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<p>This paper presents an analytical study focused on the free vibration analysis of doubly curved composite micro panels that incorporate piezoelectric layers. We derive the total potential energy of the system using a combination of the modified Sander's shell theory and the first-order shear deformation theory. Applying Hamilton's Principle leads us to establish the governing equations, resulting in five mechanical equilibrium equations and two electrical equations. In our approach, we consider panels with different boundary conditions and utilize the Chebyshev–Ritz formulation to obtain numerical results. Additionally, we explore three different distribution patterns of graphene platelets within our study. The material properties for each layer of the micro composite shell, enhanced with graphene platelets, are determined through the Halpin–Tsai model. To validate our formulation and solution, we present a comparative study. Our case studies examine how boundary conditions, material and geometrical properties, as well as the applied voltage, influence the vibration behaviors of the doubly curved composite micro panels.</p>

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A Chebyshev–Ritz formulation for vibration analysis of piezoelectric composite doubly curved micro panels with arbitrary boundary conditions

  • 期刊论文

  • 发表日期：

    2025年8月14日

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  • Pingquan Wang,
  • Fatemeh Abbaspour,
  • Shahram Hosseini

摘要

This paper presents an analytical study focused on the free vibration analysis of doubly curved composite micro panels that incorporate piezoelectric layers. We derive the total potential energy of the system using a combination of the modified Sander's shell theory and the first-order shear deformation theory. Applying Hamilton's Principle leads us to establish the governing equations, resulting in five mechanical equilibrium equations and two electrical equations. In our approach, we consider panels with different boundary conditions and utilize the Chebyshev–Ritz formulation to obtain numerical results. Additionally, we explore three different distribution patterns of graphene platelets within our study. The material properties for each layer of the micro composite shell, enhanced with graphene platelets, are determined through the Halpin–Tsai model. To validate our formulation and solution, we present a comparative study. Our case studies examine how boundary conditions, material and geometrical properties, as well as the applied voltage, influence the vibration behaviors of the doubly curved composite micro panels.