结构声学的中频预测问题是一直是业界的一个难点和热点。结构声学中频响应复杂，单一确定性的低频方法和统计性的高频方法都不合适中频问题的分析与预测。针对中频结构声学问题，引入基于单元边的梯度光滑技术，软化三维声学系统的刚度，结合统计能量法，构造基于光滑有限元和统计能量法的混合方法(ES-FE-SEA)的理论框架。算例表明，新构造的混合ES-FE-SEA能够在声固耦合系统的频响分析中得到比传统的FE-SEA混合方法更好的精度。

The predictions of the response of the vibro-acoustic problems in mid-frequency regime is one of hotspots and difficulties in academy and engineering. However, there is a broad series of mid-frequency vibro-acoustic problems that are not suited to either deterministic methods or statistic methods, due to the complexity of mixed behaviors in this frequency range. An edge-based smoothing technique is applied in the acoustic FEM model to soften the stiffness of whole system. This edge-based smooth finite element method (ES-FEM) is then embedded to achieve a similar hybrid ES-FE-SEA framework. The higher accuracy of proposed ES-FE-SEA comparing with FE-SEA is verified by various numerical examples.