Free Vibration Analysis of Elastic-Layer Double-Beam Systems Based on the Multibody System Transfer Matrix Method

This paper investigates the free vibration characteristics of elastic-layer Euler-Bernoulli double-beam systems subjected to axial forces using the linear multibody system transfer matrix method (MSTMM). The double-beam system can be arbitrarily configured with multiple spring supports that possess both translational and rotational stiffness. By sequentially multiplying the transfer matrices of elements, the overall transfer and frequency equations of the system can be directly established, enabling the method to accommodate various boundary conditions flexibly. The analytical derivation of the transfer equation for the elastic-layer double-beam prevents the accuracy deterioration commonly associated with spatial discretization methods. Numerical case studies verify the correctness and precision of the presented method, highlighting its systematic formulation and ease of implementation. This work provides significant theoretical guidance for optimal structural design and adverse vibration suppression.