Research on thermal-deformation coupling vibration of flexible beams considering axial force

Abstract

The beam-wire structure in aircraft can cause thermal deformation and vibration of flexible members during service due to alternating heat flux caused by solar thermal radiation. The deformation of the rod will further affect the magnitude and distribution of heat flux，making it a typical force shape coupling system. The stiffness， mass，or load matrix of a coupled system usually has time-varying characteristics，and the modal and response of the system can only be obtained by solving the characteristic equations multiple times and gradually integrating them. How to ensure the computational accuracy and efficiency of the solving process is a major challenge. Based on the dynamic stiffness method and the Wittrick Williams algorithm，the accurate solution of the system's natural frequency and mode has been achieved. Combining with the precise integration method，the structural response is calculated. The results show that the deviation between the first fouth natural frequencies and the finite element solution is within 1‰，and the maximum relative deviation of the response is 1%. When the variable thermal axial force approaches the critical load for structural instability，the vibration frequency of the structure rapidly decreases and tends towards 0，and the thermally induced vibration will exhibit divergence.

Keywords

• beam-wire structure
• thermally induced vibration
• time-varying thermal axial force
• dynamic stiffness method
• wittrick-williams algorithm