Response prediction for modified mechanical systems based on in-situ frequency response functions: Theoretical and numerical studies

In this paper, a general method using in-situ frequency response functions (FRFs) is proposed for predicting operational responses of modified mechanical systems. In the method responses of modified mechanical systems can be calculated by using the delta dynamic stiffness matrix, the subsystem FRF matrix and responses of the original system, even though operational forces are unknown. The proposed method is derived theoretically in a general form as well as for six specific scenarios. The six scenarios correspond respectively to: (a) modifications made on the mass; (b) changes made on the stiffness values of the link between a degree-of-freedom (DOF) and the ground; (c) the fully rigid link between a DOF and the ground; (d) changes made on the stiffness values of the link between two DOFs; (e) the null link between two DOFs and (f) the fully rigid link between two DOFs. It is found that for scenarios (a), (b) and (d) the delta dynamic stiffness matrix is required when predicting responses of the modified mechanical system. But for scenarios (c), (e) and (f), no delta dynamic stiffness matrix is required and the new system responses can be calculated solely using the subsystem FRF matrix and responses of the original system. The proposed method is illustrated by a numerical example and validated using data generated by finite element simulations. The work in this paper will be beneficial to solving vibration and noise engineering problems.