Meshless Electrodynamic Analysis of Plates with Embedded Macroscopic Piezoelectric Fibers

  • Rahimi, Javad (Koc university)
  • Simsek, Mehmet (Koc university)
  • Aghakhani, Ammirreza (Stuttgart University)
  • Basdogan, Ipek (Koc university)
  • Serhat, Gokhan (KU Leuven University)

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We present a meshless spectral Chebyshev (SC) framework for the dynamic electromechanical analysis of composite plates with embedded piezoelectric fibers. The proposed approach overcomes the limitations of conventional modal analysis techniques based on homogenization, which is accurate only when the inclusions are much smaller than the characteristic length scale of the structure. Moreover, due to its meshless formulation, the presented method exhibits reduced computational costs compared to the finite element method (FEM). Within the SC framework, plates reinforced with macro-scale piezoelectric fibers are modeled explicitly using the actual geometries of the constituents. The governing electromechanical equations are formulated using Hamilton’s principle based on the Reissner-Mindlin plate theory. The plate–fiber system is decomposed into two substructures: the host structure modeled as a perforated plate when the fibers are removed, and the individual piezoelectric fibers that are modeled independently. Due to the lack of a mesh, Gauss–Lobatto sampling points are employed to capture cross-sectional information. The mechanical and electromechanical mass, stiffness, and coupling matrices are first computed separately for the plate and each piezoelectric fiber. These substructures are then assembled using component mode synthesis (CMS) to reconstruct the original configuration of the composite plate. Finally, boundary conditions are imposed through projection matrices obtained via singular value decomposition (SVD), yielding the global electromechanical system matrices required for dynamic analysis. As case studies, natural frequencies and voltage frequency response functions (FRFs) are computed for several arrangements involving varying fiber dimensions and boundary conditions. The obtained results are validated against those from the FEM simulations, confirming the accuracy and computational efficiency of the proposed SC approach.