The mathematical theory is the same for analytical dynamic mechanics and analytical structural mechanics. In fact, the difference is just a symbol for vibration and structural mechanics. Therefore, the method of analytical mechanics can be applied to both sides. The difference for hyperbolic and elliptic partial differential equations is also a sign. Although they are different in nature, there are common theories to analyze them. This paper presents that it is not necessary to discrete time and space domain separately for the finite element analysis and that the time and space domain can be discrete mixed to form harmony finite element mesh. The numerical results show that the harmony finite element method is a promising method.