Analytical solution to transverse free vibration characteristics of a simply supported Timoshenko beam on viscoelastic Pasternak foundation

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Journal of Vibration and Shock ›› 2020, Vol. 39 ›› Issue (19) : 32-38.

FU Yanyan, YU Yunyan

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Abstract

Vibration characteristics of foundation beams receive much attention in engineering and scientific fields. Here, transverse free vibration characteristics of a simply supported Timoshenko beam on a viscoelastic Pasternak foundation were studied. Firstly, based on the reverberation-ray matrix method, the quartic frequency equation with complex coefficients was derived and solved, the analytical solutions to natural frequencies and attenuation coefficients of the simply supported Timoshenko beam on a viscoelastic Pasternak foundation were obtained. Then, the analytical expressions for modal functions of the beam were solved according to the boundary conditions under a single local coordinate system, unknown parameters were further solved according to the orthogonal normalization conditions. Finally, the correctness of the analytical solutions to transverse free vibration characteristics of the beam based on the reverberation-ray matrix method was verified with a specific example.

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viscoelastic Pasternak foundation / Timoshenko beam / transverse free vibration characteristics / analytical solution / reverberation-ray matrix method

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FU Yanyan, YU Yunyan. Analytical solution to transverse free vibration characteristics of a simply supported Timoshenko beam on viscoelastic Pasternak foundation[J]. Journal of Vibration and Shock, 2020, 39(19): 32-38

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