<p>This study proposes a theoretical model for piezoelectric nanobeams that incorporates the combined effects of dynamic flexoelectric, surface effect, and the Winkler–Pasternak linear elastic foundation. By applying Hamilton’s variational principle, the governing equations and boundary conditions are derived, and the Navier method is employed to obtain analytical expressions for the natural frequencies. The study focuses on the influence of these factors on the normalized natural frequencies of different vibration modes in Timoshenko and Euler–Bernoulli beams. The results indicate that, compared to the Euler–Bernoulli beam, the dynamic flexoelectric effect has a more significant impact on the normalized natural frequency of the Timoshenko beam. The Winkler–Pasternak foundation enhances the natural frequency, with the Pasternak parameter playing a dominant role. Surface residual stress has a significant influence on the normalized natural frequencies of both Timoshenko and Euler–Bernoulli beams. This work makes significant contributions to the theoretical analysis and material performance evaluation of piezoelectric nanobeams and provides essential guidance for the design and development of micro- and nanoscale devices.</p>

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Vibration analysis of piezoelectric nanobeams with flexoelectric and surface effects on an elastic foundation

  • Bai Qiang Liu,
  • Peng Wang,
  • Ying Hui Lv

摘要

This study proposes a theoretical model for piezoelectric nanobeams that incorporates the combined effects of dynamic flexoelectric, surface effect, and the Winkler–Pasternak linear elastic foundation. By applying Hamilton’s variational principle, the governing equations and boundary conditions are derived, and the Navier method is employed to obtain analytical expressions for the natural frequencies. The study focuses on the influence of these factors on the normalized natural frequencies of different vibration modes in Timoshenko and Euler–Bernoulli beams. The results indicate that, compared to the Euler–Bernoulli beam, the dynamic flexoelectric effect has a more significant impact on the normalized natural frequency of the Timoshenko beam. The Winkler–Pasternak foundation enhances the natural frequency, with the Pasternak parameter playing a dominant role. Surface residual stress has a significant influence on the normalized natural frequencies of both Timoshenko and Euler–Bernoulli beams. This work makes significant contributions to the theoretical analysis and material performance evaluation of piezoelectric nanobeams and provides essential guidance for the design and development of micro- and nanoscale devices.