An efficient transient analysis method for time-varying structures based on statistical energy analysis

•The SEA method is firstly applied to predict the transient energy response of time-varying systems.•The energy governing equations of time-varying systems are derived.•The effectiveness and accuracy of SEA method for time-varying system are investigated.•The effect of time-varying parameters on the transient energy response of subsystem is revealed.•The SEA method for time-varying system has a wider application scope for transient vibration response prediction of time-varying structure especially in the high frequency range.