Riesz basis and exponential stability for Euler-bernoulli beams with variable coefficients and indefinite damping under a force control in position and velocity

• Main Authors: K. Augustin Toure, Adama Coulibaly, Ayo A. Hermith Kouassi
• Format: Article
• Language: English
• Published: Texas State University 2015-02-01
• Series: Electronic Journal of Differential Equations
• Subjects: Beam equation; asymptotic analysis; Riesz basis; exponential stability
• Online Access: http://ejde.math.txstate.edu/Volumes/2015/54/abstr.html
• ISSN: 1072-6691

This article concerns the Riesz basis property and the stability of a damped Euler-Bernoulli beam with nonuniform thickness or density, that is clamped at one end and is free at the other. To stabilize the system, we apply a linear boundary control force in position and velocity at the free end of the beam. We first put some basic properties for the closed-loop system and then analyze the spectrum of the system. Using the modern spectral analysis approach for two-points parameterized ordinary differential operators, we obtain the Riesz basis property. The spectrum-determined growth condition and the exponential stability are also concluded.