Free Vibration Analysis of Laminated Composite Double‐Plate Structure System with Elastic Constraints Based on Improved Fourier Series Method

An analytical model of laminated composite double‐plate system (LCDPS) is established, which efficiently analyzes the common 3D plate structure in engineering applications. The proposed model combines the first‐order shear deformation theory (FSDT) and the classical delamination theory, and then the LCDPS’s vibration characteristics are investigated. In the process of analysis, the improved Fourier series method (IFSM) is used to describe the displacement admissible function of the LCDPS, which can remove the potential discontinuities at the boundaries. Five sets of artificial springs are introduced to simulate the elastic boundary constraints, and the restraints of the Winkler elastic layer can be adjustable. The improved Fourier series is substituted into the governing equations and boundary conditions; then, applying the Rayleigh–Ritz method, we take all the series expansion coefficients as the generalized coordinates. After that, a set of standard linear algebraic equations was obtained. On this basis, the natural frequency and mode shapes of the LCDPS can be obtained by solving the standard eigenvalue problem. By the discussion of numerical examples and the comparison with those of the reports in the literature, the convergence and the reliability of the present approach are validated. Finally, the parametric investigations of the free vibration with complex boundary conditions are carried out, including the influence of boundary conditions, lamination scheme, plate geometric parameters, and elastic coefficient between two plates.