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

• Autorzy: Moukhliss Anass , Rahmouni Abdellatif , Bouksour Othman , Benamar Rhali

Identyfikatory

DOI

10.29354/diag/155191

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

discrete model; stepped beam; free non-linear vibration; forced nonlinear vibration; AFG beam; point mass

PL

model dyskretny; belka o skokowo zmiennym przekroju; drgania swobodne; drgania wymuszone; drgania nieliniowe

• Wydawca: Polskie Towarzystwo Diagnostyki Technicznej
• Czasopismo: Diagnostyka
• Rocznik: 2022
• Tom: Vol. 23, No. 4
• Strony: art. no. 2022401
• Opis fizyczny: Bibliogr. 15 poz., rys., tab.

Twórcy

autor

Moukhliss Anass

• National Higher School of Electricity and Mechanics, ENSEM, Hassan II University of Casablanca, B.P 8118 Oasis, Casablanca, Morocco

autor

Rahmouni Abdellatif

• Laboratory of Mechanics, Production and Industrial Engineering, LMPGI, Higher School of Technology of Casablanca, ESTC, Hassan II University of Casablanca, B.P 8112 Oasis, Casablanca, Morocco

autor

Bouksour Othman

• Laboratory of Mechanics, Production and Industrial Engineering, LMPGI, Higher School of Technology of Casablanca, ESTC, Hassan II University of Casablanca, B.P 8112 Oasis, Casablanca, Morocco

autor

Benamar Rhali

• Laboratoire des Etudes et Recherches en Simulation, Instrumentation et Mesures LERSIM, Mohammed V University of Rabat-Mohammadia School of Engineering, Avenue Ibn Sina, Morocco

Bibliografia

• 1. Mao Q. Free vibration analysis of multiple-stepped beams by using Adomian decomposition method. Mathematical and Computer Modelling. 2011;54(1-2):756-764. https://doi.org/10.1016/j.mcm.2011.03.019.
• 2. Šalinić S, Obradović A, Tomović A. Free vibration analysis of axially functionally graded tapered, stepped, and continuously segmented rods and beams. Composites Part B: Engineering. 2018; 150:135-143. https://doi.org/10.1016/j.compositesb.2018.05.060.
• 3. Sınır S, Çevik M, Sınır BG. Nonlinear free and forced vibration analyses of axially functionally graded Euler-Bernoulli beams with non-uniform crosssection. Composites Part B: Engineering. 2018;148: 123-131. https://doi.org/10.1016/j.compositesb.2018.04.061.
• 4. Su Z, Jin G, Ye T. Vibration analysis of multiplestepped functionally graded beams with general boundary conditions. Composite Structures. 2018;186:315-323. https://doi.org/10.1016/j.compstruct.2017.12.018.
• 5. Adri A, Benamar R. Linear and geometrically nonlinear frequencies and mode shapes of beams carrying a point mass at various locations. an analytical approach and a parametric study. Diagnostyka. 2017; 18(2):2-9.
• 6. Fakhreddine H, Adri A, Chajdi M, Rifai S, Benamar R. A multimode approach to geometrically non-linear forced vibration of beams carrying point masses. Diagnostyka. 2020;21(4):23-33. https://doi.org/10.29354/diag/128603.
• 7. Rahmouni A, Beidouri Z, Benamar R. A discrete model for geometrically nonlinear transverse free constrained vibrations of beams with various end conditions. Journal of Sound and Vibration. 2013;332(20):5115-5134. https://doi.org/10.1016/j.jsv.2013.04.011.
• 8. Khnaijar A, Benamar R. A discrete model for nonlinear vibrations of a simply supported cracked beams resting on elastic foundations. Diagnostyka, 2017;18(3):2-8.
• 9. Rahmouni A, Benamar R. A homogenization procedure and a physical discrete model for geometrically nonlinear transverse vibrations of a clamped beam made of a functionally graded material. Diagnostyka. 2017; 18(3):2-7.
• 10. Eddanguir A, Beidouri Z, Benamar R. Geometrically nonlinear transverse steady-state periodic forced vibration of multi-degree-of-freedom discrete systems with a distributed nonlinearity. Ain Shams Engineering Journal. 2012;3(3):191-207. https://doi.org/10.1016/j.asej.2012.03.007.
• 11. Moukhliss A, Rahmouni A, Bouksour O, Benamar R. Using the discrete model for the processing of natural vibrations, tapered beams made of afg materials carrying masses at different spots. Materials Today: Proceedings. 2022;52:21-28. https://doi.org/10.1016/j.matpr.2021.10.107.
• 12. Moukhliss A, Rahmouni A, Bouksour O, Benamar R. N-dof discrete model to investigate free vibrations of cracked tapered beams and resting on winkler elastic foundations. International Journal on Technical and Physical Problems of Engineering. 2022;14(1):1-7.
• 13. Merrimi El, El Bikri K, Benamar R. Geometrically non-linear steady state periodic forced response of a clamped-clamped beam with an edge open crack. Comptes Rendus Mécanique. 2011;339(11):727-742. https://doi.org/10.1016/j.crme.2011.07.008.
• 14. Raju KK, Shastry BP, Rao GV. A finite element formulation for the large amplitude vibrations of tapered beams. Journal of Sound and Vibration. 1976;47(4):595-598. https://doi.org/10.1016/0022- 460x(76)90887-7.
• 15. Özkaya E. Non-linear transverse vibrations of a simply supported beam carrying concentrated masses. Journal of Sound and Vibration. 2002;257(3):413-424. https://doi.org/10.1006/jsvi.2002.5042.

Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).