Abstract
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.
Highlights
Plate structure is one of the most important structures in the field of engineering applications
Laminated composite plates have been widely applied in engineering owing to their excellent properties such as higher strength and hardness and lighter weight. e analysis of vibration characteristics for plates has been widely studied for decades
Most researches are based on the classical thin plate theory, studying the vibration characteristics of single-layer plate structures with classical boundary conditions [3,4,5,6,7]
Summary
Plate structure is one of the most important structures in the field of engineering applications. Most researches are based on the classical thin plate theory, studying the vibration characteristics of single-layer plate structures with classical boundary conditions [3,4,5,6,7]. Erefore, it is still necessary to develop a practical method to study the vibration behavior of laminated composite double-plate system with general boundary conditions. The upper plate and the lower plate are connected by the middle Winkler-type elastic layer, which consists of a series of face springs, and the stiffness of the middle Winkler layer is represented by Kc. When the system vibrates, the following formula denotes energy contained in the middle elastic layer: Ec. e major purpose is to establish a general solution model for the vibration characteristics of LCDPS under general boundary constraints, which are achieved by the penalty parameter method. Once the eigenvector of the given frequency Π is determined, the displacement of the double-plate structure system can be determined by substituting the coefficients into the equation
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