Polynomial stability of a joint-leg-beam system with local damping

Recent advances in the design and construction of large inflatable/rigidizable space structures and potential new applications of such structures have produced a demand for better analysis and computational tools to deal with the new class of structures. Understanding stability and damping properties of truss systems composed of these materials is central to the successful operation of future systems. In this paper, we consider a mathematical model for an assembly of two elastic beams connected to a joint through legs. The dynamic joint model is composed of two rigid-bodies (the joint-legs) with an internal moment. In an ideal design all struts and joints will have identical material and geometric properties. In this case we previously established exponential stability of the beam-joint system. However, in order to apply theoretical stability estimates to realistic systems one must deal with the case where the individual truss components Interdisciplinary Center for Applied Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, VA, 24061-0531. E-mail: [email protected], [email protected] Department of Mathematics, University of Minnesota, Duluth, MN 55812-3000. E-mail: [email protected] Instituto de Matemática Aplicada del Litoral, CONICET-UNL, Güemes 3450, and Departamento de Matemática, Facultad de Ingenier ́ia Qu ́imica, Universidad Nacional del Litoral, S3000GLN Santa Fe, Argentina. E-mail: [email protected]