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Transverse free vibration analysis of a tapered Timoshenko beam on visco-Pasternak foundations using the interpolating matrix method

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Abstract

The characteristics of transverse free vibration of a tapered Timoshenko beam under an axially conservative compression resting on visco-Pasternak foundations are investigated by the interpolating matrix method. The research is executed in view of a three-parameter foundation which includes the effects of the Winkler coefficient, Pasternak coefficient and damping coefficient of the elastic medium. The governing equations of free vibration of a non-prismatic Timoshenko beam under an axially conservative force resting on visco-Pasternak foundations are transformed into ordinary differential equations with variable coefficients in light of the bending rotation angle and transverse displacement. All the natural frequencies orders together with the corresponding mode shapes of the beam are calculated at the same time, and a good convergence and accuracy of the proposed method is verified through two numerical examples. The influences of foundation mechanical characteristics together with rotary inertia and shear deformation on natural frequencies of the beam with different taper ratios are analyzed. A comprehensive parametric numerical study is carried out emphasizing the primary parameters that describe the dynamic property of the beam.

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Acknowledgement

The authors thank the reviewers and editors for their careful work and valuable comments. They are also grateful to the funding of key university natural science research project of Anhui in 2019.

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Authors and Affiliations

  1. Institute of Engineering Safety and Disaster Prevention, Hohai University, Nanjing, 210098, China

    Zhang Jinlun & Zhang Liaojun

  2. Key Laboratory for Mechanics, Anhui Polytechnic University, Wuhu, 241000, China

    Zhang Jinlun & Ge Renyu

Authors
  1. Zhang Jinlun
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  2. Ge Renyu
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  3. Zhang Liaojun
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Corresponding author

Correspondence to Ge Renyu.

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Supported by

AHKJT of China under Grant Nos. 1708085QE121 and 1808085ME147; AHEDU of China under Grant No. TSKJ2017B13

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Jinlun, Z., Renyu, G. & Liaojun, Z. Transverse free vibration analysis of a tapered Timoshenko beam on visco-Pasternak foundations using the interpolating matrix method. Earthq. Eng. Eng. Vib. 18, 567–578 (2019). https://doi.org/10.1007/s11803-019-0522-9

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  • DOI: https://doi.org/10.1007/s11803-019-0522-9

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