Boundary stabilization of a hybrid Euler–Bernoulli beam

ABSTRACT

We consider the uniform stabilization of a hybrid model consisting of an Euler–Bernoulli beam with a tip load at the free end of the beam. Our main result proves that the semigroup associated with this model is not exponentially stable. Additionally, we prove that the semigroup decays polynomially to zero as $t^{-1}$ as time goes to infinity.

COMMUNICATED BY:

• Meir Shillor

Keywords:

• Uniform stabilization
• polynomial decay
• Euler–Bernoulli beam
• tip body
• semigroup theory
• essential radius

2000 Mathematics Subject Classifications:

• 74F05
• 74F20

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by CNPq 310249/2018-0 (Brazil).