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Spectral analysis of a non‐homogeneous rotating Timoshenko beam

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  • Jean‐Luc Akian

Abstract

In this paper we examine the spectral analysis of a spatially non‐homogeneous Timoshenko beam mounted on the periphery of a rigid root rotating about its axis at a constant angular speed. The junction between the beam and the root is assumed to be elastically restrained and damped. The unbounded operator associated to the physical problem in the associated Hilbert space is non‐self‐adjoint and with a compact resolvent. We show that under some hypotheses on the physical properties of the beam, there exists a Riesz basis of root vectors of this unbounded operator. Furthermore, the solution of the initial value problem has an expansion in terms of this Riesz basis, uniform with respect to the time in a bounded interval.

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  • Jean‐Luc Akian, 2022. "Spectral analysis of a non‐homogeneous rotating Timoshenko beam," Mathematische Nachrichten, Wiley Blackwell, vol. 295(3), pages 422-449, March.
    • Handle: RePEc:bla:mathna:v:295:y:2022:i:3:p:422-449
    DOI: 10.1002/mana.201900177
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    References listed on IDEAS

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    1. De-Xing Feng & Gen-Qi Xu & Siu-Pang Yung, 2003. "Riesz basis property of Timoshenko beams with boundary feedback control," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2003, pages 1-14, January.
    2. G. Q. Xu & S. P. Yung, 2004. "Exponential Decay Rate for a Timoshenko Beam with Boundary Damping," Journal of Optimization Theory and Applications, Springer, vol. 123(3), pages 669-693, December.
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