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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Asymptotic Distribution of Eigenfrequencies for a Coupled Euler-Bernoulli and Timoshenko Beam Model

Asymptotic Distribution of Eigenfrequencies for a Coupled Euler-Bernoulli and Timoshenko Beam Model

Peterson, Cheryl A.
Shubov, Marianna A.

Paperback

Physics

ISBN10: 1480191914
ISBN13: 9781480191914
Publisher: Createspace
Published: Oct 26 2012
Pages: 78
Weight: 0.45
Height: 0.16 Width: 8.50 Depth: 11.02
Language: English
This research is devoted to the asymptotic and spectral analysis of a coupled Euler-Bernoulli and Timoshenko beam model. The model is governed by a system of two coupled differential equations and a two parameter family of boundary conditions modelling the action of self-straining actuators. The aforementioned equations of motion together with a two-parameter family of boundary conditions form a coupled linear hyperbolic system, which is equivalent to a single operator evolution equation in the energy space. That equation defines a semigroup of bounded operators. The dynamics generator of the semigroup is our main object of interest. For each set of boundary parameters, the dynamics generator has a compact inverse. If both boundary parameters are not purely imaginary numbers, then the dynamics generator is a nonselfadjoint operator in the energy space. We calculate the spectral asymptotics of the dynamics generator. We find that the spectrum lies in a strip parallel to the horizontal axis, and is asymptotically close to the horizontal axis - thus the system is stable, but is not uniformly stable.

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