VI. Free and forced oscillations of continuous beams : Treatment by the admittance method

Abstract

The admittance method is readily applicable to the problem of determining the steady oscillation of a continuous beam of the most general kind due to impressed normal simple harmonic forces, with end thrust or tension present or absent. The method leads to a theorem of three moments, and, when impressed forces are absent, the equation of three moments is homogeneous in the amplitudes of the bending moments at the supports, while the coefficients (the angular admittances) are functions of the frequency. The eliminant of the set of such three moment equations is the frequency equation for the free oscillations of the continuous beam.