Transverse free vibration characteristics of Bernoulli-Euler beam on viscoelastic Pasternak foundation under classical boundary conditions

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Journal of Vibration and Shock ›› 2021, Vol. 40 ›› Issue (1) : 173-182.

FU Yanyan, YU Yunyan

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Abstract

Free vibration characteristics play an important role in structural dynamic analysis. Here, the method of reverberation ray matrix (MRRM) was proposed to study free vibration characteristics of foundation beams. Through node force balance equation, displacement compatibility equation and element phase relation in dual local coordinate system, reverberation-ray matrices of a Bernoulli-Euler beam on viscoelastic Pasternak foundation were established under classical boundary conditions including two-end simply supported, two-end free, two-end fixed, simply supported-free, simply supported-fixed and fixed-free, and then the beam’s frequency equations under the 6 types boundary conditions were deduced. According to boundary conditions in a single local coordinate system, analytical expressions for the beam’s modal functions were derived. Furthermore, unknown parameters in modal function expressions were solved according to the orthogonal normalization condition. Some examples were used to verify the correctness of the MRRM. Finally, natural frequencies, attenuation coefficients and modal functions of the beam under different boundary conditions were analyzed. The study results provided a theoretical basis for studying free vibration characteristics of beams on viscoelastic foundation.

Key words

viscoelastic Pasternak foundation / Bernoulli-Euler beam / transverse free vibration characteristics / method of reverberation ray matrix (MRRM)

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FU Yanyan, YU Yunyan. Transverse free vibration characteristics of Bernoulli-Euler beam on viscoelastic Pasternak foundation under classical boundary conditions[J]. Journal of Vibration and Shock, 2021, 40(1): 173-182

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