Recursive differentiation method: application to the analysis of beams on two parameter foundations

• Autorzy: Hassan M. T. , Doha E. H.

Identyfikatory

DOI

10.15632/jtam-pl.53.1.15

• Języki publikacji: EN

Abstrakty

EN

The recursive differentiation method (RDM) is introduced and employed to obtain analytical solutions for static and dynamic stability parameters of beams resting on two-parameter foundations in various different end conditions. The present analysis reflects the reliability, efficiency and simplicity of the proposed RDM in tackling boundary value problems. In fact, it is widely common that the critical load accompanied with the first buckling mode is the smallest critical load, and then it is the dominant factor in the static stability analysis. In contrast, the present analysis indicates that such a conclusion is correct only for the case of beams without foundations or in the case of a weak foundation relative to the beam. It is proved that critical loads accompanied with higher buckling modes may be smaller than those accompanied with the lower modes and then it may control the stability analysis. The same phenomenon exists for natural frequencies in the presence of an axial load. Several illustrations are introduced to highlight the effects of both the foundation stiffness and beam slenderness on the critical loads and natural frequencies.

Słowa kluczowe

EN

critical loads; natural frequencies; recursive differentiation method; beam on elastic foundation

• Wydawca: Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
• Czasopismo: Journal of Theoretical and Applied Mechanics
• Rocznik: 2015
• Tom: Vol. 53 nr 1
• Strony: 15--26
• Opis fizyczny: Bibliogr. 22 poz., rys., tab.

Twórcy

autor

Hassan M. T.

• Cairo University, Faculty of Engineering, Giza, Egypt

autor

Doha E. H.

• Cairo University, Faculty of Science, Giza, Egypt

Bibliografia

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