Dynamic Response of a Beam Subjected to Impulsive-like Rotations

Abstract

When a uniform beam is subjected to impulsive-like rotations, equations of motion in the axial and transverse directions of the beam are derived from Hamilton's principle, based on the Euler-Bernoulli hypothesis. By using of linear elasticity and other assumptions, they are simplified and decoupled. An impulsive-like velocity Ω(t) is given by Ω(t) = Ω₀ [1-exp(-ct)] The fundamental equation is transformed into a finite-difference equation and the later is numerically analyzed. The dynamic responses of the beam are obtained for various values of c in the above equation. The variations of the deflection at the beam-tip with time are discussed. The amplitude and period of the cyclic deflection at the beam-tip are obtained for c.