JAMC J Appl Math Comput (2011) 36: 441–458 DOI 10.1007/s12190-010-0412-9 Study of the nodal feedback stabilization of a string-beams network Kaïs Ammari · Michel Mehrenberger Received: 29 October 2009 / Published online: 16 June 2010 © Korean Society for Computational and Applied Mathematics 2010 Abstract We consider a stabilization problem for a string-beams network. We prove an exponential decay result. The method used is based on a frequency domain method and combine a contradiction argument with the multiplier technique to carry out a special analysis for the resolvent. Moreover, we give a numerical illustration based on the methodology introduced in Ammari and Tucsnak (ESAIM Control Optim. Calc. Var. 6, 361–386, 2001) where the exponential stability for the closed loop problem is reduced to an observability estimate for the corresponding uncontrolled system combined to a boundedness property of the transfer function of the associated open loop system. Keywords Numerical stabilization · Feedback stabilization · String-beams network Mathematics Subject Classification (2000) 35B40 · 93D15 · 93D20 · 93B07 · 65N25 1 Introduction and main results We study a network of N beams and one string, where N ≥ 1, see [17] (pages: 80–81, for example) concerning the model. More precisely we consider the following initial K. Ammari ( ) Département de Mathématiques, Faculté des Sciences de Monastir, 5019 Monastir, Tunisia e-mail: kais.ammari@fsm.rnu.tn M. Mehrenberger Institut de Recherche Mathématique Avancée, Université de Strasbourg, 7 rue René Descartes, 67084 Strasbourg, France e-mail: mehrenbe@math.u-strasbg.fr