Browsing by Subject "Timoshenko beams"
Now showing 1 - 2 of 2
Results Per Page
Sort Options
Item Asymptotic and spectral analysis of nonselfadjoint operators generated by a coupled Euler-Bernoulli/Timoshenko beam model(Texas Tech University, 2002-05) Peterson, Cheryl AnneThis dissertation 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 modeling 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 in the dissertation. 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. The latter fact has been observed in numerical simulations and in the present dissertation, it has been rigorously proven.Item The inverse medium problem for Timoshenko beams and frames : damage detection and profile reconstruction in the time-domain(2009-12) Karve, Pranav Madhav; Kallivokas, Loukas F.; Manuel, LanceWe discuss a systematic methodology that leads to the reconstruction of the material profile of either single, or assemblies of one-dimensional flexural components endowed with Timoshenko-theory assumptions. The probed structures are subjected to user-specified transient excitations: we use the complete waveforms, recorded directly in the time-domain at only a few measurement stations, to drive the profile reconstruction using a partial-differential-equation-constrained optimization approach. We discuss the solution of the ensuing state, adjoint, and control problems, and the alleviation of profile multiplicity by means of either Tikhonov or Total Variation regularization. We report on numerical experiments using synthetic data that show satisfactory reconstruction of a variety of profiles, including smoothly and sharply varying profiles, as well as profiles exhibiting localized discontinuities. The method is well suited for imaging structures for condition assessment purposes, and can handle either diffusive or localized damage without need for a reference undamaged state.