Numerical modeling of a smart structure with regard to sensitivity analysis of the system
A smart structure, a popular research object, is a complex structure with one or several sensor(s), actuator(s), and controller(s), implying it can contain more uncertainties than a passive structure. Numerical analysis is a very effective method to analyze a smart structure in comparison to the traditional method by using an analytical model, which would be extremely complex in this case. Moreover, many commercial finite element (FE) model software packages provide element and material libraries, which cover many different kinds of elements and materials and can be directly used. This makes the numerical modeling easier and more effective than the analytical modeling. This paper uses a smart beam structure as a reference system to show the process of building a numerical model of a smart structure with regard to the sensitivity analysis of this system in ANSYS. The FE model building process, including the definitions of element types, materials, structural damping matrices, and parameters of the meshing, is explained step by step in this paper. After that the structural matrices are extracted from this FE model and can be used for the controller design. This FE model aims at the system's sensitivity analysis. According to the analysis' requirements it should be able to be built and simulated with many combinations of the slightly varied structural input parameters. Therefore, the duration of the model building and simulation should be short. Moreover, the sizes of the structural matrices should also be small enough for the control design, A good solution to meet both requirements is model order reduction (MOR). For this project, MOR for ANSYS based on the Krylov subspace method is chosen. The difficulties arise in the definition of the parameters for the model reduction algorithms. As a smart structure is a complex structure with mechanical and electrical components, the general reduction in MOR for ANSYS by using only one expansion point provides singular reduced matrices, which are not invertible and cannot be used for the controller design. This paper explains in detail how to overcome this singularity problem of the reduced matrices.