randomly generating positive definite quadratic programming test problems. The test problems are constructed in the form of linear least squares problems subject to linear constraints. The probability measure for the problems so generated is invariant under orthogonal transformations. The procedure allows the user to specify the size of the least squares problem (number of unknown parameters, number of observations, and number of constraints); the relative magnitude of the residuals; the condition number of the Hessian matrix of the objective function; and the structure of the feasible region (number of equality constraints and the number of inequalities which will be active at the feasible starting point and at the optimal solution). An example is given illustrating how these problems can be used to evaluate the performance of a software package.

This report discuses results of an experimental program to characterize the fragments generated when brittle glasses and cermaics are impacted.