This research predicts the onset conditions of the free piston Stirling engines using analytical solution of the governing equations and averaging-based Lyapunov technique. In this regard, firstly, the linear dynamic equations of the free piston Stirling engines are extracted. Then, the analytical solutions of the motion equations of the displacer and the power pistons are obtained. Afterwards, these analytical solutions are put into the mean value of the time derivative of Lyapunov function to obtain a convenient relation which provides meaningful information regarding the onset condition of free piston Stirling engines. The mentioned procedure has been verified by the results of multiple numerical simulations and the experimental data (B10-B and SUTech-SR-1). In addition, the results of this method have been validated by the outcomes obtained from the state-space technique. Lastly, by comparing the results of the simulation works and the experiments, it has been confirmed that this method is capable of precisely predicting the onset condition of free piston Stirling engines. Besides, the proposed approach could be used as a powerful tool to predict the behavior of various free piston Stirling engines regardless of whether they meet the onset condition or not.

本研究使用控制方程的解析解和基于平均值的李雅普诺夫技术来预测自由活塞斯特林发动机的启动条件。在这方面，首先，提取自由活塞斯特林发动机的线性动力学方程。然后，获得了置换器和动力活塞运动方程的解析解。然后，将这些解析解输入到Lyapunov函数的时间导数的平均值中，以获得便利的关系，该关系提供有关自由活塞式斯特林发动机启动条件的有意义的信息。多次数值模拟的结果和实验数据（B10-B和SUTech-SR-1）已验证了上述步骤。此外，通过状态空间技术获得的结果验证了该方法的结果。最后，通过比较仿真工作和实验结果，已确认该方法能够精确预测自由活塞斯特林发动机的起爆条件。此外，所提出的方法可以用作预测各种自由活塞斯特林发动机性能的有力工具，而不管它们是否满足启动条件。