Free vibration analysis of composite beams via refined theories

This paper is a review of the most influential approaches to developing beam models that have been proposed over the last few decades. Essentially, primary attention has been paid to isotropic structures, while a few extensions to composites have been given for the sake of completeness. Classical models -Da Vinci, Euler-Bernoulli and Timoshenko -are described first. All those approaches that are aimed at the improvement of classical theories are then presented by considering the following main techniques: shear correction factors, warping functions, Saint-Venant based solutions and decomposition methods, variational asymptotic methods, the Generalized Beam Theory and the Carrera Unified Formulation (CUF). Special attention has been paid to the latter by carrying out a detailed review of the applications of 1D CUF and by giving numerical examples of static, dynamic and aeroelastic problems. Deep and thin-walled structures have been considered for aerospace, mechanical and civil engineering applications. Furthermore, a brief overview of two recently introduced methods, namely the mixed axiomatic/asymptotic approach and the component-wise approach, has been provided together with numerical assessments. The review presented in this paper shows that the development of advanced beam models is still extremely appealing, due to the computational efficiency of beams compared to 2D and 3D structural models. Although most of the techniques that have recently been developed are focused on a given number of applications, 1D CUF offers the breakthrough advantage of being able to deal with a vast variety of structural problems with no need for ad hoc formulations, including problems that can notoriously be dealt with exclusively by means of 2D or 3D models, such as complete aircraft wings, civil engineering constructions, as well as multiscale and wave propagation analyses. Moreover, 1D CUF leads to a complete 3D geometrical and material modeling with no need of artificial reference axes/surfaces, reduced constitutive equations or homogenization techniques.Key words : Beams, Refined theories, Structural analysis, Carrera Unified Formulation. Historical review of beam theories starting from Leonardo da VinciBeam models have been developed and exploited extensively over the last few decades for the structural analysis of slender bodies, such as columns, arches, blades, aircraft wings and bridges. The three-dimensional (3D) problem, in a beam model, is reduced to a set of one-dimensional (1D) variables, which only depend on the beam-axis coordinate. 1D structural elements, or beam elements, are simpler and computationally more efficient than 2D (plate/shell) or 3D (solid) elements. For instance, in a finite element (FE) scenario, beam models have no aspect ratio constraints. These features make beams still very appealing for the static and dynamic analyses of structures. Over the years, many beam models have been developed according to different approaches. The main contributions to the development of the beam theory are ...

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“…Closed-form solutions have been considered by Giunta et al (2013d). The shell-like capabilities of the 1D CUF were highlighted in this paper.…”

Section: Buckling Free Vibration and Dynamic Response Analysismentioning

confidence: 99%

Recent developments on refined theories for beams with applications

Carrera

Pagani

Petrolo

et al. 2015

Mechanical Engineering Reviews

100

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“…Giunta et al [40]presented a unified formulation for the free vibration and elastic stability analysis of three-dimensional sandwich beams, in which shear deformation, in-and out-of-plane warping and rotary inertia were accounted for. Giunta et al [41]investigated the free vibration of simply supported, cross-ply beams via several higher-order displacement-based theories accounting for non-classical effects. Jun Li et al [42]compared the various shear deformation theories for free vibration of laminated composite beams with general lay-ups.…”

Section: Figure 1 Three Plies With Their Fiber Arranged In Three Diffmentioning

confidence: 99%

Free Vibration Analysis of Composite Laminated Beams

2017

IJERAT

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This study addresses the problem of free vibration of laminated composite beams. Six end boundary conditions for beams are considered: clamped-clamped; hinged-hinged; free-free; clamped-hinged; clamped-free; and hinged-free beams. The problem is analyzed and solved using the energy approach which is formulated by a finite element model. This method of analysis is verified by comparing the numerical results obtained for AS

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“…Various higher order beam theories are introduced in which the straightness assumption is removed and the vanishing of shear stress at the upper and lower surfaces is accommodated. For this purpose, higher order polynomials incorporating either one, or more, extra terms [68][69][70][71][72][73][74] or trigonometric functions [75,76] or exponential functions [77] are included in the expansion of the longitudinal point-wise displacement component through the thickness of the beam. The higher order theories introduce additional unknowns that make the governing equations more complicated and provide the solutions much costly in terms of CPU time.…”

Section: Compact Support Domainmentioning

confidence: 99%

Analysis of Bending Deflections of Functionally Graded Beams by Using Different Beam Theories and Symmetric Smoothed Particle Hydrodynamics

Karamanlı

2016

International Journal of Engineering Technologies IJET

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Free vibration analysis of composite beams via refined theories

Cited by 102 publications

References 24 publications

Recent developments on refined theories for beams with applications

Recent developments on refined theories for beams with applications

Free Vibration Analysis of Composite Laminated Beams

Analysis of Bending Deflections of Functionally Graded Beams by Using Different Beam Theories and Symmetric Smoothed Particle Hydrodynamics

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