Reconstruction of time-dependent forces acting on a vibrating structure from pressure measurements

This paper proposes an approach to reconstruct the time-dependent forces acting on a vibrating structure from pressure measurements. In the approach, the pressures measured in the near field of the structure are related to the exciting forces at the reconstruction points by the transfer functions determined in an experimental way, whereupon the time-dependent forces can be reconstructed with these pressures as inputs. In the reconstruction process, an additional regularization with a mixed l_{p , q}-norm term is introduced to resolve the ill-posed inverse problem, which is able to take advantage of the prior knowledge of space and time characteristics of the forces. A numerical simulation of reconstructing the time-dependent forces acting on a plate and two experiments of reconstructing the impact forces acting on a semi-cylindrical shell and an elliptically shaped structure are carried out. The results demonstrate the feasibility of the proposed approach for reconstructing the forces in both temporal and spatial domains from pressure measurements. The proposed approach provides a non-contact and real-time way to identify the locations of forces and reconstruct their time histories, which can be further used to reveal the mechanical cause of the radiated noise.