Journal of Theoretical
and Applied Mechanics
Mohamed Taha Hassan
Cairo University, Faculty of Engineering, Giza, Egypt Eid Hassan Doha
e-mail: firstname.lastname@example.org; email@example.com
Cairo University, Faculty of Science, Giza, Egypt
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.
critical loads, natural frequencies, recursive differentiation method, beam on elastic foundation
Table of Contents of Vol 53, no.