Multistability and localization in forced cyclic symmetric structures modelled by weakly-coupled Duffing oscillators

Many engineering structures are composed of weakly coupled sectors assembled in a cyclic and ideally symmetric configuration, which can be simplified as forced Duffing oscillators. In this paper, we study the emergence of localized states in the weakly nonlinear regime. We show that multiple spatially localized solutions may exist, and the resulting bifurcation diagram strongly resembles the snaking pattern observed in a variety of fields in physics, such as optics and fluid dynamics. Moreover, in the transition from the linear to the nonlinear behaviour isolated branches of solutions are identified. Localization is caused by the hardening effect introduced by the nonlinear stiffness, and occurs at large excitation levels. Contrary to the case of mistuning, the presented localization mechanism is triggered by the nonlinearities and arises in perfectly homogeneous systems

Reconstruction of governing equations from vibration measurements for geometrically nonlinear systems

© 2019 by the authors. Data-driven system identification procedures have recently enabled the reconstruction of governing differential equations from vibration signal recordings. In this contribution, the sparse identification of nonlinear dynamics is applied to structural dynamics of a geometrically nonlinear system. First, the methodology is validated against the forced Duffing oscillator to evaluate its robustness against noise and limited data. Then, differential equations governing the dynamics of two weakly coupled cantilever beams with base excitation are reconstructed from experimental data. Results indicate the appealing abilities of data-driven system identification: underlying equations are successfully reconstructed and (non-)linear dynamic terms are identified for two experimental setups which are comprised of a quasi-linear system and a system with impacts to replicate a piecewise hardening behavior, as commonly observed in contacts

A probabilistic model of uncertainties in the substructures and interfaces of a dynamical system: application to the torsional vibration of a drill-string

International audienceIn this paper a new strategy for modeling uncertainties in the substructures and interfaces of a dynamical system is presented. This strategy is based on (1) the reduction of the dynamical model of each substructure using the Craig-Bampton method and (2) the use of the nonparametric probabilistic approach for the global modeling of uncertainties in each substructure. As an improvement with respect to existing nonparametric methods, the methodology proposed here constructs separated models of uncertainties for the inner and interface degrees of freedom, which allows to control separately the levels of fluctuation induced by these two sources of uncertainties. This methodology is applied for the analysis of the random vibration of a drill-string. Three strategies are compared: (1) a full nonparametric probabilistic approach on all the system, (2) the existing nonparametric probabilistic approach together with the Craig-Bampton substructuring method, and (3) the new nonparametric probabilistic approach proposed here with the separation of the inner and interface degrees of freedom uncertainties. It turns out that, for the same level of uncertainty, the three approaches give similar results but the new approach gives more flexibility for the control of the probabilistic model

Solitons in Cyclic and Symmetric Structures

International audienceThis research focuses on localised states arising from modulationally unstable plane waves in non-conservative cyclic and symmetric structures. The main application is on vibrations of bladed-disks of aircraft engines experiencing non-linear effects, such as large displacements, friction dissipation, and/or complex fluid-structure interactions. The investigation is based on a minimal model composed of a chain of linearly damped Duffing oscillators under external travelling wave excitation. The computed results are based on two strategies: (1) a Non-Linear Schrödinger Equation (NLSE) approximation; and (2) the periodic and quasi-periodic Harmonic Balance Methods (HBM). In both cases, the results show that unstable plane waves may self-modulate, leading to stable and unstable single and multiple solitons configurations

Nonlinear vibration localisation in a symmetric system of two coupled beams

We report nonlinear vibration localisation in a system of two symmetric weakly coupled nonlinear oscillators. A two degree-of-freedom model with piecewise linear stiffness shows bifurcations to localised solutions. An experimental investigation employing two weakly coupled beams touching against stoppers for large vibration amplitudes confirms the nonlinear localisation

Unión Ibero-Americana, Año XXIX, Núm. 4

44 páginasGRABADOS: Dr. Feliciano Viera, nuevo Presidente del Uruguay.- Excmo. Sr. D. Carlos Menéndez, Presidente de la República del Salvador.- Argentina: Casa particular en Buenos Aires.- Dr. José Ingegnieros, Ilustre psiquiatra y criminólogo argentino.- Perú: Llamas cargadas.- Vistas de España: La Catedral de Burgos.- República Argentina: Plaza de Salta.- Haití: Una calle de Puerto Príncipe. TEXTO: Noticias de España (Discurso de S. M. el Rey; Mariano de Cávia, enfermo; Comercio exterior en 1914; para el Centenario de Cervantes; Reforma en la Lista de Correos; La industria siderúrgica.- Las dos industrias, por José Echegaray.- Del Uruguay: Programa del nuevo Presidente.- Viaje del General Reyes por España.- Plegaria (poesía), por Delmira Agustini.- La riqueza española y la guerra, por César Cervera Cerezuela.- La República de El Salvador: Nuevo período presidencial de 1915-1919. Entrega del mando; D. Carlos Meléndez, por F. J. Rivas, Por España.- Americanos ilustres: José Ingegnieros, por Alejandro Navas G.- Impresiones de un pensionado español: Intereses históricos: América, Colón, España, por José M. Fontanela.- Concurso para una novela americana.- El águila y la hoja (poesía), por Santiago Arguello.- EI ausentismo, por Italo Luis Grassi.- El Congreso de neutrales: Iniciativa diplomática de Venezuela, por José María Barreto.- Un discurso de Don Quijote en manos de los soldados.- Literatura argentina, por Emilio Alonso Criado.- IV Centenario del descubrimiento del Pacífico: Catálogo de la exposición, celebrada en el Archivo General de Indias en1913 y 1914, por Pedro Torres Lanzas.- Anales de la Escena española, desde 1750, por Narciso Díaz de Escovar.- Libros Nacionales y extranjeros, por Antonio Balbín de Unquera y M. Valdemoro.- Giro postal hispanoamericano. – Biobibliografía, por Mario Méndez Bejarano.- Anuncios