Effect of rotary inertia and shear on vibration and buckling of a double beam system under compressive axial loading. (English) Zbl 1271.74187

Summary: Free transverse vibration and buckling of a double-beam continuously joined by a Winkler elastic layer under compressive axial loading with the influence of rotary inertia and shear are considered in this paper. The motion of the system is described by a homogeneous set of two partial differential equations, which is solved by using the classical Bernoulli-Fourier method. The boundary value and initial value problems are solved. The natural frequencies and associated amplitude ratios of an elastically connected double-beam complex system and the analytical solution of the critical buckling load are determined. The presented theoretical analysis is illustrated by a numerical example, in which the effect of physical parameters characterizing the vibrating system on the natural frequency, the associated amplitude ratios and the critical buckling load are discussed.


74H45 Vibrations in dynamical problems in solid mechanics
74G60 Bifurcation and buckling
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
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