Decay rates for a beam with pointwise force and moment feedback

Kais Ammari, Zhuangyi Liu, Marius Tucsnak

Research output: Contribution to journalArticlepeer-review

32 Scopus citations

Abstract

We consider the Rayleigh beam equation and the Euler-Bernoulli beam equation with pointwise feedback shear force and bending moment at the position ξ in a bounded domain (0, π) with certain boundary conditions. The energy decay rate in both cases is investigated. In the case of the Rayleigh beam, we show that the decay rate is exponential if and only if ξ/π is a rational number with coprime factorization ξ/π = p/q, where q is odd. Moreover, for any other location of the actuator we give explicit polynomial decay estimates valid for regular initial data. In the case of the Euler-Bernoulli beam, even for a nonhomogeneous material, exponential decay of the energy is proved, independently of the position of the actuator.

Original languageEnglish (US)
Pages (from-to)229-255
Number of pages27
JournalMathematics of Control, Signals, and Systems
Volume15
Issue number3
DOIs
StatePublished - Sep 18 2002

Keywords

  • Exponential decay
  • Observability inequality
  • Pointwise control
  • Polynomial decay

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