Generalized Kelvin–Voigt damping models for geometrically nonlinear beams

Strain-rate-based damping is investigated in the strong form of the intrinsic equations of three-dimensional geometrically exact beams. Kelvin–Voigt damping, often limited in the literature to linear or two-dimensional beam models, is generalized to the three-dimensional case, including rigid-body motions. The result is an elegant infinite-dimensional description of geometrically exact beams that facilitates theoretical analysis and sets the baseline for any chosen numerical implementation. In particular, the dissipation rates and equilibrium points of the system are derived for the most general case and for one in which a first-order approximation of the resulting damping terms is taken. Finally, numerical examples are given that validate the resulting model against a nonlinear damped Euler–Bernoulli beam (where detail is given on how an equivalent description using our intrinsic formulation is obtained) and support the analytical results of energy decay rates and equilibrium solutions caused by damping. Throughout the paper, the relevance of damping higher-order terms, arising from the geometrically exact description, to the accurate prediction of its effect on the dynamics of highly flexible structures is highlighted

Modal-based nonlinear model predictive control for 3D very flexible structures

In this paper a novel NMPC scheme is derived, which is tailored to the underlying structure of the intrinsic description of geometrically exact nonlinear beams (in which velocities and strains are primary variables). This is an important class of PDE models whose behaviour is fundamental to the performance of flexible structural systems (e.g., wind turbines, High-Altitude Long-Endurance aircraft). Furthermore, this class contains the much-studied Euler-Bernoulli and Timoshenko beam models, but has significant additional complexity (to capture 3D effects and arbitrarily large displacements) and requires explicit computation of rotations in the PDE dynamics to account for orientation-dependent forces such as gravity. A challenge presented by this formulation is that uncontrollable modes necessarily appear in any finite dimensional approximation to the PDE dynamics. We show, however, that an NMPC scheme can be constructed in which the error introduced by the uncontrollable modes can be explicitly controlled. Furthermore, in challenging numerical examples exhibiting considerable deformation and nonlinear effects, it is demonstrated that the asymptotic error can be made insignificant (from a practical perspective) usingour NMPC scheme and excellent performance is obtained evenwhen applied to a highly resolved numerical simulation of thePDEs. We also present a generalisation of Kelvin-Voigt dampingto the intrinsic description of geometrically-exact beams. Finally,special emphasis is placed on constructing a framework suitablefor real-time NMPC control, where the particular structure ofthe underlying PDEs is exploited to obtain both efficient finite-dimensional models and numerical schemes

Recent transformation of intertidal environments under a sea-level rise scenario: Examples from northern Spain

The transformation of two intertidal environments from northern Spain during the last 150 years shows an evolution from a tidal flat into a salt marsh environment, with an intermediate transitional stage. The environment of deposition was reconstructed based on benthic foraminifera and sand content. Sediments were put into a temporal framework using short-lived radioisotope activities and heavy metal concentrations. The observed natural evolution responds to the availability of abundant sediment and the current sea-level rise scenario, where intertidal environments are trying to adapt to increasing flooding periods by accreting sediment rapidly. © 2019 Sociedad Geologica de Espana. All rights reserved.This research was funded by the Mi nistry of Economy and Competitiveness of Spain (CGL2013-41083-P), the University of the Basque Country UPV/EHU (UFI11/09), and the Basque Government (IT976-16). Ane García-Artola was funded by the Basque Government (BFI08.180). Miriam Torrontegui Aguado carried out the micropalaeontological analysis of the PR core and Eduardo Leorri (East Carolina University, USA) helped in the field. We thank Juan Usera (Universitat de Valèn-cia), an anonymous reviewer, and Manuel Díaz Azpiroz (Assistant Editor) for their valuable comments. This work represents contribution #29 of the Geo-Q Zentroa Research Unit (Joaquín Gómez de Llarena Laboratory)

Aeroelastic control and estimation with a minimal nonlinear modal description

Modal-based, nonlinear Moving Horizon Estimation (MHE) and Model Predictive Control(MPC) strategies for very flexible aeroelastic systems are presented. They are underpinned by an aeroelastic model built from a 1D intrinsic (based on strains and velocities) description of geometrically-nonlinear beams and an unsteady Vortex Lattice aerodynamic model. Construction of a nonlinear, modal-based, reduced order model of the aeroelastic system, employing a state-space realisation of the linearised aerodynamics around an arbitrary reference point, allows us to capture the main nonlinear geometrical couplings at a very low computational cost. Embedding this model in both MHE and MPC strategies, which solve the system continuous-time adjoints efficiently to compute sensitivities, lays the foundations for real-time estimation and control of highly flexible aeroelastic systems. Finally, the performance and versatility of the framework operating in the nonlinear regime is demonstrated on two very flexible wing models, with notably different dynamics, and on two different control setups: a gust-load alleviation problem on a very high aspect ratio wing with slower dynamics, which involves substantial deflections; and flutter suppression on a flexible wing with significantly faster dynamics, where an unconventional nonlinear stabilisation mechanism is unveiled

The integration of the immigrants in spain and its regions

Este artículo presenta un novedoso sistema de medición de la integración de las personas inmigrantes en las regiones españolas. Complementando en varios aspectos la iniciativa lanzada años atrás por las instituciones europeas (Declaración de Zaragoza), el sistema de medición propuesto comprende 24 indicadores que abarcan cuatro áreas: la situación laboral; las relaciones sociales e intergrupales; el bienestar individual, y el acceso a derechos de ciudadanía. Basándose en un amplio abanico de fuentes secundarias, consigue algo inédito: una completa cobertura estadística a escala infraestatal. El sistema sienta las bases para un seguimiento longitudinal y su ejecución con datos de 2011 permite comprobar el impacto de los primeros años de crisis económica sobre la integración de la población inmigrante. Los resultados señalan cierta ambivalencia, con una situación crecientemente desfavorecida de las personas inmigrantes en los ámbitos de Empleo y Bienestar, en comparación con la población nativa. En cambio, en los ámbitos de Ciudadanía y Relaciones Sociales se observa una evolución positiva, incluso en el periodo de recesión económica. La naturaleza polifacética de estos procesos y las disparidades territoriales dan lugar a tres perfiles regionales distintos.Peer Reviewe

El rey o el papa. La crisis de lealtades del alto clero español a través de la controversia de 1799 en la Rota de la Nunciatura

Este texto examina la crisis del marco de doble lealtad que, durante el Antiguo Régimen, había vinculado al alto clero simultáneamente a la Corona y a la Santa Sede. La aproximación al desequilibrio de esta fidelidad compartida se realiza desde el nivel micro, tomando como ejemplo la controversia que tuvo lugar en la Rota de la nunciatura de España como consecuencia del real decreto de 5 de septiembre de 1799, en virtud del cual los obispos y algunos tribunales regios ejercerían, durante la vacante de la silla pontificia ocasionada por la muerte de Pío VI, algunas facultades reservadas a la Santa Sede. El seguimiento detallado de las trayectorias previas de los participantes en la controversia explica, en buena medida, la postura eclesiológica que sostuvieron.This paper examines the crisis in the long-term relationship model between the Spanish upper clergy, the Crown and the Papacy. Throughout the ancien régime, the high-ranking secular clergy divided its loyalty between two sovereign powers without any major problem. But this double loyalty underwent a crisis in the second half of the eighteenth century, aggravated by the French Revolution and the international political context. The controversy that arose between the members of the Spanish Rota tribunal concerning the royal decree of 1799, which ordered bishops and some royal courts to assume functions reserved to the Holy See, shows on a micro level the factors that led people to choose one loyalty over another