Forced transverse vibration of Rayleigh and Timoshenko double-beam system with effect of compressive axial load

Forced vibration and buckling of a Rayleigh and Timoshenko double-beam system continuously joined by a Winkler elastic layer under compressive axial loading are considered in this paper. Based on the Timoshenko beam theory, deflections of the beams are shown. The general solutions of forced vibrations of beams subjected to arbitrarily distributed continuous loads are found. The analytical solution of forced vibration with associated amplitude ratios is determined. The dynamic responses of the system caused by arbitrarily distributed continuous loads are obtained. Vibrations caused by the harmonic exciting forces are discussed, and conditions of resonance and dynamic vibration absorption are formulated. Thus the beam-type dynamic absorber can be used to suppress the excessive vibrations of corresponding beam systems. The effects of compressive axial load on the forced vibrations of the Rayleigh and Timoshenko double-beam system are discussed for three cases of particular excitation loadings. Numerical results of the present method are verified by comparing with those available in the literature.

► Forced vibrations of double system with compressive axial loading are investigated.
► The governing equations are derived from the dynamic-force equilibrium conditions.
► Changes in steady-state vibrations with effect of axial load are examined.
► Determined analytical solution of forced vibration with rotary and shear effects.
► Stationary, Uniformly distributed and Concentrated force cases are considered.