A mixed variational formulation based on exact intrinsic equations for dynamics of moving beams

Hodges, Dewey H.

doi:10.1016/0020-7683(90)90060-9

Cited by 442 publications

(296 citation statements)

References 14 publications

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“…Both elements assume small nodal displacements and require a co-rotational or multi-body formulation for geometric nonlinear analysis. A beam element that directly permits large displacement analysis is the mixed variational formulation of Hodges [6].…”

Section: Introductionmentioning

confidence: 99%

Timoshenko Beam Element With Anisotropic Cross-Sectional Properties

Stäblein¹,

Hansen²

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Abstract. Beam models are used for the aeroelastic time and frequency domain analysis of wind turbines due to their computational efficiency. Many current aeroelastic tools for the analysis of wind turbines rely on Timoshenko beam elements with classical crosssectional properties (EA, EI, etc.). Those cross-sectional properties do not reflect the various couplings arising from the anisotropic behaviour of the blade material. A twonoded, three-dimensional Timoshenko beam element was therefore extended to allow for

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Section: Introductionmentioning

confidence: 99%

Timoshenko Beam Element With Anisotropic Cross-Sectional Properties

Stäblein¹,

Hansen²

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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“…Moreover, an increase in flexibility of load carrying structures has been catalysed by the use of composite materials, which has required a parallel effort in developing geometrically-nonlinear composite beam models. Those are typically based on a two step procedure: first, a process of dimensional reduction (homogenisation) in which the three-dimensional composite structure is reduced to averaged properties along the reference line [1][2][3][4], and second the solution of the one-dimensional dynamic equations of motion on the homogenised structure (the composite beam) [5][6][7][8]. The literature on composite beam modelling is quite extensive and it is not the purpose here to present a comprehensive review, which can be found, for instance, in the monograph on the topic by Hodges [9].…”

Section: Introductionmentioning

confidence: 99%

Consistent structural linearisation in flexible-body dynamics with large rigid-body motion

Hesse

Palacios

2012

Computers & Structures

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A consistent linearisation, using perturbation methods, is obtained for the structural degrees of freedom of flexible slender bodies with large rigid-body motions. The resulting system preserves all couplings between rigid and elastic motions and can be projected onto a few vibration modes of a reference configuration. This gives equations of motion with cubic terms in the rigid-body degrees of freedom and constant coefficients which can be pre-computed prior to the time-marching simulation. Numerical results are presented to illustrate the approach and to show its advantages with respect to mean-axes approximations.

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“…Segundo Hodges (1990), as derivadas parciais da energia potencial e da energia cinética Cada variável está associada a um sistema de referência. Na modelagem da pá abordado nesse trabalho, todas as variáveis serão descritas no sistema de coordenadas a.…”

Section: Controle Ativounclassified

“…A deformação e a curvatura (Eqs. 3.6 e 3.7) geralmente são representados como um conjunto de polinômios que apresentam termos de deslocamento linear e orientação angular, levando a relações pesadas indesejáveis, que requerem a truncagem na representação dos termos de alta ordem geométrica (Hodges (1990)). Nesse caso, os multiplicadores de Lagrange são utilizados para transformar as relações cinemáticas em um conjunto de equações restritas com a utilização de rotações nitas virtuais.…”

Section: Controle Ativounclassified

“…As equações de energia interna são integradas espacialmente utilizando o método de elementos nitos. Essa formulação tem a vantagem de garantir a escolha de funções de forma simples para o deslocamento virtual (Hodges (1990)). Desta maneira, a distribuição de variáveis virtuais sobre cada elemento é descrita como uma função linear dos valores nos nós.…”

Section: Controle Ativounclassified

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Atenuação de vibrações em pás de helicópteros utilizando circuito piezelétrico semi-passivo

Anicézio¹

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The use of smart materials in vibration control problems has been investigated in several researches over the last years. Although di erent smart materials are available, the piezoelectric one has received great attention due to ease of use as sensors, actuators, or both. The main control techniques using piezoelectric materials are the active and passive ones. Passive piezoelectric networks are adjusted for speci c target frequencies and, therefore, the e ective bandwidth of such systems is small. Although active systems can achieve good vibration control performance, the amount of external power and added hardware are important issues. The synchronized switch damping (SSD) technique was developed in order to address the issues of passive damping methodologies as well as the issues of active control systems. The SSD can be classi ed as semi-passive technique or semi-active technique that introduce the nonlinear treatment of the piezoelectric element voltage output and induce an increase in mechanical to electrical energy conversion and, consequently, the shunt damping e ect. In this work, the semi-passive piezoelectric control of a rotating cantilever beam response is presented and compared with other controllers. The nonlinear electromechanical model of a rotating beam with embedded piezoceramics is derived based on the variational-asymptotic method (VAM). The coupled non-linear rotary system is solved in the time-domain by using a generalized-alpha integration method in order to guarantee numerical stability. The simulations are performed for a wide range of rotating speeds. First, a set of load resistances (ranging from short circuit condition to open circuit condition) is considered. The e ect of optimum load resistance (for maximum damping) on the elastic behavior of the beam is investigated for increasing rotating speed. Later, the synchronized switch damping on short (SSDS) technique is employed to damp the nonlinear oscillations of the rotating beam with increasing rotating speed. Results show that the SSDS technique can be a useful method of control for nonlinear rotating beams such as helicopter blades.

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A mixed variational formulation based on exact intrinsic equations for dynamics of moving beams

Cited by 442 publications

References 14 publications

Timoshenko Beam Element With Anisotropic Cross-Sectional Properties

Timoshenko Beam Element With Anisotropic Cross-Sectional Properties

Consistent structural linearisation in flexible-body dynamics with large rigid-body motion

Atenuação de vibrações em pás de helicópteros utilizando circuito piezelétrico semi-passivo

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