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Natural Vibration of Axially Graded Multi-cracked Nanobeams in Thermal Environment Using Power Series

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Abstract

Purpose

In this study, a numerical investigation of the dynamic behavior of axially graded multi cracked nanobeams in a thermal environment is demonstrated. The nanobeam is axially graded where the material properties are varying exponentially from one end to another end. The nanobeam is subjected to thermal load due to temperature variation. Multiple open and stable cracks are considered on the beam.

Method

Euler-Bernoulli beam theory and nonlocal theory of elasticity are employed for the modeling of the nanobeam. Each crack is modeled as a rotational spring. The power series solution technique is applied effectively to solve this problem.

Results

Mode shape diagrams are illustrated for single and multiple cracks to analyze the effects of nonhomogeneity and thermal load on the vibration of cracked nanobeams. The effects of crack severity, crack location, and nonlocal parameter on the vibration of nanobeams are presented.

Conclusion

Mode shapes of the single and multi-cracked nanobeams are diverse for the different values of nonhomogeneity of the material. The outcomes of this analysis are verified with the outcomes of other researchers in the existing literature.

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Acknowledgements

This research has been financed by the University of Tartu ASTRA Project PER ASPERA (European Regional Development Fund).

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Author notes

  1. Jaan Lellep contributed equally to this work.

Authors and Affiliations

  1. Institute of Mathematics and Statistics, University of Tartu, Narva mnt 18, Tartu, 51009, Estonia

    Mainul Hossain & Jaan Lellep

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  1. Mainul Hossain
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  2. Jaan Lellep
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Correspondence to Mainul Hossain.

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Hossain, M., Lellep, J. Natural Vibration of Axially Graded Multi-cracked Nanobeams in Thermal Environment Using Power Series. J. Vib. Eng. Technol. 11, 1–18 (2023). https://doi.org/10.1007/s42417-022-00555-3

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  • DOI: https://doi.org/10.1007/s42417-022-00555-3

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