Analysis of transverse natural frequency of two-span continuous Timoshenko beam on viscoelastic Pasternak foundation

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Journal of Vibration and Shock ›› 2023, Vol. 42 ›› Issue (11) : 1-10.

YU Yunyan1, FU Yanyan1, ZHANG Wei2

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Abstract

Timoshenko beams on viscoelastic Pasternak foundations are studied for their self-vibration frequencies, attenuation coefficients and modalities for single-span foundation beams and two-span continuous foundation beams (both equal-span and unequal-span conditions) under classical boundary conditions including two-end simply supported, two-end fixed, simply supported-fixed. Based on the method of reverberation-ray matrix, the transverse vibration frequency equations are derived based on the nodal coupling conditions under various constraints. By observing the frequency equations of two-span continuous foundation beams and single-span foundation beams, and by using specific arithmetic examples, the connection and difference between the self-vibration frequencies of two-span continuous foundation beams and single-span foundation beams are investigated, and the first three orders of modes are further given. The results show that the frequency equation for a two-span continuous foundation beam can be divided into two parts, which are similar in form to the frequency equation for a single-span foundation beam under simply-supported and simply-supported-solidly-supported boundary conditions at both ends, respectively. The amplitude of the modal function curve for a two-span continuous Timoshenko foundation beam with unequal spans decreases fastest with increasing order.

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two-span continuous foundation beam / Timoshenko beam / viscoelastic Pasternak foundation / method of reverberation-ray matrix (MRRM) / free vibration characteristics

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YU Yunyan1, FU Yanyan1, ZHANG Wei2. Analysis of transverse natural frequency of two-span continuous Timoshenko beam on viscoelastic Pasternak foundation[J]. Journal of Vibration and Shock, 2023, 42(11): 1-10

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