A dynamic stiffness-based modal analysis method for a double-beam system with elastic supports

Abstract

The double-beam system with several elastic supports is one of most significant mechanical models in engineering structures. Its dynamic characteristics are crucial for structural design, vibration control, health monitoring, and other dynamic issues. In the dynamic analysis of double-beam systems, since existing researches often need to make some assumptions or approximations to the displacement function, the accuracy and application range of the analysis results are limited. In view of this, this article proposes an exact modal analysis method for the double-beam system based on the dynamic stiffness method. It can consider the effect of boundary conditions, the differences in the material and structural of the two beams, the axial forces and other factors simultaneously without any approximation. During the analysis, the accuracy of the proposed method is verified first by comparing with finite element solutions. Then, the influence of elastic supports on modal characteristic is discussed, and the variation law of the dynamic stiffness in frequency domain is investigated. Finally, a dynamic stiffness-based method for determining the contributions of the two beams to each mode of the system is provided. The method can be extended to quickly obtain the frequency and mode shape information of the system without solving the frequency equation or characteristic equation.