A fundamental objective of a modal survey is to verify that a finite element model (FEM) of a structure is sufficiently accurate to predict the structure’s response to operating environments. The modal survey experimentally measures the natural frequencies, mode shapes, and damping of the test article. The mode shapes are obtained at the accelerometer locations which, for typical aerospace structures, usually include 100-400 locations.
In general, the FEM will have many more degrees of freedom (DOF) than the number of accelerometers on the test article. In order to directly compare the FEM with the test results, a reduced representation called a test-analysis model (TAM) must be generated. The degrees of freedom of the TAM will correspond one-to-one with accelerometers in the modal survey test configuration.
The development of a TAM serves several major functions. The successful selection of TAM DOF optimizes the test measurements and excitation locations. The reduced TAM mass matrix provides an ability to calculate on-site orthogonality checks of the test modes. Finally, the TAM enables a quantitative comparison of the accuracy of the FEM during posttest correlation activities in the form of orthogonality and cross-orthogonality checks. All of these tasks require an accurate reduction of the FEM mass and stiffness matrices to the TAM DOF. Otherwise, the TAM will not be able to perform its functions.
A number of different methods can be used to reduce the FEM to the TAM DOF. The methods used in TAMKIT include:
1. Static (Guyan) reduction [1]
2. Dynamic reduction
3. Improved Reduction System (IRS) method [2]
4. Modal reduction [3]
5. Hybrid reduction [4].
These reduction methods have been shown [5] to differ in both accuracy and robustness. “Accuracy” is a measure of the TAM’s ability to predict the modal frequencies and mode shapes of the finite element model. “Robustness” is a measure of a TAM’s ability to show orthogonality of test modes when the finite element model has inaccuracies. Robustness is of particular importance because showing orthogonal test modes is a common requirement for determining the success of a modal survey.
As a general rule, the static TAM, the default in Nastran, is the most robust but least accurate. The alternate TAMs all increase accuracy, but at the cost of decreased robustness. Because a FEM is never an exact representation of a structure, and because test data is not perfect, the robustness of the static TAM makes it the overwhelming method of choice for most modal tests. The goal of most pretest analysis, therefore, is to choose DOF that result in a sufficiently accurate static TAM. The alternative TAMs can be used in those situations where it is not possible to find a sufficiently accurate static TAM.
This chapter reviews the theory for each TAM reduction method. The accuracy and robustness of the various TAM methods will also be addressed. The implementation of these methods using TAMKIT is presented in Chapter 3.