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**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.

### MSC:

74H45 | Vibrations in dynamical problems in solid mechanics |

74G60 | Bifurcation and buckling |

74K10 | Rods (beams, columns, shafts, arches, rings, etc.) |

### Keywords:

Timoshenko beam; Winkler elastic layer; boundary conditions; critical buckling force; eigenvalue
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\textit{V. Stojanović} et al., Arch. Appl. Mech. 81, No. 12, 1993--2005 (2011; Zbl 1271.74187)

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### References:

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