An exact solution for dynamic analysis of a complex double-beam system

As the commonly found double-beam structures in engineering have a distributed spring connection layer, the dynamic stiffness method is employed to establish the exact dynamic stiffness matrix and frequency equation. The complex transcendental frequency equation of the double-beam structure considered herein is solved by an improved Wittrick-Williams algorithm, resulting in an accurate analysis of its dynamic characteristics. Based on this, the effect of various parameters on its dynamic characteristics is investigated. The results indicate that owing to the impact of the spring connection layer, structural parameters, boundary conditions, and other factors, the periodicity of the modal frequencies of the double-beam is disrupted; consequently, the values of two adjacent frequencies are very close or even equal. In addition, the modal shapes of the double-beam are also affected by the above factors. The influencing law is complex and varies with different orders. However, for a single-beam structure, a reverse modal shape may form at some orders of the modes of the double-beam structures.