Vibration analysis for a modified Timoshenko beam on Winkler elastic foundation

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Journal of Vibration and Shock ›› 2020, Vol. 39 ›› Issue (3) : 30-37.

WANG Jiale, XIA Guiyun

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Abstract

The elastic foundation beam model based on Bernoulli-Euler beam theory is widely used, but it has larger errors in calculations of higher order natural frequencies and deep beams.Here, based on the modified Timoshenko beam theory, a new vibration differential equation of an elastic foundation beam was established.Due to considering the moment of inertia caused by shear deformation based on Timoshenko beam theory, it has a better accuracy.The beam54 element of the finite element software ANSYS was used to do the finite element calculation for the beam’s vibration modes, and the results basically had no errors compared with the theoretical solution to verify the correctness of the proposed theoretical model.Based on the modified Timoshenko beam theory, the elastic foundation beam’s natural frequency transcendental equations and modal functions under various boundary conditions including free-free, pinned-pinned, pinned-free and clamped-clamped were deduced.The calculation results of an elastic foundation beam under different theories, different boundary conditions and different ratios of height to span were analyzed to verify the applicability of the proposed theoretical model.The relations among wave velocity, group velocity and wave number under different theories were analyzed.It was shown that constraint conditions and beam length have important effects on an elastic foundation beam’s vibration modes; foundation stiffness affects an elastic foundation beam’s natural vibration frequencies significantly.

Key words

elastic foundation beam / shear deformation / moment of inertia / boundary constraint / high frequency section / wave velocity / group velocity / vibration mode

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WANG Jiale, XIA Guiyun. Vibration analysis for a modified Timoshenko beam on Winkler elastic foundation[J]. Journal of Vibration and Shock, 2020, 39(3): 30-37

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