Dispersion characteristics of shear horizontal waves in piezoelectric nanoplates: a nonlocal strain gradient theory incorporating surface effects

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Authors

  • X.H. Chen School of Mechanical and Power Engineering, Henan Polytechnic University, China 0009-0007-2257-8451
  • X.M. Zhang School of Mechanical and Power Engineering, Henan Polytechnic University and Mechanical Monitoring and Fault Diagnosis Research Institute, Henan Polytechnic University, China 0000-0002-0149-4618
  • H.M. Zhou School of Mechanical and Power Engineering, Henan Polytechnic University and Mechanical Monitoring and Fault Diagnosis Research Institute, Henan Polytechnic University, China 0000-0002-1993-0238

Abstract

This paper investigates the propagation of shear horizontal (SH) waves in piezoelectric nanoplates by coupling the Gurtin-Murdoch surface model with the nonlocal strain gradient theory. The Legendre polynomial expansion method with analytical integration is developed, which reformulates the complex acoustic wave partial differential equation (PDE) solution problem into a standard generalized eigenvalue problem, thereby obtaining its dispersion relation. In contrast to conventional polynomial techniques, this approach obviates the necessity of redundant integration, thereby facilitating the derivation of comprehensive solutions over the full frequency spectrum. The validity of the proposed method is verified by calculating the phase velocities of SH waves in a piezoelectric nanoplate without surface and strain gradient effects and comparing the results with literature data. The convergence and computational efficiency of the method are also demonstrated. Results indicate that the stiffness softening dominated by the surface effect and the hardening induced by the strain gradient effect form a competitive mechanical response. The surface effect increases wave velocity, while the nonlocal strain gradient effect decreases it. This interplay is frequency-dependent, with the surface effect dominating at low frequencies and the nonlocal strain gradient effect becoming dominant at higher frequencies. These findings offer valuable insights for the design of smart nano-devices.

Keywords:

piezoelectric nanoplate, SH wave, Legendre polynomial expansion method, surface effect, nonlocal effect, strain gradient effect

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