Geometrically nonlinear free and forced vibrations analysis of clamped-clamped functionally graded beams with multicracks

Chajdi, Mohcine; Adri, Ahmed; Bikri, Khalid El; Benamar, Rhali

doi:10.1051/matecconf/201821102002

Cited by 4 publications

(2 citation statements)

References 9 publications

(8 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The readers interested in more details on this topic can refer to [23]. The present article is an extension of our previous work [24], based on the single mode approach. The objective was particularly focused on the prediction of the nonlinear frequency response curves in the neighbourhood of the resonances considered.…”

Section: Introductionmentioning

confidence: 93%

See 1 more Smart Citation

Analysis of the associated stress distributions to the nonlinear forced vibrations of functionally graded multi-cracked beams

Chajdi¹,

Adri²,

Bikri³

et al. 2021

Diagnostyka

Self Cite

View full text Add to dashboard Cite

Geometrically non-linear vibrations of functionally graded Euler-Bernoulli beams with multi-cracks, subjected to a harmonic distributed force, are examined in this paper using a theoretical model based on Hamilton's principle and spectral analysis. The homogenisation procedure is performed, based on the neutral surface approach, and reduces the FG beams analysis to that of an equivalent homogeneous multi-cracked beam. The so-called multidimensional Duffing equation obtained and solved using a simplified method (second formulation) previously applied to various non-linear structural vibration problems. The curvature distributions associated to the multi-cracked beam forced deflection shapes are obtained for each value of the excitation level and frequency. The parametric study performed in the case of a beam and the detailed numerical results are given in hand to demonstrate the effectiveness of the proposed procedure, and in the other hand conducted to analyse many effects such as the beam material property, the presence of crack, the vibration amplitudes and the applied harmonic force on the non-linear dynamic behaviour of FG beams.

show abstract

Section: Introductionmentioning

confidence: 93%

“…The basic idea behind this method consists on writing the contribution vector to the non-linear mode considered as Substituting and rearranging permits one to write Eq. (40) in a matrix form as: [24,34] from the single-mode approach application.…”

Section: The Multi-mode Approachmentioning

confidence: 99%

Analysis of the associated stress distributions to the nonlinear forced vibrations of functionally graded multi-cracked beams

Chajdi¹,

Adri²,

Bikri³

et al. 2021

Diagnostyka

Self Cite

View full text Add to dashboard Cite

show abstract

Geometrically nonlinear forced vibrations of fully clamped multi-span beams carrying multiple masses and resting on a finite number of simple supports

Fakhreddine

Adri

Chajdi

et al. 2019

J. Phys.: Conf. Ser.

View full text Add to dashboard Cite

Geometrically nonlinear forced vibrations of fully clamped multi-span beams resting on multiple simple supports and carrying multiple masses may be encountered in many mechanical and civil engineering applications. The theoretical model developed here is based on the Euler-Bernoulli beam theory and the Von Karman geometrical non-linearity assumptions. Harmonic motion is assumed and the nonlinear beam transverse displacement function is expanded as a series of the linear modes, determined by solving first the linear problem. The discretised expressions for the beam total strain and kinetic energies are then derived, and by applying Hamilton’s principle, the problem is reduced to a nonlinear algebraic system solved using an approximate method (the so-called second formulation). The basic function contribution coefficients to the structure non-linear response function and the corresponding backbone curves giving the non-linear amplitude-frequency dependence is determined. Numerical results are given in the neighbourhood of the predominant nonlinear mode shape, based on the single mode approach, for a wide range of vibration amplitudes, showing the effect of the added masses and their locations, as well as the applied uniformly distributed harmonic force on its non-linear dynamic response.

show abstract

Geometrically non-linear forced vibrations of fully clamped functionally graded beams with multi-cracks resting on intermediate simple supports

Chajdi

Fakhreddine

Adri

et al. 2019

J. Phys.: Conf. Ser.

View full text Add to dashboard Cite

The objective of this work is to investigate the non-linear forced dynamic response at large vibration amplitudes of fully clamped functionally graded beams containing a multiple open edge cracks and resting on intermediate simple supports. The theoretical model is based on the Euler-Bernoulli beam theory and the crack rotational spring model. The functionally graded beam properties are supposed to vary continuously through the beam thickness. A homogenization procedure based on the neutral surface approach taking into account the presence of the crack is developed to reduce the problem examined to that of an equivalent isotropic homogeneous multi-cracked beam. In the non-linear analysis, harmonic motion is assumed and the discretized expressions for the beam total strain and kinetic energies are derived by applying Hamilton’s Principle, so as to reduce the problem to a non-linear algebraic system solved using an approximate explicit method previously applied to various non-linear structural vibration problems. Considering the forced vibration case, the non-linear frequency response functions are obtained numerically in the neighbourhood of the predominant non-linear mode shape using a single mode approach. The effects of crack, the beam material gradient and the applied harmonic force are presented and discussed.

show abstract

Geometrically nonlinear free and forced vibrations analysis of clamped-clamped functionally graded beams with multicracks

Cited by 4 publications

References 9 publications

Analysis of the associated stress distributions to the nonlinear forced vibrations of functionally graded multi-cracked beams

Analysis of the associated stress distributions to the nonlinear forced vibrations of functionally graded multi-cracked beams

Geometrically nonlinear forced vibrations of fully clamped multi-span beams carrying multiple masses and resting on a finite number of simple supports

Geometrically non-linear forced vibrations of fully clamped functionally graded beams with multi-cracks resting on intermediate simple supports

Contact Info

Product

Resources

About