A numerically stable dynamic coefficient method and its application in free vibration of partial-interaction continuous composite beams

It has long been recognized that traditional exact methods may encounter numerical instability when analyzing the free vibration of a continuous partial-interaction composite beam, a type of composite beam which considers the interfacial slip. In contrast to the Euler–Bernoulli beam theory, the form of the general solution for the free-vibration governing equations of partial-interaction composite beams based on Timoshenko beam theory will change dramatically when the frequency is sufficiently high, indicating that shear deformation cannot be ignored at high-order frequencies. To tackle this difficulty, this paper presents a numerically stable and theoretically exact method to analyze the dynamic responses of continuous composite beams with partial-interaction. The new method can effectively overcome the problem of numerical instability encountered by traditional theoretical solutions such as the dynamic stiffness matrix method and transfer matrix method, particularly for high-order vibrations or long-span continuous beams. Some numerical examples are provided to demonstrate the performance of the proposed method.