Semi-analytical solution for natural vibration of rectangular stiffened plates

Stiffened plate structures are widely used in aerospace, shipbuilding and other engineering fields, so the research on its vibration characteristics has significant academic and practical value. Based on the Rayleigh quotient and Rayleigh-Ritz method, this paper presents a semi-analytical method to solve the natural modes of rectangular stiffened plates. In this method, the closed-form mode functions of thin plates are used as the basis functions of the mode functions of stiffened plates, and the natural frequency equation and the mode functions of rectangular stiffened plates are derived according to the Rayleigh quotient. In addition, the governing differential equation of the simply supported stiffened rectangular plate with single stiffener is derived according to the Rayleigh quotient, and the exact solution is obtained using the separation-of-variable method. The effectiveness and accuracy of the proposed method are verified by comparing the present results with those of the finite element method and literature. The proposed method in this work can be used for theoretical analysis and parametric design of stiffened plates.