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The objective of this paper is to present an analytical methodology to evaluate the dynamic phenomena produced by the interaction between the initial curvature of a beam and the occurrence of parametric resonance under the condition when the excitation created by the motion of the attached mass is near the fundamental mode of vibration. In the analysis, a mass traveling with constant speed is assumed. The method of multiple time scales is employed to obtain the weak form of the occurrence of parametric resonance of a beam-mass system with an initially curved beam under primary resonance. Result of present study indicates that under certain conditions, the interaction between the geometric imperfection of beam and the parametric resonance plays an important role to the dynamics of the system.

journal of solid mechanics and materials engineering

The Dynamics of a Beam-Mass System due to the Interaction between the Initial Curvature of the Beam and the Existence of Parametric Resonance under Primary Resonance