PARAMETRIC RESONANCES OF FRAMED STRUCTURES INDUCED BY A NORMAL RESONANCE

Abstract eng:
Considering the geometric-stiffness effect of beam-element produced by the internal axial force, the beamelement equation of motion is derived by the extended Hamilton’s principle. The global finite-element equations of the framed structures under the periodic loading are assembled as the non-homogeneous Mathieu-Hill equations. The Newmark’s method is introduced to solve the unstable responses of the nonhomogeneous Mathieu-Hill equations. The parametric resonance problem was investigated for some framed structures. The numerical results have shown that a parametric resonance may be induced by a normal resonance. When the normal resonance occurs, the member internal axial force of the framed structure may be amplified during the process of load transmission, and the effect of the parametric resonance is greatly magnified. The consequence of this parametric resonance will be disastrous.

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