Frequency and mode veering phenomena of axially functionally graded non-uniform beams with nonlocal residuals

Sari, Ma’en S.; Shaat, Mohamed; Abdelkefi, Abdessattar

doi:10.1016/j.compstruct.2016.11.093

Cited by 36 publications

(15 citation statements)

References 41 publications

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“…The most important achievements in modelling and analysis of the material and structures were reported in the surveys given by Birman and Byrd [1] and Gupta and Talha [2]. Various problems in dynamic analysis of functionally graded beams were studied in the widespread literature, for instance, in the works [3][4][5][6][7]. A large number of works is devoted also to study vibrations of the beams with localized damages such as cracks [8][9][10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

Effect of piezoelectric patch on natural frequencies of Timoshenko beam made of functionally graded material

Khiem

Hai

Huong

2020

Mater. Res. Express

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The present paper addresses developing the Dynamic Stiffness Method (DSM) for natural frequency analysis of functionally graded beam with piezoelectric patch based on the Timoshenko beam theory and power law of material grading. Governing equations and general solution of free vibration are conducted for the beam element with piezoelectric layer that is modelled as a homogeneous Timoshenko beam. The obtained solution allows establishing dynamic stiffness matrix for modal analysis of FGM beam with bonded piezoelectric distributed sensors/actuators. Effect of thickness and position of the smart sensors/actuators and material parameters on natural frequencies is studied with the aim for dynamic testing and health monitoring of FGM structures. The theoretical developments are validated and illustrated by numerical examples.

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Section: Introductionmentioning

confidence: 99%

Effect of piezoelectric patch on natural frequencies of Timoshenko beam made of functionally graded material

Khiem

Hai

Huong

2020

Mater. Res. Express

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“…The eigenvalue loci veering is mainly due to a rapid variation in the eigenvectors, which would result in either a mode inversion 52 (band inversion 53 ) or a mode localization 54 , 55 (band localization). This is further investigated in Fig.…”

Section: Resultsmentioning

confidence: 99%

Nonreciprocal elasticity and the realization of static and dynamic nonreciprocity

Shaat¹

2020

Sci Rep

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The realization of the mechanical nonreciprocity requires breaking either the time-reversal symmetry or the material deformation symmetry. The time-reversal asymmetry was the commonly adopted approach to realize dynamic nonreciprocity. However, a static nonreciprocity requires—with no any other option—breaking the material deformation symmetry. By virtue of the Maxwell–Betti reciprocal theorem, the achievement of the static nonreciprocity seems to be conditional by the use of a nonlinear material. Here, we further investigate this and demonstrate a novel “nonreciprocal elasticity” concept. We investigated the conditions of the attainment of effective static nonreciprocity. We revealed that the realization of static nonreciprocity requires breaking the material deformation symmetry under the same kinematical and kinetical conditions, which can be achieved only and only if the material exhibits a nonreciprocal elasticity. By means of experimental and topological mechanics, we demonstrate that the realization of static nonreciprocity requires nonreciprocal elasticity no matter what the material is linear or nonlinear. We experimentally demonstrated linear and nonlinear metamaterials with nonreciprocal elasticities. The developed metamaterials were used to demonstrate that nonreciprocal elasticity is essential to realize static nonreciprocal-topological systems. The nonreciprocal elasticity developed here will open new venues of the design of metamaterials that can effectively break the material deformation symmetry and achieve, both, static and dynamic nonreciprocity.

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“…In the current research, the axial direction x is adjusted to be in the interval [0, 1]; hence, the entries of the [D] N matrix will have different values than those given in Equation 2as these entries are functions of the Chebyshev points. Due to its stability, rapid convergence, and accuracy, the CSCM has been successfully utilized to perform the natural vibrations and buckling characteristics of different continuous systems [33][34][35]. When using this method to discretize ordinary and partial differential equations, the n th derivative of an unknown function (the transverse displacement in the current study) is expressed as Dn = (D N ) n .…”

Section: Chebyshev Spectral Collocation Methodsmentioning

confidence: 99%

Transverse Vibration of Functionally Graded Tapered Double Nanobeams Resting on Elastic Foundation

2020

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The natural vibration behavior of axially functionally graded (AFG) double nanobeams is studied based on the Euler–Bernoulli beam and Eringen’s non-local elasticity theory. The double nanobeams are continuously connected by a layer of linear springs. The oscillatory differential equation of motion is established using the Hamilton’s principle and the constitutive relations. The Chebyshev spectral collocation method (CSCM) is used to transform the coupled governing differential equations of motion into algebraic equations. The discretized boundary conditions are used to modify the Chebyshev differentiation matrices, and the system of equations is put in the matrix-vector form. Then, the dimensionless transverse frequencies and the mode shapes are obtained by solving the standard eigenvalue problem. The effects of the coupling springs, Winkler stiffness, the shear stiffness parameter, the breadth and taper ratios, the small-scale parameter, and the boundary conditions on the natural transverse frequencies are carried out. Several numerical examples were conducted, and the authors believe that the results may be interesting in designing and analyzing double and multiple one-dimensional nano structures.

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Frequency and mode veering phenomena of axially functionally graded non-uniform beams with nonlocal residuals

Cited by 36 publications

References 41 publications

Effect of piezoelectric patch on natural frequencies of Timoshenko beam made of functionally graded material

Effect of piezoelectric patch on natural frequencies of Timoshenko beam made of functionally graded material

Nonreciprocal elasticity and the realization of static and dynamic nonreciprocity

Transverse Vibration of Functionally Graded Tapered Double Nanobeams Resting on Elastic Foundation

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