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Free vibration investigation of nano mass sensor using differential transformation method

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Abstract

In the present study, transverse vibration of nano-cantilever beam with attached mass and two rotational and transverse springs at its end is studied. Resonance frequency of vibrating system is influenced by changing mass particle and stiffness coefficients. Euler–Bernoulli beam theory, nonlocal constitutive equations of Eringen, and Hamilton’s principle are used to develop equations of motion. Differential transformation method (DTM) is applied to solve the governing equations of the nanobeam with attached mass particle. Accurate results with minimum mathematical calculation are the advantages of DTM. A detailed parametric study is conducted to investigate the influences of nonlocal parameter. The results can be used in designing of nanoelectromechanical systems. To verify the results, some comparisons are presented between differential transform method results and open literature to show the accuracy of this new approach.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Guilan University, Rasht, Iran

    Misagh Zarepour

  2. Department of Mechanical Engineering, University of Zanjan, Zanjan, Iran

    S. Amirhosein Hosseini

  3. Department of Mechanical Engineering, Imam Khomeini International University, Ghazvin, Iran

    Majid Ghadiri

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  1. Misagh Zarepour
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  2. S. Amirhosein Hosseini
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  3. Majid Ghadiri
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Correspondence to Misagh Zarepour.

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Zarepour, M., Hosseini, S.A. & Ghadiri, M. Free vibration investigation of nano mass sensor using differential transformation method. Appl. Phys. A 123, 181 (2017). https://doi.org/10.1007/s00339-017-0796-6

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