Structural Dynamic Modification Based on Combined Approximations Method

Structural dynamic modification plays an important role in structural dynamic design. This paper presents an algorithm for dynamic modification of the structure, which is based on the Combined Approximations (CA) approach, sensitivity analysis, Taylor series expansion and the least square method. The feasibility of the algorithm is verified by a numerical example and the results show that the algorithm is accurate enough and easy to be implemented.

Structural Reanalysis Based on FRFs Using Sherman–Morrison–Woodbury Formula

Structural dynamic modification is a popular approach to obtain desire frequencies and dynamic characteristics. It has been observed that reanalyzing the modified structure usually involves complicated calculations when modifications are concerned with numerous degrees of freedom (DOFs), especially adding substructures to these DOFs. This paper proposed a method to reanalyze the frequency response functions (FRFs) of structures with multiple co-ordinates modifications. Two different cases are taken into consideration in the modifications, including adding (or decreasing) masses, stiffness, and damping, as well as adding spring-mass substructures, which makes the method more practical. This method is developed by employing Sherman–Morrison and Woodbury (SMW) formula based on the FRFs related to the modifications coordinates of the original system. The advantage of this method is that neither a physical model nor a modal model is required; instead, it needs only the FRFs, which can be directly measured by experimental modal testing. Another salient feature of this proposed strategy is that the FRFs of the modified structure can be calculated in only one step. Validation of this proposed method is demonstrated using various numerical examples. It is shown that the method is very effective and can be considered for real applications.

Dynamic Behavior of Supported Structures from Free-Free Modal Tests Using Structural Dynamic Modification

Several structures are completely or partially manufactured in a factory and then transported to the final situation where they are going to be located. An accurate methodology to check the serviceability of the structure in the factory, previously to the transportation and final assembly, will diminish significantly the costs of validation of its dynamic behavior. The structural dynamic modification (SDM) can be used to predict the modal parameters of a supported structure from the experimental modal parameters corresponding to the same structure but tested in a configuration easy to reproduce in a factory, such as the free-free condition. However, the accuracy obtained with this technique depends on how well the boundary conditions modelled with the SDM replicate the real support conditions. In this paper the SDM theory is used to predict the modal parameters of a pinned-free beam, a cantilever beam, and a 3D steel beam structure from the experimental natural frequencies and mode shapes of the same structures tested in free-free configuration. The predictions provided by the SDM theory are validated by operational modal testing on the supported structures. It is shown how the aforementioned boundary conditions can be modelled with the SDM, and the accuracy provided by the technique is investigated.