Numerical analysis of nonlinear free and forced vibrations of buckled curved beams resting on nonlinear elastic foundations

Mohamed, Norhan A.; Eltaher, Mohamed A.; Mohamed, S.A.; Seddek, Laila F.

doi:10.1016/j.ijnonlinmec.2018.02.014

Cited by 69 publications

(23 citation statements)

References 39 publications

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“…In this segment, we exhibit the computational technique employed to solve the nonlinear system of PDEs (14)- (15) with boundary conditions (16). Newton's linearization method (NLM) was utilized to linearize the non-linear system (14)- (16), which was subsequently solved using the differential quadrature method (DQM) [27][28][29][30][31][32][33][34][35][36][37][38][39] and two-point backward finite difference method. Applying NLM on (14)- (16) gives:…”

Section: Hybrid Linearization-differential Quadrature Methods (Hldqm)mentioning

confidence: 99%

“…To solve the linearized system (18)- (19), we employed the DQM using Lagrange interpolation polynomial as our based functions over Chebyshev-Gauss-Lobatto grid points in η-direction and the two-point backward finite difference method in ξ-direction. The problem mesh grid-points (ξ j , η k ) are defined by [30,33,38]:…”

Section: Hybrid Linearization-differential Quadrature Methods (Hldqm)mentioning

confidence: 99%

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The Impact of Sinusoidal Surface Temperature on the Natural Convective Flow of a Ferrofluid along a Vertical Plate

2019

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The spotlight of this investigation is primarily the effectiveness of the magnetic field on the natural convective for a Fe 3 O 4 ferrofluid flow over a vertical radiate plate using streamwise sinusoidal variation in surface temperature. The energy equation is reduplicated by interpolating the non-linear radiation effectiveness. The original equations describing the ferrofluid motion and energy are converted into non-dimensional equations and solved numerically using a new hybrid linearization-differential quadrature method (HLDQM). HLDQM is a high order semi-analytical numerical method that results in analytical solutions in η-direction, and so the solutions are valid overall in the η domain, not only at grid points. The dimensionless velocity and temperature curves are elaborated. Furthermore, the engineering curiosity of the drag coefficient and local Nusselt number are debated and sketched in view of various emerging parameters. The analyzed numerical results display that applying the magnetic field to the ferroliquid generates a dragging force that diminishes the ferrofluid velocity, whereas it is found to boost the temperature curves. Furthermore, the drag coefficient sufficiently minifies, while an evolution in the heat transfer rate occurs as nanoparticle volume fraction builds. Additionally, the augmentation in temperature ratio parameter signifies a considerable growth in the drag coefficient and Nusselt number. The current theoretical investigation may be beneficial in manufacturing processes, development of transport of energy, and heat resources. Mathematics 2019, 7, 1014 2 of 12 naturalistic kind of boundary condition which considers the effectiveness of thermophoresis Brownian movement. Khan and Pop [4] utilized the idea in [3] to contemplate the principal deal with nanofluid flow over an extending sheet. Bachok et al. [5] implemented an investigation of nanofluid flow past a semi-infinite plate. Rashad et al. [6] inspected the enhancement of heat transfer in a Darcy nanofluid convective flow past a porous cone. Rashad et al. [7] also probed the non-Darcy problem of a thermally stratified nanofluid flow over a vertical cylinder. They explored how heat transfer rate declined as the Brownian motion parameter boosted. However, abundant fundamental investigations are performed in this field, as can be seen in [8-13].Magnetic nanofluids (or ferrofluids) are the colloidal suspension of magneto-nanoparticles in a regular fluid (water, kerosene, mineral oil). Ferrofluids are magnetically controllable nanofluids, which contain magnetic nanoparticles, such as iron, cobalt, nickel, magnetite, ferrite, spinel-type. Since ferrofluids can be easily manipulated by means of an external magnetic force, the use of these fluids is promoted in numerous significant industrial applications, such as in vacuum seals, vibration-dampers, loudspeakers, shock absorbers, transformers coolant, and stepper motors [14][15][16][17][18][19]. Hayat et al. [20,21] probed the magneto-flow of Newtonian and viscoelastic nanofluids over ...

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Section: Hybrid Linearization-differential Quadrature Methods (Hldqm)mentioning

confidence: 99%

Section: Hybrid Linearization-differential Quadrature Methods (Hldqm)mentioning

confidence: 99%

The Impact of Sinusoidal Surface Temperature on the Natural Convective Flow of a Ferrofluid along a Vertical Plate

2019

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“…Nonlinearities in piezoceramic actuators are analysed in [43]. Nonlinear free and forced vibrations of beams are investigated in [44]. Nonlinear free vibrations of shells are analysed in [45].…”

Section: Introductionmentioning

confidence: 99%

Vibroimpact mechanism in one separate case

Ragulskis¹,

Ragulskis²

2019

Math. models, eng.

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It is known that in the vibroimpact system at the chosen values of parameters linear relationship between impact velocities and eigenfrequencies may exist. The purpose of this paper is to reveal the qualities of the systems of this type. Investigations are performed by analytical and numerical methods. It is determined that in the systems of this type nonlinear solutions with infinite series of harmonics exist. Multivalued stable and unstable regimes do not exist in the systems. The obtained analytical relationships enabled to reveal new qualities of the systems and to make useful conclusions. Keywords: characteristics of impact velocity and eigenfrequencies, free and decaying vibrations, phase trajectories of motions, harmonics of motions up to infinity.

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“…Pegios et al, (2018) have recently developed a model for finite element free and forced vibration analysis of gradient elastic beam structures. Mohamed et al, (2018) presented a novel numerical procedure for analysis of nonlinear free and forced vibrations of buckled curved beams resting on nonlinear elastic foundations. (Mehmood, 2015) proposed a work using finite element method vibration analysis of frame structure subject to moving loads.…”

Section: Introductionmentioning

confidence: 99%

Forced Vibration Numerical Analysis of Reticulate Systems by Dynamic Finite Element Method

Passoli¹,

Olodo²,

Doko³

et al. 2019

MAS

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This work is devoted to forced vibration numerical analysis of reticulate bar systems. The dynamic finite element method was used for determination of frequencies, displacement amplitudes, rotation angles and the dynamic effort factors. By this method the components of the dynamic rigidity matrix and inertia matrix depend on applied external excitation frequency. Obtained results are compared with those calculated by the classical finite element method as well as by analytical method. It is shown that the dynamic finite element allows for exact solutions to the problems in forced vibration of structures. Accuracy of dynamic finite element solution is verified through obtaining analytical solutions on simple systems. In case of complex systems where analytical calculations are complicated the dynamic finite element can become a universal tool for dynamic analysis.

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Numerical analysis of nonlinear free and forced vibrations of buckled curved beams resting on nonlinear elastic foundations

Cited by 69 publications

References 39 publications

The Impact of Sinusoidal Surface Temperature on the Natural Convective Flow of a Ferrofluid along a Vertical Plate

The Impact of Sinusoidal Surface Temperature on the Natural Convective Flow of a Ferrofluid along a Vertical Plate

Vibroimpact mechanism in one separate case

Forced Vibration Numerical Analysis of Reticulate Systems by Dynamic Finite Element Method

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