Large amplitude free vibration analysis of shear deformable FGM shallow arches on nonlinear elastic foundation

Babaei, Hadi; Kiani, Y.; Eslami, Mohammad H.

doi:10.1016/j.tws.2019.106237

Cited by 47 publications

(11 citation statements)

References 43 publications

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“…When modeling the vibrations of structural members containing CNTs, it is important to study the effect of the reinforcement phase and elastic foundations on the frequency-amplitude relationships. Up to date, most works from the literature have been devoted to the solution of linear vibration problems, by means of different numerical techniques [27][28][29][30][31][32][33][34][35]. More specifically, Tornabene et al [27] examined the influence of Winkler-Pasternak foundations on the static and dynamic analysis of laminated double-curved shells and panels using the differential quadrature method.…”

Section: Introductionmentioning

confidence: 99%

“…Dinh and Nguyen [30] applied a fourth-order Runge-Kutta method and Galerkin method to solve the dynamic and vibration problem of FG-CNTRC truncated conical shells on elastic foundations. Shen and He [31] performed a large amplitude vibration analysis of FG-CNTRC double-curved panels on elastic foundation by applying a two-step perturbation approach, as also implemented in [32] to analyze the large amplitude vibration of FG shallow arches on a nonlinear elastic foundation. A further linear formulation was proposed by Sobhy and Zenkour [33] to study the vibrations of FG graphene platelet reinforced composite double-curved shallow shells on an elastic foundation; Sofiyev et al [34,35] investigated the stability of CNTRC conical shells resting on an elastic foundation under hydrostatic pressure and combined loads in different settings.…”

Section: Introductionmentioning

confidence: 99%

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Free Vibration of Thin-Walled Composite Shell Structures Reinforced with Uniform and Linear Carbon Nanotubes: Effect of the Elastic Foundation and Nonlinearity

et al. 2021

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In this work, we discuss the free vibration behavior of thin-walled composite shell structures reinforced with carbon nanotubes (CNTs) in a nonlinear setting and resting on a Winkler–Pasternak Foundation (WPF). The theoretical model and the differential equations associated with the problem account for different distributions of CNTs (with uniform or nonuniform linear patterns), together with the presence of an elastic foundation, and von-Karman type nonlinearities. The basic equations of the problem are solved by using the Galerkin and Grigolyuk methods, in order to determine the frequencies associated with linear and nonlinear free vibrations. The reliability of the proposed methodology is verified against further predictions from the literature. Then, we examine the model for the sensitivity of the vibration response to different input parameters, such as the mechanical properties of the soil, or the nonlinearities and distributions of the reinforcing CNT phase, as useful for design purposes and benchmark solutions for more complicated computational studies on the topic.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Free Vibration of Thin-Walled Composite Shell Structures Reinforced with Uniform and Linear Carbon Nanotubes: Effect of the Elastic Foundation and Nonlinearity

et al. 2021

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“…The three-dimensional vibrational behavior of laminated composite arches and flat beams with variable thickness is analyzed by Tornabene et al [13] on the basis of refined shear deformation theories. Large amplitude free vibration analysis of shallow arches made of FG materials resting on nonlinear elastic foundation is investigated by Babaei et al [14]. A shear deformation theory including logarithmic function of the radius of arch is developed by Fariborz and Batra [15] to obtain the natural frequencies of bi-directional FGM circular curved beams using the GDQ method.…”

Section: Introductionmentioning

confidence: 99%

Study on nonlinear vibrations of temperature- and size-dependent FG porous arches on elastic foundation using nonlocal strain gradient theory

Babaei

Eslami

2021

Eur. Phys. J. Plus

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A nonlocal strain gradient theory is developed in this paper to study the large amplitude vibrations of arches made of functionally graded (FG) porous material. The case of shallow arches resting on nonlinear elastic foundation is modeled via a general higherorder shear deformation theory. The third-order model of Reddy, the first-order model of Timoshenko, and the classical model of Euler-Bernoulli are analyzed. Thermomechanical properties of the arch exposed to the uniform thermal field are assumed to be temperature dependent. The nonlinear motion equations of the arch are established by employing Hamilton's principle and the von Kármán type of geometric nonlinearity. The two-step perturbation technique and the Galerkin method are utilized to solve the nonlinear governing equations. The size-dependent linear and nonlinear frequencies of the arch are obtained for the immovable pinned-pinned boundary conditions. The comparison studies are performed to verify the present solution method with the provided data in the literature, and a good agreement is observed. The novel parametric studies covered in this research include the effects of several parameters such as elastic foundation, nonlocal and length scale parameters, porosity, temperature field, power law index, and geometrical parameters on the frequencies of FG porous arches in detail.

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“…The free vibration and static behavior of functionally graded magnetoelectro-elastic plate were conducted by Vinyas et al 33 Bansal et al 34 studied the Vibration of porous functionally graded plates with geometric discontinuities and partial supports. The mechanical behaviour of functionally graded plates under static and dynamic loading were conducted by Akbarzadeh et al 35 Next, Kiani et al [36][37][38][39][40][41] carried out a study on free vibration of novel structures in which the authors focused on free vibration of long FGM cylindrical panels, Graphene Reinforced Laminated Plates, composite conical panels reinforced with FG-CNTs and FGM shallow arches.…”

Section: Introductionmentioning

confidence: 99%

Effects of lattice stiffeners and blast load on nonlinear dynamic response and vibration of auxetic honeycomb plates

Cong

Quyet

Duc

2021

Proceedings of the Institution of Mechanical Engineers, Part C:

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In this paper, the effects of lattice stiffeners and blast load on nonlinear dynamic response and vibration of auxetic sandwich honeycomb plates on Pasternak elastic foundations are considered. The remarkable point of this study is that the outer surfaces of the system reinforced by lattice stiffeners (including orthogonal stiffeners and oblique stiffeners) are made of functionally graded materials. Based on the analytical solution, the Reddy’s FSDT, the Airy’s stress functions, the Galerkin and the fourth-order Runge-Kutta methods, fundamental frequency, dynamic response and frequency–amplitude curves of the plates reinforced by lattice stiffeners under blast and mechanical loads are determined. Then, the result analyses the effect of lattice stiffeners, blast and mechanical loads, elastic foundations on nonlinear dynamic response and vibration of auxetic honeycomb plates. The optimal angle of oblique stiffeners which maximizes natural frequency and contemporaneously minimizes amplitude when changing geometrical parameters of auxetic honeycomb is also determined.

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Large amplitude free vibration analysis of shear deformable FGM shallow arches on nonlinear elastic foundation

Cited by 47 publications

References 43 publications

Free Vibration of Thin-Walled Composite Shell Structures Reinforced with Uniform and Linear Carbon Nanotubes: Effect of the Elastic Foundation and Nonlinearity

Free Vibration of Thin-Walled Composite Shell Structures Reinforced with Uniform and Linear Carbon Nanotubes: Effect of the Elastic Foundation and Nonlinearity

Study on nonlinear vibrations of temperature- and size-dependent FG porous arches on elastic foundation using nonlocal strain gradient theory

Effects of lattice stiffeners and blast load on nonlinear dynamic response and vibration of auxetic honeycomb plates

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