Linear and geometrically nonlinear free and forced vibrations of multi-cracked beams

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

doi:10.29354/diag/103125

Artykuł - szczegóły

Tytuł artykułu

Linear and geometrically nonlinear free and forced vibrations of multi-cracked beams

Autorzy

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

Treść / Zawartość

Pełne teksty:

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Identyfikatory

DOI

10.29354/diag/103125

Warianty tytułu

Języki publikacji

Abstrakty

The linear and geometrically nonlinear free and forced vibrations of Euler-Bernoulli beams with multicracks are investigated using the crack equivalent rotational spring model and the beam transfer matrix method. The Newton Raphson solution of the transcendental frequency equation corresponding to the linear case leads to the cracked beam linear frequencies and mode shapes. Considering the nonlinear case, the beam transverse displacement is expanded as a series of the linear modes calculated before. Using the discretised expressions for the total strain and kinetic energies and Hamilton’s principle, the nonlinear amplitude equation is obtained and solved using the so-called second formulation, developed previously for similar nonlinear structural dynamic problems, to obtain the multi-cracked beam backbone curves and the corresponding amplitude dependent nonlinear mode shapes. Considering the forced vibration case, the nonlinear frequency response functions obtained numerically near to the fundamental nonlinear mode using a single mode approach show the effects of the number of cracks, their locations and depths, and the level of the concentric harmonic force. The inverse problem is explored using the frequency contour plot method to identify crack parameters, such as the crack locations and depths. Satisfactory comparisons are made with previous analytical results.

Słowa kluczowe

nonlinear vibrations multi-crack Euler-Bernoulli beams free vibrations forced vibrations

drgania nieliniowe drgania własne drgania wymuszone teoria Bernoulliego-Eulera

Wydawca

Polskie Towarzystwo Diagnostyki Technicznej

Czasopismo

Diagnostyka

Rocznik

2019

Tom

Vol. 20, No. 1

Strony

111--125

Opis fizyczny

Bibliogr. 58 poz., rys.

Twórcy

autor

Chajdi Mohcine

mohcine.chajdi@um5s.net.ma

Mohammed V University in Rabat, ENSET - Rabat, MSSM, B.P.6207, Rabat Instituts, Rabat, Morocco

autor

Adri Ahmed

ahmedadri@gmail.com

Hassan II University of Casablanca, EST - Casablanca, LMPGI, B.P.8012, Oasis Casablanca, Morocco

autor

El Bikri Khalid

k.elbikri@um5s.net.ma

Mohammed V University in Rabat, ENSET - Rabat, MSSM, B.P.6207, Rabat Instituts, Rabat, Morocco

autor

Benamar Rhali

rhali.benamar@gmail.com

Mohammed V University in Rabat, EMI - Rabat, LERSIM, B.P.765, Agdal, Rabat, Morocco

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Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).

Typ dokumentu

Bibliografia

Identyfikator YADDA

bwmeta1.element.baztech-59471e0f-3f75-47c8-b39c-8d6cce373bda