Natural oscillations of single span beam placed on cylindrical supports

Abstract

Oscillations of a single spanbeam placed on two circular cylindrical supports are investigated. Contact line of the beam and the support surface changes its location therefore the span length also alternates. Nonlinear equa-tion of motion is transformed to linear differential equa-tion, where displacement instead of time is the independent variable and the first integral in a phase plane velocity-displacement is deduced. Dependence of displacement on time is expressed in Jacobian elliptic functions in the second integral. The complete period of the oscillations is almost the same as when supports are hinges but the half-periods and the half-amplitudes in upper and lower portions of the motion are significantly distorted. The level of the distortion is increasing when amplitude of oscillations and radius of the support circle are growing. The beam, placed on cylindrical supports, oscillates about a center shifted up compared with the same hinged beam.

DOI: http://dx.doi.org/10.5755/j01.mech.20.3.6365