Next week: Richard James, 14-Feb-23, 12:20pm Central
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Ellad Tadmor
Feb 7, 2023, 8:21:46 AM2/7/23
to aem-solid...@umn.edu
AEM Mechanics Research Seminar
Tuesday 14-Feb-2023, 12:20pm Central
Prof. Richard James
Department of Aerospace Engineering and Mechanics, University of Minnesota
Title: Options for dynamic similarity of interacting fluids, elastic solids and rigid bodies
Abstract: The topic of dynamical similarity is a classic topic, apparently known in some way to Archimedes. Motivated by a design of a vertical axis wind turbine, we present a theory of dynamical similarity for mechanical systems consisting of interacting elastic solids, rigid bodies and incompressible fluids. Throughout, we focus on the geometrically nonlinear case. We approach the analysis by analyzing the equations of motion: we ask that a change of variables take these equations and mutual boundary conditions to themselves, while allowing a rescaling of space and time. Whereas the disparity between the Eulerian and Lagrangian descriptions of motion — Eulerian for the fluid, Lagrangian for the elastic or rigid solid — might seem to limit the possibilities, we find numerous cases that apparently have not been identified, especially for stiff nonlinear elastic materials (defined in the lecture). We discuss specific applications. We finish the lecture by addressing the following related question: how would one build on earth a drone or rover that, after rescaling various dimensions and possibly substituting different materials, would behave on the Moon or Mars in a precisely predictable way from its behavior on earth?
For more information, visit the AEM Mechanics Research Seminar website:
Tuesday 14-Feb-2023, 12:20pm Central
In-person: Room 25, Mechanical Engineering Building, University of Minnesota
Online: Webinar registration link
Department of Aerospace Engineering and Mechanics, University of Minnesota
Title: Options for dynamic similarity of interacting fluids, elastic solids and rigid bodies
Abstract: The topic of dynamical similarity is a classic topic, apparently known in some way to Archimedes. Motivated by a design of a vertical axis wind turbine, we present a theory of dynamical similarity for mechanical systems consisting of interacting elastic solids, rigid bodies and incompressible fluids. Throughout, we focus on the geometrically nonlinear case. We approach the analysis by analyzing the equations of motion: we ask that a change of variables take these equations and mutual boundary conditions to themselves, while allowing a rescaling of space and time. Whereas the disparity between the Eulerian and Lagrangian descriptions of motion — Eulerian for the fluid, Lagrangian for the elastic or rigid solid — might seem to limit the possibilities, we find numerous cases that apparently have not been identified, especially for stiff nonlinear elastic materials (defined in the lecture). We discuss specific applications. We finish the lecture by addressing the following related question: how would one build on earth a drone or rover that, after rescaling various dimensions and possibly substituting different materials, would behave on the Moon or Mars in a precisely predictable way from its behavior on earth?
For more information, visit the AEM Mechanics Research Seminar website:
_________________________________________________________________
Ellad B. Tadmor, Professor
Department of Aerospace Engineering and Mechanics
University of Minnesota
107 Akerman Hall, 110 Union St SE
Minneapolis, MN 55455, USA
tel: 612-625-6642
fax: 612-626-1558
web: Tadmor Website | Modeling Materials Book Website
_________________________________________________________________
Ellad B. Tadmor, Professor
Department of Aerospace Engineering and Mechanics
University of Minnesota
107 Akerman Hall, 110 Union St SE
Minneapolis, MN 55455, USA
tel: 612-625-6642
fax: 612-626-1558
web: Tadmor Website | Modeling Materials Book Website
_________________________________________________________________
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