Local force identification on flexural plates using reduced Finite Element models

• The Force Analysis Technique using a local Finite Element Method is proposed.
• Free boundary conditions and dynamic condensation of non measurable DOFs are used.
• To deal with a high number of DOFs, a Craig–Bampton reduction option is proposed.
• The ability to reconstruct equivalent forces due to moments is discussed.
• General guidance, numerical and experimental results are given on plates.

The identification of excitations on plates by an inverse method using local Finite Element modeling is studied. A dynamic condensation is proposed in order to eliminate Degrees Of Freedom not directly measurable like rotations. Before the condensation, the Craig–Bampton method can be optionally used to reduce the model (decrease of both computational and measurement times). Regularization based on the Tikhonov method and a double inversion of the operator is performed. After a numerical study of the accuracy of each step for different excitations, an experimental validation finally proved that it was both possible to locate accurately a shaker over a wide range of frequency and to estimate the amplitude of the injected force. Both dynamic condensation and Craig–Bampton reduction were used. Even if it induces some imprecision, the Craig–Bampton reduction was found to be a fundamental step to reduce both computational cost and the measurement effort which were the main problems to address in such an approach.