{"product_id":"asymptotic-distribution-of-eigenfrequencies-for-cheryl-a-peterson-9781480191914","title":"Asymptotic Distribution of Eigenfrequencies for a Coupled Euler-Bernoulli and Timoshenko Beam Model","description":"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.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Cheryl A. Peterson, Marianna A. Shubov\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 1480191914\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9781480191914\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Createspace Independent Publishing Platform\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 10\/26\/2012\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 78\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Paperback\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 0.45lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 11.02h x 8.50w x 0.16d","brand":"Cheryl A. Peterson","offers":[{"title":"Paperback","offer_id":44365237092607,"sku":"9781480191914","price":17.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_b8366118-0424-4d26-9a0c-680c35b0371d.jpg?v=1697057396","url":"https:\/\/www.whiterainbookhouse.com\/products\/asymptotic-distribution-of-eigenfrequencies-for-cheryl-a-peterson-9781480191914","provider":"WR Book House","version":"1.0","type":"link"}