Decay Rates for a Beam with Pointwise Force and Moment Feedback View Full Text


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Article Info

DATE

2002-07

AUTHORS

Kais Ammari, Zhuangyi Liu, Marius Tucsnak

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. More... »

PAGES

229-255

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s004980200009

DOI

http://dx.doi.org/10.1007/s004980200009

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1043044748


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