Buckling and longterm dynamics of a nonlinear model for the extensible beam

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Longtime behavior for oscillations of an extensible viscoelastic beam with elastic external supply

This work is focused on a nonlinear equation describing the oscillations of an extensible viscoelastic beam with fixed ends, subject to distributed elastic external force. For a general axial load $\beta$, the existence of a finite/infinite set of stationary solutions and buckling occurrence are scrutinized. The exponential stability of the straight position is discussed. Finally, the related dynamical system in the history space framework is shown to possess a regular global attractor.Comment: 16 pages, 2 figure

Steady-state solutions for a suspension bridge with intermediate supports

2This work is focused on a system of boundary value problems whose solutions represent the equilibria of a bridge suspended by continuously distributed cables and supported by M intermediate piers. The road bed is modeled as the junction of N=M+1 extensible elastic beams which are clamped each other and pinned at their ends to each pier. The suspending cables are modeled as one-sided springs with stiffness k. Stationary solutions of these doubly nonlinear problems are explicitly and analytically derived for arbitrary k and a general axial load p applied at the ends of the bridge. In particular, we scrutinize the occurrence of buckled solutions in connection with the length of each sub-span of the bridge.openopenGiorgi C.; Vuk E.Giorgi, Claudio; Vuk, Elen

Buckling and longterm dynamics of a nonlinear model for the extensible beam

This work is focused on the longtime behavior of a non linear evolution problem describing the vibrations of an extensible elastic homogeneous beam resting on a viscoelastic foundation with stiffness k>0 and positive damping constant. Buckling of solutions occurs as the axial load exceeds the first critical value, \beta_c, which turns out to increase piecewise-linearly with k. Under hinged boundary conditions and for a general axial load P, the existence of a global attractor, along with its characterization, is proved by exploiting a previous result on the extensible viscoelastic beam. As P<\beta_c, the stability of the straight position is shown for all values of k. But, unlike the case with null stiffness, the exponential decay of the related energy is proved if P<\bar\beta(k), where \bar\beta(k) < \beta_c(k) and the equality holds only for small values of k.Comment: 14 pages, 2 figure

On the extensible viscoelastic beam

This work is focused on the equation \ptt u+\partial_{xxxx}u +\int_0^\infty \mu(s) \partial_{xxxx}[u(t)-u(t-s)]ds- \big(\beta+\|\partial_x u\|_{L^2(0,1)}^2\big)\partial_{xx}u= f describing the motion of an extensible viscoelastic beam. Under suitable boundary conditions, the related dynamical system in the history space framework is shown to possess a global attractor of optimal regularity. The result is obtained by exploiting an appropriate decomposition of the solution semigroup, together with the existence of a Lyapunov functional

Long-Term Damped Dynamics of the Extensible Suspension Bridge

This work is focused on the doubly nonlinear equation, whose solutions represent the bending motion of an extensible, elastic bridge suspended by continuously distributed cables which are flexible and elastic with stiffness k^2. When the ends are pinned, long-term dynamics is scrutinized for arbitrary values of axial load p and stiffness k^2. For a general external source f, we prove the existence of bounded absorbing sets.When f is timeindependent, the related semigroup of solutions is shown to possess the global attractor of optimal regularity and its characterization is given in terms of the steady states of the problem.Comment: 19 pages, 1 figur

Non rectification of heat in graded Si-Ge alloys

We investigate the possibility to obtain a thermal diode with functionally graded Si-Ge alloys. A wire with variable section is considered. After the introduction of a formula giving the thermal conductivity of the wire as a function of the species content and of the diameter of the wire, numerical and analytical results are presented supporting the impracticability to get a thermal diode with the characteristics here considered. However, the present study opens the way to further generalisations amenable to give applicative promising results.Comment: 9 pages, 3 figures, conference pape

Post-stroke dementia - a comprehensive review

Post-stroke dementia (PSD) or post-stroke cognitive impairment (PSCI) may affect up to one third of stroke survivors. Various definitions of PSCI and PSD have been described. We propose PSD as a label for any dementia following stroke in temporal relation. Various tools are available to screen and assess cognition, with few PSD-specific instruments. Choice will depend on purpose of assessment, with differing instruments needed for brief screening (e.g., Montreal Cognitive Assessment) or diagnostic formulation (e.g., NINDS VCI battery). A comprehensive evaluation should include assessment of pre-stroke cognition (e.g., using Informant Questionnaire for Cognitive Decline in the Elderly), mood (e.g., using Hospital Anxiety and Depression Scale), and functional consequences of cognitive impairments (e.g., using modified Rankin Scale). A large number of biomarkers for PSD, including indicators for genetic polymorphisms, biomarkers in the cerebrospinal fluid and in the serum, inflammatory mediators, and peripheral microRNA profiles have been proposed. Currently, no specific biomarkers have been proven to robustly discriminate vulnerable patients (‘at risk brains’) from those with better prognosis or to discriminate Alzheimer’s disease dementia from PSD. Further, neuroimaging is an important diagnostic tool in PSD. The role of computerized tomography is limited to demonstrating type and location of the underlying primary lesion and indicating atrophy and severe white matter changes. Magnetic resonance imaging is the key neuroimaging modality and has high sensitivity and specificity for detecting pathological changes, including small vessel disease. Advanced multi-modal imaging includes diffusion tensor imaging for fiber tracking, by which changes in networks can be detected. Quantitative imaging of cerebral blood flow and metabolism by positron emission tomography can differentiate between vascular dementia and degenerative dementia and show the interaction between vascular and metabolic changes. Additionally, inflammatory changes after ischemia in the brain can be detected, which may play a role together with amyloid deposition in the development of PSD. Prevention of PSD can be achieved by prevention of stroke. As treatment strategies to inhibit the development and mitigate the course of PSD, lowering of blood pressure, statins, neuroprotective drugs, and anti-inflammatory agents have all been studied without convincing evidence of efficacy. Lifestyle interventions, physical activity, and cognitive training have been recently tested, but large controlled trials are still missing

Hysteresis in deformable ferro-electroelastic materials

Within the framework of continuum thermodynamics, the paper develops rate-type models of deformable piezo-ferroelectric materials with the purpose of modeling hysteresis and electro-mechanical cross couplings. To this end constitutive functions are assumed to depend on a set of variables that includes their time derivatives. In order to obtain constitutive equations which are form-invariant within the set of Euclidean frames we follow an invariant formulation in which Lagrangian (or material) rather than Eulerian variables are used. While the second law states that the entropy production is non-negative for every admissible thermodynamic process, here the entropy production is viewed as a non-negative constitutive function