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Full-Text Articles in Physical Sciences and Mathematics
Stability Of Self-Similar Solutions For Van Der Waals Driven Thin Film Rupture, Thomas P. Witelski, Andrew J. Bernoff
Stability Of Self-Similar Solutions For Van Der Waals Driven Thin Film Rupture, Thomas P. Witelski, Andrew J. Bernoff
All HMC Faculty Publications and Research
Recent studies of pinch-off of filaments and rupture in thin films have found infinite sets of first-type similarity solutions. Of these, the dynamically stable similarity solutions produce observable rupture behavior as localized, finite-time singularities in the models of the flow. In this letter we describe a systematic technique for calculating such solutions and determining their linear stability. For the problem of axisymmetric van der Waals driven rupture (recently studied by Zhang and Lister), we identify the unique stable similarity solution for point rupture of a thin film and an alternative mode of singularity formation corresponding to annular “ring rupture.”
Model Updating By Adding Known Masses And Stiffnesses, Philip D. Cha, Lisette G. De Pillis
Model Updating By Adding Known Masses And Stiffnesses, Philip D. Cha, Lisette G. De Pillis
All HMC Faculty Publications and Research
New approaches are developed to update the analytical mass and stiffness matrices of a system. By adding known masses to the structure of interest, measuring the modes of vibration of this mass-modified system, and finally using this set of new data in conjunction with the initial modal survey, the mass matrix of the structure can be corrected. A similar approach can also be used to update the stiffness matrix of the system by attaching known stiffnesses. Manipulating the mass and stiffness correction matrices into vector forms, the connectivity information can be enforced, thereby preserving the physical configuration of the system, …