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Analysis of the associated stress distributions to the nonlinear forced vibrations of functionally graded multi-cracked beams
Mohcine Chajdi 1  
,   Adri Ahmed 2  
,   Khalid El Bikri 1  
,   Rhali Benamar 3  
 
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1
Mohammed V University in Rabat, ENSET - Rabat, MSSM, B.P.6207, Rabat Instituts, Rabat, Morocco,
2
Hassan II University of Casablanca, EST - Casablanca, LMPGI, B.P.8012, Oasis Casablanca, Morocco
3
Mohammed V University in Rabat, EMI - Rabat, LERSIM, B.P.765, Agdal, Rabat, Morocco
CORRESPONDING AUTHOR
Mohcine Chajdi   

Mohammed V University in Rabat, ENSET - Rabat, MSSM, B.P.6207, Rabat Instituts, Rabat, Morocco,
Submission date: 2020-10-23
Final revision date: 2021-02-21
Acceptance date: 2021-02-25
Online publication date: 2021-02-26
Publication date: 2021-02-26
 
Diagnostyka 2021;22(1):101–112
 
KEYWORDS
TOPICS
ABSTRACT
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.
 
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