A systematic method for free and forced vibration analysis of axially loaded hybrid double-beam systems

This article presents a systematic method for analyzing the free and forced vibrations of axially loaded hybrid double-beam systems using the linear multibody system transfer matrix method (linear MSTMM). The method defines two new types of elements to construct the hybrid double-beam system as a chain system, allowing for efficient modeling and analysis. The derivation of the transfer equation for axially loaded Timoshenko beams is discussed, and the orthogonality of the augmented eigenvectors of the hybrid double-beam system is mathematically proven. The article provides a detailed description of the free vibration analysis, including the derivation of transfer equations for spring-supported double rigid bodies and axially loaded Timoshenko double-beams, as well as the overall system transfer equation and frequency equation. The forced vibration analysis is also covered, demonstrating the method's accuracy and versatility through numerical examples. The effects of axial force, spring support stiffness, and rigid body mass on the vibration characteristics of hybrid double-beam systems are investigated, and the method's effectiveness in analyzing forced vibrations is verified. The conclusions highlight the systematicity, simplicity, and high accuracy of the proposed method, as well as its potential for practical engineering applications.