Free Vibration of MultiSegment Beams With Arbitrary Boundary Conditions

BAO Siyuan; ZHOU Jing; LU Jianwei

doi:10.21656/1000-0887.410045

Volume 41 Issue 9

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BAO Siyuan, ZHOU Jing, LU Jianwei. Free Vibration of MultiSegment Beams With Arbitrary Boundary Conditions[J]. Applied Mathematics and Mechanics, 2020, 41(9): 985-993. doi: 10.21656/1000-0887.410045

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Free Vibration of MultiSegment Beams With Arbitrary Boundary Conditions

doi: 10.21656/1000-0887.410045

Department of Engineering Mechanics, Suzhou University of Science and Technology, Suzhou, Jiangsu 215011, P.R.China

Funds: The National Natural Science Foundation of China（11202146）

Received Date: 2020-01-23
Rev Recd Date: 2020-03-08
Publish Date: 2020-09-01

Abstract

Abstract

The vibration characteristics of continuous multi-segment beams were studied. Other than classical boundary conditions (such as simple supports), the elastic constraints were considered to analyze the free vibration characteristics of multi-segment beams. Firstly, according to the spectro-geometric method, 4 auxiliary functions were added on the basis of the traditional Fourier series to construct the lateral displacement function for each segment of the beam. Secondly, new expressions of the Lagrangian functions for the beam structure were obtained by substitution of the supposed spectro-geometric form into the Lagrangian functions. The free vibration problem was transformed into the standard matrix eigenvalue form from the Hamiltonian principle, and the natural frequencies and modes of the beam under arbitrary boundary conditions were obtained. For 4 numerical examples, the natural frequencies and modes of the continuous multi-segment beams were calculated under different boundary conditions of variant spring stiffness values. Comparison of the results between existing literatures and this work shows correctness, standardization and efficiency of the proposed method.
- spectro-geometric method,
- arbitrary boundary,
- continuous multi-segment beam,
- free vibration

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References(15)

References

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