A quasi-3D SinZZ model-driven multi-field Chebyshev FEM for nonlinear vibration control in multilayer multiferroic composite plates

Abstract

This paper presents an advanced numerical method for modeling and mitigating nonlinear vibrations in thin multilayered fiber-reinforced multiferroic composite plates, addressing complex multi-physical interactions. The proposed methodology leverages a multi-physical coupling Chebyshev finite element formulation, utilizing high-order shape functions derived from Chebyshev polynomials. By integrating the strengths of spectral element methods and Legendre spectral finite element methods, this approach effectively overcomes challenges such as shear locking and spurious zero energy modes while ensuring high convergence rates in multi-physical problems. A quasi-3D refined model, incorporating the Murakami zig-zag model and sinusoidal shear deformation theory, is employed to accurately capture the nonlinear Von Kármán strain–displacement relationship and the magneto-electro-elastic coupling in multilayer structures with thickness-dependent material properties. To suppress nonlinear vibrations, the study utilizes a closed-loop multiphysical Chebyshev finite element model for time-domain analysis of viscoelastically damped systems, employing the Golla–Hughes–McTavish model. The results underscore the significant influence of multiferroic properties and the strategic distribution of ferroelectric fibers within the substrate on the dynamic behavior of the plate. The numerical validation, supported by rigorous verification, demonstrates the robustness of the proposed method in effectively simulating and controlling multilayer fiber-reinforced multiferroic composite plates. Additionally, this research highlights the potential for significant vibration reduction through semi-active damping mechanisms, offering valuable insights for practical applications in industries where precision and stability are critical.