A Novel Approximate Analytical Method for Nonlinear Vibration Analysis of Euler–Bernoulli and Rayleigh Beams on the Nonlinear Elastic Foundation

Rafieipour, Hossein; Tabatabaei, S. Mehrdad; Abbaspour, Mohammad

doi:10.1007/s13369-014-0962-5

Cited by 7 publications

(2 citation statements)

References 10 publications

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“…A Cartesian coordinate system (x, y, z) is selected in the central cross section of the beam, in which the x, y and z are along the length, width and height direction, respectively. Therefore, the displacement field based on the EBB theory is as follows [16]:…”

Section: Euler-bernoulli Beam Theorymentioning

confidence: 99%

Dynamic Response of Viscoelastic CNT Conveying Pulsating Fluid Considering Surface Stress and Magnetic Field

et al. 2015

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A viscoelastic carbon nanotube (CNT) conveying pulsating fluid is presented which is based on EulerBernoulli beam theory. Runge-Kutta scheme is chosen in order to illustrate the transverse and longitudinal behavior of structure. The effects of surface stress, magnetic field and nonlocal small-scale theory on motion of structure are expressed in this study. Equilibrium equations of CNT conveying pulsating fluid are obtained using energy method. Galerkin, differential quadrature and Runge-Kutta methods are applied to solve equations of motion. In this paper, the effect of pulsating fluid on longitudinal behavior of CNT and transverse displacement of CNT are presented. The static and dynamic transverse distributed loads and their effects on CNT are expressed. In this study, regions of CNT with chaotic, quasi-periodic and periodic behaviors are presented. Also the effects of various parameters such as distributed loads, surface stress and magnetic field on those regions are demonstrated. The results of this work could be helpful in design and manufacturing of nano-/micromechanical system in advanced medical applications such as drug delivery systems with magnetic field as a parametric controller.

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Section: Euler-bernoulli Beam Theorymentioning

confidence: 99%

Dynamic Response of Viscoelastic CNT Conveying Pulsating Fluid Considering Surface Stress and Magnetic Field

et al. 2015

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“…Pakar and Bayat (2013) applied a max-min approach, also by He, to investigate the nonlinear vibrational response of Euler-Bernoulli beams subjected to an axial load. Nonlinear behavior of Euler-Bernoulli beam with different end conditions has also been studied by Rafieipour et al (2014) using Laplace iteration method. Lindstedt-Poincare techniques for non linear vibrational analysis have been employed to double-clamped and simply-supported beams subjected to an axial load by Ahmadian et al (2009).…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Vibration Analysis of Euler-Bernoulli Beams by Using Continuous Galerkin-Petrov Time-Discretization Method

Khan

Kaneez

2017

Lat. Am. j. solids struct.

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In this paper, we present a new numerical method for nonlinear vibrational analysis of Euler-Bernoulli beams. Our approach is based on the continuous Galerkin-Petrov time discretization method. The Euler-Bernoulli beam equation which governs its vibrations is transformed into set of ordinary differential equations and the presented method is employed in order to investigate the vibrational response. A comparison is made between present method and different other methods available in literature. It is observed that the obtained results are in strong agreement with other results in literature. We conclude that the present method has a great potential to deal with nonlinear vibration analysis problems of beams and related structures like rods and shafts.

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On the geometrically nonlinear vibration of a piezo‐flexomagnetic nanotube

Malikan

Eremeyev

2020

Math Methods in App Sciences

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In order to describe the behavior of thin elements used in micro‐electro‐mechanical systems (MEMS) and nano‐electro‐mechanical systems (NEMS), it is essential to study a nonlinear free vibration of nanotubes under complicated external fields such as magnetic environment. In this regard, the magnetic force applied to the conductive nanotube with piezo‐flexomagnetic elastic wall is considered. By the inclusion of Euler‐Bernoulli beam and using Hamilton's principle, the equations governing the system are extracted. More importantly, a principal effect existed in a nonlinear behavior such as axial inertia is thoroughly analyzed which is not commonly investigated. We then consider the effects of nanoscale size using the nonlocal strain gradient theory (NSGT). Hereafter, the frequencies are solved as semianalytical solutions on the basis of Rayleigh‐Ritz method. The piezo‐flexomagnetic nanotube (PF‐NT) is calculated with different boundary conditions. In order to validate, the results attained from the present solution have been compared with those available in the open literature. We realized that the nonlinear frequency analysis is so significant when a nanotube has fewer degrees of freedom at both ends and its length is long.

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A Novel Approximate Analytical Method for Nonlinear Vibration Analysis of Euler–Bernoulli and Rayleigh Beams on the Nonlinear Elastic Foundation

Cited by 7 publications

References 10 publications

Dynamic Response of Viscoelastic CNT Conveying Pulsating Fluid Considering Surface Stress and Magnetic Field

Dynamic Response of Viscoelastic CNT Conveying Pulsating Fluid Considering Surface Stress and Magnetic Field

Nonlinear Vibration Analysis of Euler-Bernoulli Beams by Using Continuous Galerkin-Petrov Time-Discretization Method

On the geometrically nonlinear vibration of a piezo‐flexomagnetic nanotube

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