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Wave analysis and control of double cascade-connected damped mass-spring systems
Institution:1. Department of Civil and Environmental Engineering, Virginia Tech, Blacksburg, VA 24061, USA;2. Department of Mechanical Engineering and Materials Science, Duke University, Durham, NC 27708, USA;1. University of Porto, Faculty of Engineering, Department of Mechanical Engineering, Portugal;2. University of Aveiro, Department of Mechanical Engineering, Portugal;1. Universidad de Ciencias Informáticas, Departamento de Ciencias Básicas, Boyeros CP 19370, Cuba;2. Facultad de Matemática y Computación, Universidad de La Habana, San Lázaro y L, Vedado CP 10400, Cuba;3. Universidade Federal de Pelotas, Departamento de Matemática e Estatística, Instituto de Física e Matemática, Caixa Postal 354, CEP 96010-900 Pelotas, Rio Grande do Sul, Brazil;4. Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autńoma de México, Delegación Álvaro Obregón, Apartado Postal 20-726, 01000 México, D.F., Mexico;1. California Institute of Technology, Department of Aerospace Engineering (GALCIT), 1200 E California Blvd, Pasadena California, CA 91125, USA;2. ETH-Zurich, Department of Mechanical and Process Engineering (D-MAVT), Tannenstrasse 3 8092 Zurich, Switzerland;3. Sorbonne Universités, CNRS - UPMC, Institut Jean le Rond d’Alembert (UMR 7190), 75005 Paris, France
Abstract:This paper presents wave analysis and control for double cascade-connected damped mass-spring systems, whose mass is connected beyond the adjacent masses. The system is motivated by a cantilevered tensegrity beam supporting tensile and compressive forces. The wave solution is derived from a recurrent formula, and the properties of the propagation constants are precisely investigated. Elimination of reflected waves provides the impedance matching controller. We show that the impedance matching controller can be constructed from a similarity transformation of the characteristic impedance matrix by a matrix composed of the propagation constants. A numerical example of vibration control of a tensegrity beam is shown.
Keywords:Vibration control  Wave analysis  Damped mass-spring  Tensegrity  Impedance matching
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