# Simplification of Complex Structural Dynamic Models:
## 1 Introduction
Epistemic uncertainties are characterized by a lack of completeness, or by simplification. This is the case when complex physical relations are modelled with simplified mathematical assumptions, for example ideal stiff boundary conditions in the FE-model. This kind of uncertainty can be reduced through increased knowledge and physical understanding. [PERSON] et al. [20] investigated the minimization of sound radiation from finite beams over a frequency range of interest. The optimization was run for different cases of excitation and boundary conditions. They found that the density, thickness, and Young's modulus significantly accounted for the optimization variables. Regarding the uncertainties in finite element modelling, boundary conditions may be one of the most critical factors. This statement is proven in this study. Therefore, an analytical formulation of a beam with a large end mass is developed according to [PERSON] [21] and [PERSON] et al. [22] and validated with numerical and experimental results. This analytical theory demonstrates the influence of ideal boundary conditions (BC) as a fundamental issue in the modelling process. To exemplify the importance of \"simple\" modelling procedures and in order to not over-analyse the model, we chose to not include a flexible boundary condition between the beam and the mass. In the structural dynamics community, including a non-ideally rigid connection and investigating the ratio of masses between the two objects would clearly be a necessary option to consider, but seeking an optimal solution is not the subject of this work. However, it is shown that, in the process of simplifying the finite element models, choosing appropriate boundary conditions must be done carefully, and some possibilities for simplifying a large mass in a 3D finite element model are validated. The influence of unavoidable uncertainties, such as materials and geometry, are quantified in this work and implemented in the experimental modal analysis via the interval method, described in [23; 24; 25; 26]. Here, the primary focus is the evaluation of a structure's modal behaviour for engineering purposes, and thus only the first few eigenfrequencies are treated. The original structure, then, is investigated under four variations of a finite element model with varying degrees of simplification in each. Free vibration results from the models, without uncertainty, are compared against experimental modal analysis, which includes uncertainty. An analytical model is also included as a fifth variation since this is an important element in an engineering design scheme. Although we consider many variations for a single configuration, the results reflecting beam-like structures may be generalized to other structures that are normally encountered in mechanical design, such as a point-mass approximation. The manuscript is structured as follows: in Section 2, descriptions of the test sample, the uncertainty in the material and geometrical parameters, and the investigated numerical models are provided. The performed experimental modal analysis and the analytic theory are also presented here. To perform the finite element analyses, the computational software ABAQUS/CAE [1] is used as the numerical tool. In Section 3, the experimental, analytical, and numerical results are compared and discussed, while our conclusions are drawn in Section 4.