Nonlinear vibration model and response characteristic of drilling risers in deep-sea under soft suspension evacuation condition

•A dynamic model for drilling risers under soft suspension evacuation is established.•The nonlinear coupling of longitudinal-CF-IL in three directions is considered.•The correctness and effectiveness of model are verified by experimental results.•The progressiveness of model is verified by comparing with the hard suspension model.•The effect of environmental and operation parameters on response characteristics are investigated.