Effects of temperatures on dynamic parameters of Vuilleumier machine with dwell motion based on developed third-order numerical model

•Developed a third-order model for Hofbauer cycle machine.•Model is validated by experiments.•Damping coefficient Cd and spring coefficient K are obtained at various conditions.•Respective effects of Th, Tw and Tc on Cd and K are also obtained.•Analytical solution based on Cd and K has high accuracy in free stroke's prediction.