1,720,967 research outputs found
Torsional instability in a nonlinear isolated model for suspension bridges with fixed cables and extensible hangers
No full textRegularity for the 3D evolution Navier-Stokes equations under Navier boundary conditions in some Lipschitz domains
Full text linkFor the evolution Navier-Stokes equations in bounded 3D domains, it is well-known that the uniqueness of a solution is related to the existence of a regular solution. They may be obtained under suitable assumptions on the data and smoothness assumptions on the domain (at least C^2,1). With a symmetrization technique, we prove these results in the case of Navier boundary conditions in a wide class of merely Lipschitz domains of physical interest, that we call sectors
Analysis of a nonlinear fish-bone model for suspension bridges with rigid hangers in the presence of flow effects
No full textWe consider a dynamical system of nonlinear partial differential equations modeling the motions of a suspension bridge. This fish-bone model captures the flexural displacements of the bridge deck’s mid-line, and each chordal filament’s rotation angle from the centerline. These two dynamics are strongly coupled through the effect of cable-hanger, appearing through a sublinear function. Additionally, a structural nonlinearity of Woinowsky-Krieger type is included, allowing for large displacements. Well-posedness of weak solutions is shown and long-time dynamics are studied. In particular, to force the dynamics, we invoke a non-conservative potential flow approximation which, although greatly simplified from the full multi-physics fluid-structure interaction, provides a driver for non-trivial end behaviors. We describe the conditions under which the dynamics are uniformly stable, as well as demonstrate the existence of a compact global attractor under all nonlinear and non-conservative effects. To do so, we invoke the theory of quasi-stability, first explicitly constructing an absorbing ball via stability estimates and, subsequently, demonstrating a stabilizability estimate on trajectory differences applied to the aforesaid absorbing ball. Finally, numerical simulations are performed to examine the possible end behaviors of the dynamics
On the Stability of a Nonlinear Nonhomogeneous Multiply Hinged Beam
Full text linkThe paper deals with a nonlinear evolution equation describing the dynamics of a nonhomogeneous
multiply hinged beam, subject to a nonlocal restoring force of displacement type. First, a spectral
analysis for the associated weighted stationary problem is performed, providing a complete system
of eigenfunctions. Then, a linear stability analysis for bimodal solutions of the evolution problem is
carried out, with the final goal of suggesting optimal choices of the density and of the position of
the internal hinged points in order to improve the stability of the beam. The analysis exploits both
analytical and numerical methods; the main conclusion of the investigation is that nonhomogeneous
density functions improve the stability of the structure
Some remarks about a worst-case problem for the torsional response of a plate
No full textWe consider an optimization problem aiming to improve the torsional performance of rectangular plates modeling bridges. The involved functional is the gap function, namely the maximum difference of displacements between the two free edges of the plate. We compute the explicit expression of the gap function for some forces that appear to be the most prone to generate torsional instability in the structure and we exploit it to partially prove a conjecture about a worst-case problem stated in a paper by A. Antunes and F. Gazzola of 2018
The Kernel of the Strain Tensor for Solenoidal Vector Fields with Homogeneous Normal Trace
No full textOn the long-time behaviour of solutions to unforced evolution Navier–Stokes equations under Navier boundary conditions
No full textWe study the asymptotic behaviour of the solutions to Navier–Stokes unforced equations under Navier boundary conditions in a wide class of merely Lipschitz domains of physical interest. The paper draws its main motivation from celebrated results by Foias and Saut (1984) under Dirichlet conditions; here the choice of the boundary conditions requires carefully considering the geometry of the domain Ω, due to the possible lack of the Poincaré inequality in presence of symmetries. In non-axially symmetric domains we show the validity of the Foias–Saut result about the limit at infinity of the Dirichlet quotient, in axially symmetric domains we provide two invariants of the flow which completely characterize the motion and we prove that the Foias–Saut result holds for initial data belonging to one of the invariants
Bridges and Calculus
No full textThe workshop’s goal is to describe analytically and numerically the shape
of cables in two types of suspension bridges. As bridges design and construction are emblematic tasks of engineering, we aim to immerse students in the challenges
and responsibilities of engineering
On the first frequency of reinforced partially hinged plates
Full text linkWe consider a partially hinged rectangular plate and its normal modes. The dynamical properties of the plate are influenced by the spectrum of the associated eigenvalue problem. In order to improve the stability of the plate, we place a certain amount of denser material in appropriate regions. If we look at the partial differential equation appearing in the model, this corresponds to insert a suitable weight coefficient inside the equation. A possible way to locate such regions is to study the eigenvalue problem associated to the aforementioned weighted equation. In this paper, we focus our attention essentially on the first eigenvalue and on its minimization in terms of the weight. We prove the existence of minimizing weights inside special classes and we try to describe them together with the corresponding eigenfunctions
On a 3D eigenvalue problem under Navier slip-with-friction boundary conditions and applications to Navier-Stokes equations
Full text linkIn this paper we consider, by means of a precise spectral analysis, the 3D Navier-Stokes equations endowed with Navier slip-with-friction boundary conditions. We study the problem in a very simple geometric situation as the region between two parallel planes, with periodicity along the two planes. This setting, which is often used in the theory of boundary layers, requires some special treatment for what concerns the functional setting and allows us to characterize in a rather explicit manner eigenvalues and eigenfunctions of the associated Stokes problem. These, will be then used in order to identify infinite dimensional classes of data leading to global strong solutions for the corresponding evolution Navier-Stokes equations
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