Medium and High-Frequency Vibration Analysis of Thin Plates by a Hybrid Distributed Transfer Function Method 2021-01-1052

Vibrations of plates are widely seen in various applications of automobile, aerospace, mechanical and civil engineering. Vibration analysis of plates in medium and high-frequency regions plays an important role in optimal design and safe operation of machines and structures in these applications. Medium and high-frequency vibration analysis of plates is usually performed by using numerical methods. Proposed in this paper is a new analytical solution method for mid- and high-frequency analysis of thin rectangular plates modeled by the Kirchhoff-Love plate theory. In the development, analytical solutions for a class of thin plates are obtained based on a hybrid formulation that combines the Distributed Transfer Function Method (DTFM) and modal expansion. The proposed method, which is an extension of the DTFM for one-dimensional continua, is called the hybrid Distributed Transfer Function Method (hybrid DTFM). The hybrid DTFM is simple and flexible in treating general loadings and boundary conditions. Different from existing analytical solutions, like the Naiver solution and the Lévy solution, the new method can handle boundary excitations with ease and is applicable to plates with partially distributed spring and damping. Unlike numerical methods, such as the Finite Element Analysis (FEA) and Energy Flow Analysis (EFA), the new method is able to deliver local displacement, bending moment, and shear force more efficiently in medium and high-frequency regions. The proposed hybrid DTFM is illustrated in numerical examples, where the accuracy and efficiency of the method is validated, and the flexibility of the method in different loading cases is demonstrated. The hybrid DTFM can be extended to medium and high-frequency vibration analysis of more complex plate structures.