Geometrically nonlinear transverse steady-state periodic forced vibration of multi-degree-of-freedom discrete systems with a distributed nonlinearity

Eddanguir, Ahmed; Beidouri, Zitouni; Benamar, Rhali

doi:10.1016/j.asej.2012.03.007

Cited by 9 publications

(9 citation statements)

References 45 publications

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“…where , , , and are, respectively, the general terms of the mass tensor, the linear rigidity tensors corresponding to the spiral and longitudinal vertical springs, and the nonlinear rigidity tensor in MB. The relationships between the expressions for these tensors in DB and MB can be obtained using the transition matrix [Φ] as follows [19,23]:…”

Section: Discrete Modelmentioning

confidence: 99%

“…−1 4 ) 0 = +1 = 0. (B.12)One obvious conclusion coming to sight is that the last expression for the potential energy stored in the ( +1) linear longitudinal springs contains the terms4 , −1 4 , 3 −1 ,−On the other hand, the symmetry relations Advances in Acoustics and Vibration 23 usually encountered in the previous cases examined by the present method, for example,[20,23], are adopted here as follows:…”

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confidence: 99%

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A Discrete Model for Nonlinear Vibration of Beams Resting on Various Types of Elastic Foundations

Khnaijar

Benamar

2017

Advances in Acoustics and Vibration

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This paper presents a discrete physical model to approach the problem of nonlinear vibrations of beams resting on elastic foundations. The model consists of a beam made of several small bars, evenly spaced. The bending stiffness is modeled by spiral springs, and the Winkler soil stiffness is modeled using linear vertical springs. Concentrated masses, presenting the inertia of the beam, are located at the bar ends. Finally, the nonlinear effect is presented by the axial forces in the bars, assumed to behave as longitudinal springs, due to the change in their length induced by the Pythagorean Theorem. This model has the advantage of simplifying parametric studies, because of its discrete nature, allowing any modification in the mass matrix, the stiffness matrix, and the nonlinearity tensor to be made separately. Therefore, once the model is established, various practical applications may be performed without the need of going through all the formulation again. The study of the nonlinear behavior makes the solution of the movement equation rise in complexity. By considering this discrete model and using the linearization method, one can achieve an idealized approach to this nonlinear problem and obtain quite easily approximate solutions.

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Section: Discrete Modelmentioning

confidence: 99%

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confidence: 99%

A Discrete Model for Nonlinear Vibration of Beams Resting on Various Types of Elastic Foundations

Khnaijar

Benamar

2017

Advances in Acoustics and Vibration

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“…Using the multimode and single-mode approaches, Merimi et al [28] studied the case of a cracked beam excited by a harmonic concentrated force. Eddanguir et al [29] used the so-called first formulation to investigate the geometrically nonlinear transverse forced vibration of multidegree-of-freedom systems. Boutahar et al [30] used the iterative method of solution to investigate the nonlinear free vibration of functionally graded annular plates resting on elastic foundations.…”

Section: Introductionmentioning

confidence: 99%

Multimode Analysis of Geometrically Nonlinear Transverse Free and Forced Vibrations of Tapered Beams

Hantati

Adri

Fakhreddine

et al. 2022

Shock and Vibration

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In this study, the geometrically nonlinear free and forced vibrations of tapered beams are investigated on the basis of the Euler-Bernoulli beam theory and the von Karman geometric nonlinearity assumptions. The aim of the analysis is to determine tapered beams nonlinear frequencies and modes, and the associated stress distributions by means of bending moment diagrams. The linear problem is first solved. Then, to tackle the nonlinear problem, the displacement function is expanded as a series of the linear modes and the discrete expressions for the strain and kinetic energies are derived. Assuming a point excitation of the beam, the algebraic nonlinear system obtained based on Hamilton’s principle is solved by an approximate method. The effect of the geometric nonlinearity in both the free and forced cases was illustrated and discussed and the effect of the variation of various tapered beam geometrical parameters. The effect of varying the excitation level was also examined.

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“…Many researchers have studied this behavior both experimentally and theoretically, and often consider sources of nonlinearity in vibrating systems due to the physical nonlinearity, geometric nonlinearity, and nonlinearity of boundary conditions (Sedighi et al., 2012). In several studies, geometric nonlinearity is considered in case of nonlinear transverse vibration (Eddanguir et al., 2012; Jamal-Omidi et al., 2016; Kumar et al., 2015; Rahmouni et al., 2013). In these circumstances, the system is under large deflection, which thus allows the study of free or forced vibrational behavior (Arafat, 1999; Malatkar, 2003; Motallebi et al., 2016; Nayfeh and Nayfeh, 1993; Oliveira and Greco, 2015).…”

Section: Introductionmentioning

confidence: 99%

An experimental study on the nonlinear free vibration response of epoxy and carbon fiber-reinforced composite containing single-walled carbon nanotubes

Jamal‐Omidi

ShayanMehr

2017

Journal of Vibration and Control

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In this paper, the effects of additives of a single-walled carbon nanotube (SWCNT) on the nonlinear free vibration of neat resin and carbon fiber reinforced polymer composites (CFRPs) are investigated experimentally. To establish this purpose a sensitive noncontact setup is designed and prepared. In order to obtain a proper SWCNT dispersion pattern, a simple multistage method is presented to fabricate and test nanocomposite beams. First, the increase in the Young's modulus of the nanocomposites by adding carbon nanotube is investigated using the mechanical bending test and validated with available test results. Next, the nonlinear free vibration behavior of cantilever beams under small to large-deflection is investigated. The results of the vibration tests indicate that the nonlinear vibration behavior of all models is close to homogenous materials with increasing SWCNT. The results also show that transverse initial excitation (displacement) imposed an axial load on the slender beams, which thus leads to an increase in the nonlinear frequency of oscillation. In addition, the increase in frequency bears a relation to the initial displacement. Also, large initial displacements, especially on models without carbon fiber (reinforced epoxy), cause that the convergence of frequencies under different initial excitation did not occur. The results of this study show that adding SWCNT can lead to convergences of frequencies’ hybrid composites and reinforced epoxy during final cycles.

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Geometrically nonlinear transverse steady-state periodic forced vibration of multi-degree-of-freedom discrete systems with a distributed nonlinearity

Cited by 9 publications

References 45 publications

A Discrete Model for Nonlinear Vibration of Beams Resting on Various Types of Elastic Foundations

A Discrete Model for Nonlinear Vibration of Beams Resting on Various Types of Elastic Foundations

Multimode Analysis of Geometrically Nonlinear Transverse Free and Forced Vibrations of Tapered Beams

An experimental study on the nonlinear free vibration response of epoxy and carbon fiber-reinforced composite containing single-walled carbon nanotubes

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