Based on the approach that ‘replace curved by straight’, the steady combined force is introduced directly into the fluid structure interaction vibration differential equation of straight pipe to describe straight-curved one’s transverse motion. Taking clamped-elastically supported combined pipe as an example, the new transfer matrix based on Laplace transform is used to derive the system’s characteristic equation calculating its natural frequency, and then the vibration characteristics such as natural frequency and critical velocity are studied. During this process, influences of the steady-state combined tension, flow model modification factor, and system’s components etc. on the vibration characteristics are investigated. According to the above investigation, the ‘fake coupled-mode divergence’ is firstly put forward, it can be concluded that different steady-state combined combined tension may lead to different critical velocity, change of system’s components may lead to distinguishing judgement for stability. The vibration differential equation is also established based on the approach ‘replacing straight by curved’, results of the above two thoughts are verified to be the same. The above investigation can provide insights for studying vibration characteristics of other types of pipes and behaviors of other fluid structure interaction mechanics as well, and be of high guiding meanings for theory and values for practice.