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

This paper introduces a systematic method for analyzing the free and forced vibrations of hybrid double-beam systems under axial force, utilizing the linear multibody system transfer matrix method. The hybrid double-beam system consists of two types of elements, the double-beam segments and the spring-supported rigid bodies. This configuration is commonly found in research and engineering applications. The frequency equation of the system can be directly obtained through successive multiplication of the element transfer matrices, accommodating arbitrary boundary conditions. The transfer equation for the axially loaded Timoshenko beam are derived analytically, thereby avoiding the accuracy loss due to spatial discretization. And there is no need to discuss the derivation for different cases. The orthogonality of the augmented eigenvectors of the hybrid double-beam system is mathematically proven. The forced vibration of the system is solved using the modal superposition method. Three numerical examples verify the systematicity, simplicity and high accuracy of the proposed method. Furthermore, the effects of axial force, spring support stiffness, and rigid body mass on the vibration characteristics of the hybrid double-beam system are analyzed, providing valuable insights for optimizing designs and avoiding undesirable vibrations.