Using the discrete model for the processing of natural vibrations, tapered beams made of AFG materials carrying masses at different spots

Moukhliss, Anass; Rahmouni, Abdellatif; Bouksour, Otmane; Benamar, Rhali

doi:10.1016/j.matpr.2021.10.107

Cited by 2 publications

(5 citation statements)

References 7 publications

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“…It is considered that the motion of the system is harmonic according to the law [7], [8], [11], [12]:…”

Section: Description Of the Discrete Modelmentioning

confidence: 99%

“…If we take into account the n point masses, we apply a parameter ηi (normalized mass), which is defined as the ratio of the concentric mass' intensity located at the abscissa Xi and the mass of a homogeneous and uniform beam (also named reference mass) of section S1 and density ρ1. [11] (Related to the cross-section located at x=0).…”

Section: Description Of the Discrete Modelmentioning

confidence: 99%

“…The expression of the potential energy stored in the N+2 spiral springs of the N-Dof system is given by [7], [11]:…”

Section: Description Of the Discrete Modelmentioning

confidence: 99%

“…The elementary potential energy dVbr stored in SAFGB, corresponding to an elementary bar in the continuous beam of length 𝑑𝑥 , is given by [7], [11], [12]:…”

Section: Description Of the Discrete Modelmentioning

confidence: 99%

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A discrete model for geometrically nonlinear free and forced vibrations of stepped and continuously segmented Euler-Bernoulli AFG beams (SAFGB) carrying point masses

Moukhliss¹,

Rahmouni²,

Bouksour³

et al. 2022

Diagnostyka

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A discrete model is applied to handle the geometrically nonlinear free and forced vibrations of beams consisting of several different segments whose mechanical characteristics vary in the length direction and contain multiple point masses located at different positions. The beam is presented by an N degree of freedom system (N-Dof). An approach based on Hamilton's principle and spectral analysis is applied, leading to a nonlinear algebraic system. A change of basis from the displacement basis to the modal basis has been performed. The mechanical behavior of the N-Dof system is described in terms of the mass tensor mij, the linear stiffness tensor kij, and the nonlinear stiffness tensor bijkl. The nonlinear vibration frequencies as functions of the amplitude of the associated vibrations in the free and forced cases are predicted using the single mode approach. Once the formulation is established, several applications are considered in this study. Different parameters control the frequency-amplitude dependence curve: the laws that describe the variation of the mechanical properties along the beam length, the number of added masses, the magnitude of excitation force, and so on. Comparisons are made to show the reliability and applicability of this model to non-uniform and non-homogeneous beams in free and forced cases.

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“…It is considered that the motion of the system is harmonic according to the law [7], [8], [11], [12]:…”

Section: Description Of the Discrete Modelmentioning

confidence: 99%

Section: Description Of the Discrete Modelmentioning

confidence: 99%

“…The expression of the potential energy stored in the N+2 spiral springs of the N-Dof system is given by [7], [11]:…”

Section: Description Of the Discrete Modelmentioning

confidence: 99%

“…The elementary potential energy dVbr stored in SAFGB, corresponding to an elementary bar in the continuous beam of length 𝑑𝑥 , is given by [7], [11], [12]:…”

Section: Description Of the Discrete Modelmentioning

confidence: 99%

See 2 more Smart Citations

A discrete model for geometrically nonlinear free and forced vibrations of stepped and continuously segmented Euler-Bernoulli AFG beams (SAFGB) carrying point masses

Moukhliss¹,

Rahmouni²,

Bouksour³

et al. 2022

Diagnostyka

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“…Moukhliss et al 27 constructed the axial FGM model for a tapered beam. The linear free vibration analysis was performed with discrete mass placement at different points.…”

Section: Introductionmentioning

confidence: 99%

Natural Frequencies of a Viscoelastic Supported Axially Functionally Graded Bar With Tip Masses

Demir¹

2023

The International Journal of Acoustics and Vibration

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The frequency parameters of an Axially Functionally Graded (AFG) bar for viscoelastic and point mass boundary conditions are studied in this paper. The structures with functionally graded materials under axial loads can be modelled as AFG bars. Those may be considered as support elements with spring and dashpot in the vibration isolation. Keeping the ratio of force frequency and natural frequency at a certain level is ensured to control the natural frequency therefore dynamic amplification factor with different material combinations. Various boundary conditions are attained by changing the spring and damping coefficients of viscoelastic support elements and the ratio of rod mass to tip mass. Researchers assume that the beam material properties in directions of length and thickness change exponentially, individually, or both in their studies. There are a few studies on the AFG rods in the existing studies. Analysis is carried out via the finite element method for the non-dimensional frequency parameters of the bar in MATLAB. The energy equations of the motion are obtained in the frame of axial bar theory considering the material properties of the bar vary longitudinally according to the power-law distribution. The effects of material distribution, spring, damping and tip mass values on the bar's frequency parameters and structural behaviour have been extensively investigated.

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Using the discrete model for the processing of natural vibrations, tapered beams made of AFG materials carrying masses at different spots

Cited by 2 publications

References 7 publications

A discrete model for geometrically nonlinear free and forced vibrations of stepped and continuously segmented Euler-Bernoulli AFG beams (SAFGB) carrying point masses

A discrete model for geometrically nonlinear free and forced vibrations of stepped and continuously segmented Euler-Bernoulli AFG beams (SAFGB) carrying point masses

Natural Frequencies of a Viscoelastic Supported Axially Functionally Graded Bar With Tip Masses

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