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Spectral analysis of a non‐homogeneous rotating Timoshenko beam

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.