Riesz basis property and related results for a Rao-Nakra sandwich  beam

Scott W. Hansen; Rajeev Rajaram

doi:10.3934/proc.2005.2005.365

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2005, Volume 2005: 365-375. Doi: 10.3934/proc.2005.2005.365 open access

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Riesz basis property and related results for a Rao-Nakra sandwich beam

Scott W. Hansen^1, and
Rajeev Rajaram²

1.
Department of Mathematics, Iowa State University, Ames, IA 50011
2.
Iowa State University, Department of Mathematics, Ames, IA 50011

Received: August 31, 2004

Revised: April 30, 2005

Published: August 2005

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Abstract

We consider a three layer Rao-Nakra sandwich beam with distinct wave speeds. We prove that the eigenvectors form a Riesz basis for the natural energy space. In the damped case, we give precise conditions under which there is a uniform exponential decay of energy. We also consider the problem of boundary control using bending moment and lateral force control at one end. We prove that the space of exact controllability has finite co-dimension and provide sufficient conditions (related to small damping) for exact controllability to a zero energy state.

Keywords:

Sandwich beam; exact controllability,
boundary control.

Mathematics Subject Classification: 93B05, 80A20; Secondary: 70H25.

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