Closed-form eigensolutions of nonviscously, nonproportionally damped systems based on continuous damping sensitivity

[EN] In this paper, nonviscous, nonproportional, vibrating structures are considered. Nonviscously damped systems are characterized by dissipative mechanisms which depend on the history of the response velocities via hereditary kernel functions. Solutions of the free motion equation lead to a nonlinear eigenvalue problem involving mass, stiffness and damping matrices. Viscoelasticity leads to a frequency dependence of this latter. In this work, a novel closed-form expression to estimate complex eigenvalues is derived. The key point is to consider the damping model as perturbed by a continuous fictitious parameter. Assuming then the eigensolutions as function of this parameter, the computation of the eigenvalues sensitivity leads to an ordinary differential equation, from whose solution arises the proposed analytical formula. The resulting expression explicitly depends on the viscoelasticity (frequency derivatives of the damping function), the nonproportionality (influence of the modal damping matrix off-diagonal terms). Eigenvectors are obtained using existing methods requiring only the corresponding eigenvalue. The method is validated using a numerical example which compares proposed with exact ones and with those determined from the linear first order approximation in terms of the damping matrix. Frequency response functions are also plotted showing that the proposed approach is valid even for moderately or highly damped systems.Lázaro, M. (2018). Closed-form eigensolutions of nonviscously, nonproportionally damped systems based on continuous damping sensitivity. Journal of Sound and Vibration. 413:368-382. https://doi.org/10.1016/j.jsv.2017.10.011S36838241

Critical damping in nonviscously damped linear systems

[EN] In structural dynamics, energy dissipative mechanisms with nonviscous damping are characterized by their dependence on the time-history of the response velocity, mathematically represented by convolution integrals involving hereditary functions. Combination of damping parameters in the dissipative model can lead the system to be overdamped in some (or all) modes. In the domain of the damping parameters, the thresholds between induced oscillatory and non-oscillatory motion are named critical damping surfaces (or critical manifolds, since several parameters can be involved). In this paper the theoretical foundations to determine critical damping surfaces in nonviscously damped systems are established. In addition, a numerical method to obtain critical curves is developed. The approach is based on the transformation of the algebraic equations, which define implicitly the critical curves, into a system of differential equations. The derivations are validated with three numerical methods covering single and multiple degree of freedom systems.The author gratefully acknowledges the support and help provided by Professor Marcelo Epstein of the University of Calgary (Canada) in the edition of this manuscript during the summer of 2017. The author also acknowledges the support of the Universitat Politecnica de Valencia with its Programa de Apoyo a la Carrera Academica del Profesorado 2017 oriented to Research Stays in other Universities and Research Centers.Lázaro, M. (2019). Critical damping in nonviscously damped linear systems. Applied Mathematical Modelling. 65:661-675. https://doi.org/10.1016/j.apm.2018.09.011S6616756

Exact determination of critical damping in multiple exponential kernel-based viscoelastic single-degree-of-freedom systems

[EN] In this paper, exact closed forms of critical damping manifolds for multiple-kernel-based nonviscous single-degree-of-freedom oscillators are derived. The dissipative forces are assumed to depend on the past history of the velocity response via hereditary exponential kernels. The damping model depends on several parameters, considered variables in the context of this paper. Those parameter combinations which establish thresholds between induced overdamped and underdamped motion are called critical damping manifolds. If such manifolds are represented on a coordinate plane of two damping parameters, then they are named critical curves, so that overdamped regions are bounded by them. Analytical expressions of critical curves are deduced in parametric form, considering certain local nondimensional parameters based on the Laplace variable in the frequency domain. The definition of the new parameter (called the critical parameter) is supported by several theoretical results. The proposed expressions are validated through numerical examples showing perfect fitting of the determined critical curves and overdamped regions.Lázaro, M. (2019). Exact determination of critical damping in multiple exponential kernel-based viscoelastic single-degree-of-freedom systems. Mathematics and Mechanics of Solids. 24(12):3843-3861. https://doi.org/10.1177/1081286519858382S38433861241

Approximate critical curves in exponentially damped nonviscous systems

[EN] In this paper a new approximate numerical method to obtain critical curves in exponentially damped nonviscous systems is proposed. The assumed viscoelastic forces depend on the past history of the velocity response via convolution integrals over exponential kernel functions. Critical surfaces are manifolds in the multidimensional domain defined by the damping parameters, depicting thresholds between the induced oscillatory and non-oscillatory motion. If these surfaces are formed by two parameters, then they are named critical curves. The available method in the literature to construct these curves involves the analytical manipulation of the transcendental matrix determinant, something that can become highly inefficient for large systems. In this paper, it is proved that approximate critical curves can be constructed eliminating the Laplace parameter from two eigenvalue problems: the original one controlled by the dynamical stiffness matrix and another one defined by its derivative respect to the Laplace parameter. The theoretical background of the approach is derived with help of the implicit function theorem. It turns out that the so-found approximate overdamped regions are enclosed by a set of critical curves, which can be derived in parametric form. The proposed method is validated through two numerical examples involving multiple degrees of freedom.Lázaro, M. (2019). Approximate critical curves in exponentially damped nonviscous systems. Mechanical Systems and Signal Processing. 122:720-736. https://doi.org/10.1016/j.ymssp.2018.12.044S72073612

Damping Perturbation Based Time Integration Asymptotic Method for Structural Dynamics

