A unified method for in-plane vibration analysis of double-beam systems with translational springs

Double-beam structures with many translational springs are a class of significant engineering structures, which have been widely used in civil, aerospace, and mechanical engineering. The dynamic characteristics of such structures is significant to their structural design, vibration abatement and condition assessment. Since the motion differential equation of a double-beam system is a system of complex fourth-order variable coefficient partial differential equations. The existing analytical methods either need to simplify the structural mechanics model or make some prior assumptions about the form of the solution of the equation, which is convenient for the simplification and solution of the equation, and finally reduces the universality of the whole analysis process, and has many limitations in the practical application. An alternative solution is the finite element method, but it can only give an approximate solution to distributed parameter systems. In view of this, this article developed a unified approach for the free vibration of the double-beam structures by employing the dynamic stiffness method (DSM), which has no re-strictions on the geometric characteristics and boundary conditions of the structure, and can obtain the exact dynamic characteristics of the system without any approximation. The correct-ness of the proposed method is validated by comparison with literatures and the finite element solutions. Finally, a comprehensive parametric study is performed to investigate the influence of key parameters on modal frequencies and mode shapes.