Energy flow analysis of mid-frequency vibration of coupled plate structures with a hybrid analytical wave and finite element model

• The propagative waves of the plates are considered as subsystems that carry and spread energy.
• Symplectic analytical solutions for modal density and group velocity of each subsystem are obtained.
• The input mobility and coupling factor are obtained using a hybrid analytical and finite element formulation.

The medium frequency vibration of a built-up plate structure is studied by an energy flow analysis which extends the concept of statistical energy analysis. The propagative waves of the plates are considered as subsystems that carry and spread energy. Symplectic analytical solutions for mode count, modal density and group velocity of each wave subsystem are obtained based on accurate consideration of the plate geometry and boundary conditions, while the joint vibrational behavior is described by a finite element model. The input mobility and coupling factor associated with each wave subsystem are accurately obtained using a hybrid analytical wave and finite element formulation. Based on the power balance relation of each wave subsystem, the system energy equations are established. Numerical examples for built-up structures comprising rectangular plates demonstrate high accuracy and efficiency. In contrast with statistical energy analysis, the energy of each wave subsystem can be obtained, facilitating the understanding and control of structural vibration and local response. The computational time of the hybrid formulation decreases significantly with increasing length/width ratio of the plates. The wave scattering property of the joint can also be obtained and used to replace the finite element model in repetitive analysis.