The first frequency of cantilevered bars with geometric effect: a mathematical and experimental evaluation

Wahrhaftig, Alexandre de Macêdo; Brasil, Reyolando Manoel Lopes Rebello da Fonseca; Balthazar, José Manoel

doi:10.1007/s40430-013-0043-9

Cited by 23 publications

(13 citation statements)

References 27 publications

(29 reference statements)

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“…The material behavior is mainly restricted to linear elastic and studies of beam-column problems involving extra-large-deflection, where in-plane force takes upper-hand over transverse one, are discussed quite briefly. On the other hand, vibration characteristic of curved beams under large deformation is a vast research area and several theoretical and experimental studies, for example the papers [10,11], have been published. Hence, dynamic analysis of curved beam incorporating geometrical nonlinearities requires a separate review work and is altogether excluded from the scope of the present paper.…”

Section: Volume 11mentioning

confidence: 99%

A Review on Stress and Deformation Analysis of Curved Beams under Large Deflection

Ghuku

Saha

2017

IJET

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Abstract. The paper presents a review on large deflection behavior of curved beams, as manifested through the responses under static loading. The term large deflection behavior refers to the inherent nonlinearity present in the analysis of such beam system response. The analysis leads to the field of geometric nonlinearity, in which equation of equilibrium is generally written in deformed configuration. Hence, the domain of large deflection analysis treats beam of any initial configuration as curved beam. The term curved designates the geometry of center line of beam, distinguishing it from the usual straight or circular arc configuration. Different methods adopted by researchers, to analyze large deflection behavior of beam bending, have been taken into consideration. The methods have been categorized based on their application in various formats of problems. The nonlinear response of a beam under static loading is also a function of different parameters of the particular problem. These include boundary condition, loading pattern, initial geometry of the beam, etc. In addition, another class of nonlinearity is commonly encountered in structural analysis, which is associated with nonlinear stress-strain relations and known as material nonlinearity. However the present paper mainly focuses on geometric nonlinear analysis of beam, and analysis associated with nonlinear material behavior is covered briefly as it belongs to another class of study. Research works on bifurcation instability and vibration responses of curved beams under large deflection is also excluded from the scope of the present review paper.

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Section: Volume 11mentioning

confidence: 99%

A Review on Stress and Deformation Analysis of Curved Beams under Large Deflection

Ghuku

Saha

2017

IJET

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“…It is worth mentioning that the equation (22) was comparatively evaluated by experimental activity, in physical laboratory, and by modeling using the finite element method -FEM, by Wahrhaftig;Balthazar (2013), and again using the FEM by Wahrhaftig and Brasil (2016), studying the frequency of a real structure, considering for both studies, linear and isotropic elastic material, presenting excellent convergence of results in both cases.…”

Section: V X T X Q T V X T X Q T V X T X Q T V X T X Q T V X T X Q mentioning

confidence: 99%

Creep in the Fundamental Frequency and Stability of a Slender Wooden Column of Composite Section

2016

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-Creep is a phenomenon that can occur in wooden structures since wood is a viscoelastic material. Creep may change the purely elastic parameters determined in wood characterization initial tests, as its behavior depends on the rheology of the material, even under a constant stress level. Mathematically, creep can be characterized by models in which the immediate elastic deformation is increased by a viscous deformation, resulting in a temporal function. For this reason, the calculation of the natural frequency of vibration and the stability verification of a slender column should include the reducing effects of stiffness both of axial force and creep. The first one can be considered through the geometrical portion and the second one by the introduction, in the conventional portion, of a variable elasticity modulus over time, obtained in relation to the adopted rheological model. A numerical simulation was performed to evaluate the aspects above, considering a bar compressed by a force at the free end equivalent to 10% of the Euler critical force, plus its own weight, adopting a rheological model with three parameters for the variation of the elasticity modulus. The results show differences of 60% and 50% for the frequency and elasticity modulus, besides defining the exact instant of column collapse in the case of its non-observance.Keywords: Three-parameter model; Vibration; Stability.A FLUÊNCIA NA FREQUÊNCIA FUNDAMENTAL E NA ESTABILIDADE DE UMA COLUNA ESBELTA DE MADEIRA DE SEÇÃO COMPOSTA RESUMO -A fluência é um fenômeno que pode ocorrer em estruturas de madeira por ser esse um material viscoelástico. A fluência pode alterar os parâmetros puramente elásticos determinados nos ensaios iniciais de caracterização da madeira, pois o seu comportamento depende da reologia do material, mesmo com um nível de tensão constante. Matematicamente, a fluência pode ser caracterizada por modelos onde a deformação elástica imediata é acrescida de uma deformação viscosa, resultando em uma função temporal. Por essa razão, o cálculo da frequência natural de vibração e a verificação da estabilidade de uma coluna esbelta devem incluir os efeitos redutores da rigidez tanto da força axial quanto da fluência. O primeiro pode ser considerado por meio da parcela geométrica e o segundo pela introdução, na parcela convencional, de um módulo de elasticidade variável com o tempo, obtido em relação ao modelo reológico adotado. Para avaliar os aspectos mencionados, foi realizada uma simulação numérica, considerando uma peça comprimida por uma força na extremidade livre equivalente a 10% da força crítica de Euler, mais o seu peso próprio, adotando-se um modelo reológico de três parâmetros para a variação do módulo de elasticidade. Os resultados indicaram diferenças de 60% e 50% para a frequência e para o módulo de elasticidade, além de definir o instante exato de colapso da coluna em caso de sua inobservância.Palavras-chave: Modelo de três parâmetros; Vibração; Estabilidade.

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“…For a more detailed information about the development this analytical procedure Wahrhaftig et all [5] can be consulted.…”

Section: A Quick Overview About the Mathematics Considerationsmentioning

confidence: 99%

Calculating the Frequency of an Actual Structure Using the Rayleigh Technique

Wahrhaftig¹,

Brasil²

2015

Proceedings of the 5th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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The first frequency of cantilevered bars with geometric effect: a mathematical and experimental evaluation

Cited by 23 publications

References 27 publications

A Review on Stress and Deformation Analysis of Curved Beams under Large Deflection

A Review on Stress and Deformation Analysis of Curved Beams under Large Deflection

Creep in the Fundamental Frequency and Stability of a Slender Wooden Column of Composite Section

Calculating the Frequency of an Actual Structure Using the Rayleigh Technique

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