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

Pages: 365 - 375, Issue Special, August 2005

 Abstract        Full Text (246.9K)              

Scott W. Hansen - Department of Mathematics, Iowa State University, Ames, IA 50011, United States (email)
Rajeev Rajaram - Iowa State University, Department of Mathematics, Ames, IA 50011, United States (email)

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.

Received: September 2004;      Revised: May 2005;      Published: September 2005.