This paper proves the boundedness of boundary and distributed damped strings and Euler-Bernoulli beams under combined distributed and boundary inputs. Distributed viscous or Kelvin-Voigt damping or a translational boundary damper stabilize strings and beams. Pointwise bounded response is proven using the energy multiplier method. Without disturbances, the method proves strong exponential stability. With disturbances, the response is shown to be strongly bounded.
Banks, H. T. and Inman, D. J. , 1991, “On damping mechanisms in beams,”Journal of Applied Mechanics58, 716-723 .
2.
Chen, C. T. , 1999, Linear System Theory and Design, Third edition, Oxford University Press, New York .
3.
Hughes, P. C. , 1986, Spacecraft Attitude Dynamics, Wiley, New York .
4.
Komornik, V. , 1994, Exact Controllability and Stabilization - the Multiplier Method, Wiley, New York .
5.
Luo, Z.-H. , Guo, B.-Z. , and Morgul, O. , 1999, Stability and Stabilization of Inf inite Dimensional Systems with Applications, Springer-Verlag, London .
6.
Meirovitch, L. , 1997, Principles and Techniques of Vibrations, Prentice Hall, Upper Saddle River, New Jersey .
7.
Rahn, C. D. , 2001, Mechatronic Control of Distributed Vibration and Noise, Springer-Verlag, Berlin .
