Geometrically nonlinear dynamic analysis of functionally graded material plate excited by a moving load applying first-order shear deformation theory via generalized differential quadrature method

Nazari, Hesam; Babaei, Masoud; Kiarasi, Faraz; Asemi, Kamran

doi:10.1007/s42452-021-04825-9

Cited by 7 publications

(3 citation statements)

References 39 publications

(40 reference statements)

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“…In this theory, the transverse normal values at the mid-plane of the plate remain straight and rotate such that they do not remain perpendicular to the mid-surface after deformation. Applying the FSDT of the shells, the displacement constituents of the shell are considered to be as follows [71]:…”

Section: Governing Equations (Fsdt-virtual Work Principle)mentioning

confidence: 99%

Free Vibration Analyses of Stiffened Functionally Graded Graphene-Reinforced Composite Multilayer Cylindrical Panel

Zhou,

Zhang,

Nyasha Chirukam

et al. 2023

Mathematics

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In this paper, the free vibration response of a stiffened functionally graded graphene nanoplatelet (GPL)-reinforced composite multilayer cylindrical shell panel is studied for the first time. The shell is stiffened by both stringers and rings. Additionally, the effect of reinforcing the shell panel, ring and stinger with GPLs is independently studied. Halpin–Tsai relations are employed to evaluate the mechanical properties of the shell panel, rings and stringers. The first-order shear deformation shell theory, accompanied by the Lekhnitsky smeared stiffener model, using the numerical finite element method and Hamilton principle, is employed to develop the governing motion equations of the shell panel. Four different types of GPL patterns, including FG-A, FG-X, FG-O and UD, are assumed across the thickness of the shell panel, rings and stringers. The effects of different factors, including various weight fractions and patterns of GPLs nanofillers, the geometry of the shell panel and stiffeners and two displacement boundary conditions, on the natural frequencies of the shell panel, have been studied.

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Section: Governing Equations (Fsdt-virtual Work Principle)mentioning

confidence: 99%

Free Vibration Analyses of Stiffened Functionally Graded Graphene-Reinforced Composite Multilayer Cylindrical Panel

Zhou,

Zhang,

Nyasha Chirukam

et al. 2023

Mathematics

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“…26,27 A TSDT is utilised 28 to analyse the nonlinear dynamic behaviour of FG plates exposed to external dynamic load. FSDT and VKNST are employed in Nguyen et al 29 and Nazari et al 30 for the computation of nonlinear flexural deflection and/or dynamic responses of the FG plates. Similarly, FSDT and GLNST are used to examine the nonlinear transient responses of cylindrical FG panels 31 and porous FG conical panels.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear static and dynamic (deflection/stress) responses of porous functionally graded shell panel and experimental validation

Ramteke

Panda

2023

Proceedings of the Institution of Mechanical Engineers, Part C:

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The static and dynamic characteristics of functionally graded (FG) structures have been investigated in this article, considering full geometrical nonlinearity. The finite element (FE) solutions are obtained for the graded panel by modelling through higher-order kinematics (HSDT) and Green-Lagrange strain-displacement relations (GLNST). The desired graded panel properties are obtained through Voigt’s micromechanical approach, considering different grading patterns (exponential, EPL; sigmoid, SGM and power law, POL). Additionally, to maintain the generality of the graded structure, different porosity distribution types (even and uneven, EVP and UEP) are incorporated into the proposed mathematical model. Further, the numerical solutions are obtained using Newmark’s method’s direct iterative technique and constant integration steps. The solution sensitivities are verified for the developed algorithm via adequate convergence and comparison tests. In addition, the experimental validation is performed using the layerwise fabricated luffa-fibre reinforced FG plates to validate the proposed theoretical model’s accuracy. Lastly, the responses are computed using the newly derived model for the variable design-dependent parameters associated with the FG structural geometry and properties. The final deliverables, that is the nonlinear deflection responses (NDFR)/stress values, are discussed under mechanical loadings (static and dynamic).

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“…Damghanian et al [29], via the application of modified stress theory, investigated the static as well as the dynamic response of a beam element. Nazari et al [30] presented a novel solution technique that was solely based on the shear-deformation theory to explore the lateral response of moving plates. Liu et al [31] compared the dynamic instabilities of clamped and simply supported axially moving nanoplates.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Characteristics of a Small-Size Beam Mounted on an Accelerating Structure

Ali

Hawwa

2023

Micromachines

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This study focuses on the nonlinear vibration of a small-size beam hosted in a high-speed moving structure. The equation of the beam’s motion is derived using the coordinate transformation. The small-size effect is introduced by applying the modified coupled stress theory. The equation of motion involves quadratic and cubic terms due to mid-plane stretching. Discretization of the equation of motion is achieved via the Galerkin method. The impact of several parameters on the non-linear response of the beam is investigated. Bifurcation diagrams are used to investigate the stability of the response, whereas softening/hardening characteristics of the frequency curves are used as an indication of nonlinearity. Results indicate that increasing the magnitude of the applied force tends to signify the nonlinear hardening behavior. In terms of the periodicity of the response, at a lower amplitude of the applied force, the response appears to be a one-period stable oscillation. Increasing the length scale parameter, the response moves from chaotic to period-doubling to the stable one-period response. The impact of the axial acceleration of the moving structure on the stability as well as on the nonlinearity of the response of the beam is also investigated.

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Geometrically nonlinear dynamic analysis of functionally graded material plate excited by a moving load applying first-order shear deformation theory via generalized differential quadrature method

Cited by 7 publications

References 39 publications

Free Vibration Analyses of Stiffened Functionally Graded Graphene-Reinforced Composite Multilayer Cylindrical Panel

Free Vibration Analyses of Stiffened Functionally Graded Graphene-Reinforced Composite Multilayer Cylindrical Panel

Nonlinear static and dynamic (deflection/stress) responses of porous functionally graded shell panel and experimental validation

Dynamic Characteristics of a Small-Size Beam Mounted on an Accelerating Structure

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