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Vibration analysis of piezoelectric sandwich nanobeam with flexoelectricity based on nonlocal strain gradient theory

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Abstract

A nonlocal strain gradient theory (NSGT) accounts for not only the nongradient nonlocal elastic stress but also the nonlocality of higher-order strain gradients, which makes it benefit from both hardening and softening effects in small-scale structures. In this study, based on the NSGT, an analytical model for the vibration behavior of a piezoelectric sandwich nanobeam is developed with consideration of flexoelectricity. The sandwich nanobeam consists of two piezoelectric sheets and a non-piezoelectric core. The governing equation of vibration of the sandwich beam is obtained by the Hamiltonian principle. The natural vibration frequency of the nanobeam is calculated for the simply supported (SS) boundary, the clamped-clamped (CC) boundary, the clamped-free (CF) boundary, and the clamped-simply supported (CS) boundary. Effects of geometric dimensions, length scale parameters, nonlocal parameters, piezoelectric constants, as well as the flexoelectric constants are discussed. Results demonstrate that both the flexoelectric and piezoelectric constants enhance the vibration frequency of the nanobeam. The nonlocal stress decreases the natural vibration frequency, while the strain gradient increases the natural vibration frequency. The natural vibration frequency based on the NSGT can be increased or decreased, depending on the value of the nonlocal parameter to length scale parameter ratio.

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Authors and Affiliations

  1. Jiangxi Key Laboratory of Micro Aeroengine, School of Aircraft Engineering, Nanchang Hangkong University, Nanchang, 330063, China

    Shan Zeng & Jinwu Wu

  2. Graduate School at Shenzhen, Harbin Institute of Technology, Harbin, 150001, China

    Kaifa Wang

  3. School of Engineering, Western Sydney University, Penrith, NSW, 2751, Australia

    Baolin Wang

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  1. Shan Zeng
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  2. Kaifa Wang
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  3. Baolin Wang
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  4. Jinwu Wu
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Correspondence to Shan Zeng.

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Citation: ZENG, S., WANG, K. F., WANG, B. L., and WU, J. W. Vibration analysis of piezoelectric sandwich nanobeam with flexoelectricity based on nonlocal strain gradient theory. Applied Mathematics and Mechanics (English Edition), 41(6), 859–880 (2020) https://doi.org/10.1007/s10483-020-2620-8

Project supported by the National Natural Science Foundation of China (Nos. 51965041, 1197237, and 11602072)

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Zeng, S., Wang, K., Wang, B. et al. Vibration analysis of piezoelectric sandwich nanobeam with flexoelectricity based on nonlocal strain gradient theory. Appl. Math. Mech.-Engl. Ed. 41, 859–880 (2020). https://doi.org/10.1007/s10483-020-2620-8

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