Numerical investigation of geometrically nonlinear clamped uniform rods and rods with sections varying exponentially free vibration

• Autorzy: Abdeddine E. , Majid A. , Bouzida N. , Bouzida Z. , Zarbane Kh.

Identyfikatory

DOI

10.5604/01.3001.0016.0703

• Języki publikacji: EN

Abstrakty

EN

Purpose: The present paper is intended to investigate the problem of linear and non-linear longitudinal free vibration of uniform rods and rods whose cross-sections vary exponentially at large vibration amplitudes. Design/methodology/approach: The method adopted consists in discretizing the energy term on linear kij and non-linear rigidity tensor bijkl, as well as the mass tensor mij. Therefore, the formulation of this structure is based on Lagrange equations and the harmonic balance method so as to obtain the nonlinear algebraic equations. These latter are solved numerically and analytically through the explicit and linearized method. Findings: The response of Clamped-Clamped uniform and non-uniform rods on our structure are highlighted in the amplitude frequency and associated first three mode shapes. Moreover, this research leads to study the influence of the exponential slope on the maximum displacement, thus emphasizing the non-uniform bars usefulness. The obtained results are then compared with the available literature with a view to validating this theory. Research limitations/implications: As a perspective, the method used in this paper would be pushed to study the FDM material, taking into account other parameters related to additive manufacturing, and later to be validated experimentally. Practical implications: Longitudinal vibrations are important in mechanical structures; therefore, the determination of their dynamic behaviour needs to be understood. In the present study, the effect of the displacement amplitude on the exponential slope of the structure was analysed, which led to the determination of the reduction range of the vibration amplitude under resonance. However, this should be taken into account in the design process. Besides, the usefulness of the non-linearity geometric effects was demonstrated to examine these structures by considering all the parameters involved. Originality/value: A linearized procedure is used to solve a nonlinear algebra equation. The use of this method leads to reduce calculation time contrary to iterative methods.

Słowa kluczowe

EN

non-linear longitudinal vibration; Lagrange equations; harmonic balance method; linearized approach

PL

drgania nieliniowe; drgania podłużne; równania Lagrange'a; metoda bilansu harmonicznych; podejście linearne

• Wydawca: International OCSCO World Press
• Czasopismo: Journal of Achievements in Materials and Manufacturing Engineering
• Rocznik: 2022
• Tom: Vol. 112, nr 2
• Strony: 49--63
• Opis fizyczny: Bibliogr. 32 poz., rys., tab., wykr.

Twórcy

autor

Abdeddine E.

• Laboratory of Advanced Research in Industrial and Logistic Engineering (LARILE), National Higher School of Electricity and Mechanics, Hassan II University of Casablanca, Km7 Route El Jadida, Casablanca, Morocco

• https://orcid.org/0000-0002-0385-3928

autor

Majid A.

• Laboratory of Advanced Research in Industrial and Logistic Engineering (LARILE), National Higher School of Electricity and Mechanics, Hassan II University of Casablanca, Km7 Route El Jadida, Casablanca, Morocco

autor

Bouzida N.

• Laboratory of Advanced Research in Industrial and Logistic Engineering (LARILE), National Higher School of Electricity and Mechanics, Hassan II University of Casablanca, Km7 Route El Jadida, Casablanca, Morocco

autor

Bouzida Z.

• Laboratory of Advanced Research in Industrial and Logistic Engineering (LARILE), National Higher School of Electricity and Mechanics, Hassan II University of Casablanca, Km7 Route El Jadida, Casablanca, Morocco

autor

Zarbane Kh.

• Laboratory of Advanced Research in Industrial and Logistic Engineering (LARILE), National Higher School of Electricity and Mechanics, Hassan II University of Casablanca, Km7 Route El Jadida, Casablanca, Morocco

• https://orcid.org/0000-0002-6048-5279

Bibliografia

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Uwagi

PL

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).