Abstract
We investigate the dynamical response of a beam-column system with hinged ends subjected to an axial pulsating force of elliptic type. It is shown that the resulting equation is of the form d 2y 1 dτ 2 +y 1[d 1+d 2cn 2(τ,k 2)]=0, which is the well-known Lamé equation [Higher Transcendental Functions, Bateman Manuscript Project, edited by McGraw-Hill, New York, vol. 3]. In this paper, we obtain the general exact solution of this equation that reveals stable behavior of the beam-column system if the assigned initial conditions are of the form y 1(0)= y 10 and y ̇ 1(0)=0 . It is also found that at a certain value of the modulus of the elliptic force, the lateral vibrational frequency is independent of the material properties of the beam-column system.
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