Analysis of Wave Propagation Properties of Flexoelectric Phononic Crystal Beams

YANG Shasha; KONG Yifan; SHEN Cheng

doi:10.21656/1000-0887.460003

Volume 46 Issue 8

Aug. 2025

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YANG Shasha, KONG Yifan, SHEN Cheng. Analysis of Wave Propagation Properties of Flexoelectric Phononic Crystal Beams[J]. Applied Mathematics and Mechanics, 2025, 46(8): 1037-1049. doi: 10.21656/1000-0887.460003

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Analysis of Wave Propagation Properties of Flexoelectric Phononic Crystal Beams

doi: 10.21656/1000-0887.460003

YANG Shasha^1,2,
KONG Yifan^2,3,
SHEN Cheng^{2,3
,
,}

1. School of Mechanical Engineering, Nanjing University of Industry Technology, Nanjing 210023, P.R.China;
2. State Key Laboratory of Mechanics and Control for Aerospace Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, P.R.China;
3. MIIT Key Laboratory of Multifunctional Lightweight Materials and Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, P.R.China

Funds:

The National Science Foundation of China(12202183； 12472089)

Received Date: 2025-01-07
Rev Recd Date: 2025-02-15

Available Online: 2025-09-10

Abstract

Abstract

When the structural scale is reduced to the micro and nano sizes, a new type of electromechanical coupling effect (i.e. the flexoelectric effect) becomes increasingly important. A phononic crystal beam model with the flexoelectric effect in micro scale was established. The dispersion curves and vibration responses of the structure were studied. Based on the nanodielectric theory under flexoelectric effects, the constitutive equation for flexoelectric materials was derived from the electrical Gibbs free energy density. Based on the theoretical hypothesis of the Bernoulli-Euler beam and the variational principle, the governing vibration equation for the beam under flexoelectric effects, micro-inertial effects and dynamic flexoelectric effects, was derived. The energy band structure of a phonon crystal beam under flexoelectric effects and the natural frequencies of a finite length cantilever beam were calculated with the transfer matrix method. The flexoelectric effects and the influences of structural parameters on natural frequencies and band gaps were studied. The results show that, the flexoelectric effect significantly increases the natural frequency, and the wider band gap can be obtained by the change of the structural parameters. The simulation results are in good agreement with the theoretical ones, which proves the validity of the theoretical method. The work provides a theoretical guidance for the future design of micro and nano phonon crystal beams under the flexoelectric effects.
- flexoelectric effect,
- phononic crystal beam,
- dispersion curve,
- natural frequency,
- transfer matrix

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References(29)

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