Transient aeroelasticity of structures subjected to thunderstorm outflows

•A mathematical model to evaluate motion-induced forces on slender structures subjected to thunderstorm outflows is proposed.•Time-varying aerodynamic damping matrix and aerodynamic stiffness matrix of the system are defined.•Three levels of analysis are addressed, according to the characteristics of the wind event.•The classical solution for synoptic winds is found as a particular case.•Suitable wind fields compatible with single-point records are rebuilt and applied on two configuration of a structure, estimating the motion-induced forces.•The effects of the transient aeroelasticity are analysed and critically commented.•Motion-induced forces are evaluated on slender real structures.