[EN] In this paper a novel time integration numerical method based on artificial perturbation of damping is proposed. Viscous dissipative terms in the structural dynamics equations of motion are perturbed by an artificial parameter. The subsequent asymptotic expansion of the transient response results in an infinite series which can be summed, leading to a well-defined new step-by-step explicit iterative scheme. Precise integration algorithms are designed for the construction of the main matrices. Conditions for convergence and numerical properties, i.e., stability and accuracy are also studied in detail. The proposed approach is validated with a numerical example, showing high accuracy with respect to other existing methods in literature.This research was partially supported by the Grant PID2020-112759GB-I00 funded by MCIN/AEI/10.13039/501100011033. The author is also grateful for the partial support and funding of the open access from the grant CIGE/2021/141 funded by Generalitat Valenciana (Emerging Research Groups Grants) and by the European Social Fund.Lázaro, M. (2022). Damping Perturbation Based Time Integration Asymptotic Method for Structural Dynamics. International Journal of Computational Methods. 19(10):1-33. https://doi.org/10.1142/S0219876222500220133191

La Història Militar de la Corona d’Aragó a la Baixa Edat Mitjana: passat present i futur

La història militar de la Corona d’Aragó començà quan els reis d’Aragó escrigueren les seves cròniques i els seus documents, i diversos historiadores basaren les seves recerques en aquestes fonts. Quan les noves tendències historiogràfiques desenvolupades a mitjan segle XX arribaren a Espanya, la història militar de l’Edat Mitjana va quedar marginada. Aquest article mostra la manera com aquest problema afectà la recerca històrica sobre la Corona d’Aragó a l’Edat Mitjana, i com la disciplina s’està recuperant lentament per a esdevenir un nou i interessant enfocament per al medievalisme.The military history of the Aragon medieval Crown began when the kings of Aragon wrote their chronicles and records, and several historians developed their research on these sources. When the historiographical tendencies developed from the middle of the XXth century arrived in Spain, the military history of the Middle Ages became marginalized. This paper shows the way this problem affected the historical research on the Aragon medieval Crown, and how the discipline is slowly recovering and becoming an interesting new focus for medieval research

Dispositiu naval en una armada del rei d'Aragó. L'exemple de l'estol enviat a Sardenya el 1354

Dins la Mediterrània i l’Europa baixmedievals, les capacitats polítiques i estratègiques de qualsevol poder depenien, entre d’altres factors, d’una organització militar adient. Aquesta, relacionant-se amb els sistemes d’organització social i militar heretats de la societat feudal i de l’adaptació de les monarquies a la seva conjuntura, va transformar radicalment, entre els segles XIII i XV, la manera de fer la guerra. La incorporació de la Corona d’Aragó a aquest procés de canvi polític i militar va ser, sens dubte, decidida, desenvolupada paral·lelament a l’expansió mediterrània i adaptada a les necessitats del joc de les potències europees i mediterrànies de mitjan segle XIV. El funcionament dels estols catalanoaragonesos fou una part importantíssima d’aquest procés històric i està encara pendent de ser estudiat i difós. Aquestes pàgines poden constituir una primera aproximació per a tot aquell qui hi estigui interessat, esperem que contribuint a obrir aquesta petita part de la nostra Història al públic general.Peer reviewe

Vaguerosos e malendrins y ballesters bons e bé atreçats. Notas sobre la infantería de Pedro el Ceremonioso en una armada real a Cerdeña (1354)

Este estudio intenta trazar el perfil de la infantería catalanoaragonesa que sirvió en la campaña llevada a cabo en Cerdeña, en 1354, por Pedro el Ceremonioso, rey de Aragón (1336-1387). Esta expedición militar de la monarquía, que terminó con una victoria de escaso impacto y estuvo a punto de convertirse en una derrota para las fuerzas del rey de Aragón, fue una dura prueba para quienes lucharon en ella, espe- cialmente para quienes combatían a pie. Las características de los infantes se anali- zan desde un amplio punto de vista, que comprende equipamiento, tácticas y capaci- dades de combate, sistemas de reclutamiento, salarios y contexto político, tratando de desarrollar un retrato militar y social de estos combatientes. La campaña de 1354 estuvo relacionada con numerosas transformaciones en el arte militar, en las finanzas y en la burocracia, desarrolladas en la Europa tardomedieval por las monarquías feu- dales, que aumentaron considerablemente sus capacidades militares y políticas. Puesto que la infantería jugó un rol esencial en estos cambios, este estudio trata no sólo de definir algunos de sus rasgos básicos, sino también de sugerir investigaciones que ahonden más en estas evidencias históricas, enmarcadas en procesos de larga duración.Peer reviewe

Les dotacions dels vaixells de l'armada de 1354 : motivacions, context social i costos humans

Aquest treball pretén ser una primera aproximació a un dels aspectes de les armades: la component humana o, dit d’una altra manera –a propòsit per a aquestes pàgines–, la gent. L’abast d’aquest estudi és incomplet, tant temàticament com cronològica, i a canvi prova de definir les línies mestres del funcionament d’un tot a través d’un exemple concret. D’entre la nombrosíssima gent que participa en tot l’entramat d’una armada, he triat només les dotacions que tripulen els vaixells; de les nombroses armades que organitzaren els reis d’Aragó, n’he triat una de les més potents: la que dirigí Pere el Cerimoniós en persona entre 1354 i 1355 per colpir els genovesos i els rebels de Sardenya.Treball realitzat en el marc del projecte «Entre la península Ibèrica i el Mediterrani. Interaccions polítiques, econòmiques i culturals de la Corona d’Aragó en la baixa edat mitjana» (HUM2004-00916), aprovat i finançat per la Direcció General de Ciència y Tecnologia del Ministeri d’Educació i Ciència amb el suport del Departament d’Educació i Universitats de la Generalitat de Catalunya i del Fons Social Europeu.Peer reviewe