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Effect of Ritz Vectors on Random Seismic Response of Cantilever Beam

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Abstract

Purpose

To understand the effect of Ritz vectors on the random seismic response of non-uniform cantilever beam, the following works are performed:

Method

Firstly, the equation of random seismic response of non-uniform cantilever beam based on Hamilton theory is presented. The solution is derived using the combined classical Ritz and pseudo-excitation method. Secondly, by considering the principle of virtual displacement, the pertinent function can be obtained from the characteristics of pseudo-excitation method. The mode of analysis is transformed from structural stationary random to structural harmonic response. Finally, the results of the analysis of the cantilever beam samples of different Ritz vectors are presented. The functional extremum corresponding to increasing Ritz vectors is compared.

Results and conclusions

It can be concluded based on the result findings that the Ritz vectors, which satisfy both the geometrical and the natural boundary conditions, do not necessarily lead to accurate results. It is, therefore, recommended that the extreme value of the function for the whole system should be considered as an evaluation criterion for the Ritz vectors.

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Acknowledgements

The research work presented in this paper is supported by “the Fundamental Research Funds for the Central Universities”.

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Authors and Affiliations

  1. Marine Engineering College, Dalian Maritime University, Dalian, 116026, People’s Republic of China

    Xiaoshuang Han

  2. State Key Laboratory of Structural Analysis for Industrial Equipment, School of Naval Architecture Engineering, Dalian University of Technology, Dalian, 116024, People’s Republic of China

    Bo Zhou

  3. Maritime Production Research Pte. Ltd, Singapore, 915806, Singapore

    Wie-Min Gho

  4. School of Civil and Environmental Engineering, Nanyang Technological University, Singapore, 639798, Singapore

    Soon-Keat Tan

Authors
  1. Xiaoshuang Han
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  2. Bo Zhou
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  3. Wie-Min Gho
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  4. Soon-Keat Tan
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Correspondence to Bo Zhou.

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Han, X., Zhou, B., Gho, WM. et al. Effect of Ritz Vectors on Random Seismic Response of Cantilever Beam. J. Vib. Eng. Technol. 7, 321–333 (2019). https://doi.org/10.1007/s42417-019-00121-4

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  • DOI: https://doi.org/10.1007/s42417-019-00121-4

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