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<p>The vibrational characteristics of a bidirectional, functionally graded, piezoelectric (BEFGPM) beam are investigated in the present study. The excitation is facilitated through the shear coupling coefficient inherent to piezoelectric materials. The material properties are assumed to vary continuously along both the length and thickness of the beam, following an exponential law. The width of the beam along its length varies according to an exponential function. The first shear deformation theory is utilized to derive the strain components. By applying the plane stress condition, the constitutive equations for the BEFGPM beam are formulated. The reliability of the current numerical method is corroborated through comparison with results derived from previously published studies for a specific scenario. Hamilton’s principle is invoked to derive the governing equations of motion alongside the corresponding boundary conditions. The clamped-clamped (C-C) boundary condition is analyzed in detail. Thus, the equations are solved using the Generalized Differential Quadrature (GDQ) technique. Impacts of the exponential function’s degree, boundary conditions, geometric parameters, and exponent parameters on the natural frequencies are thoroughly documented.</p>

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Numerical Modeling and Vibration Analysis of Shear-Actuated Bi-Directional Exponential FGPM Beam

  • 期刊论文

  • 发表日期：

    2026年1月1日

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  • A. Sharma,
  • P. Sharma,
  • S. K. Parashar

摘要

The vibrational characteristics of a bidirectional, functionally graded, piezoelectric (BEFGPM) beam are investigated in the present study. The excitation is facilitated through the shear coupling coefficient inherent to piezoelectric materials. The material properties are assumed to vary continuously along both the length and thickness of the beam, following an exponential law. The width of the beam along its length varies according to an exponential function. The first shear deformation theory is utilized to derive the strain components. By applying the plane stress condition, the constitutive equations for the BEFGPM beam are formulated. The reliability of the current numerical method is corroborated through comparison with results derived from previously published studies for a specific scenario. Hamilton’s principle is invoked to derive the governing equations of motion alongside the corresponding boundary conditions. The clamped-clamped (C-C) boundary condition is analyzed in detail. Thus, the equations are solved using the Generalized Differential Quadrature (GDQ) technique. Impacts of the exponential function’s degree, boundary conditions, geometric parameters, and exponent parameters on the natural frequencies are thoroughly documented.