# Effects of Central Cut Width on the Dynamical Characteristics of Box Assembly Structure
## 1 Introduction
Nonlinear softening and hardening occur when the responses of the system bend one way or the other when the input excitation is increased. Typically, when frequency response curves show an increase in frequency, nonlinear hardening is present. When frequency response curves show a bend to the decrease in frequency, nonlinear softening is present [20; 21]. To further understand the relationship between nonlinearities and substructured components, a system with enough complexity and connections had to be developed. The Box Assembly with Removable Component (BARC) system was a collaboration of effort between researchers at both Sandia National Laboratories and the Kansas City National Security Campus which has led to an extensive study into its dynamical behaviors during shock, vibration, and modal tests [22]. It was initially introduced as a test article to evaluate fixture influence within different dynamic environments. The BARC is designed to mimic real-world testing conditions, where the system is made of a flexible box assembly and a removable component that represents a test article [23]. This is similar to that of aircraft engines mounted to a flexible wing or other payloads where the influence of the wing on the engine's dynamics would like to be understood. To replicate real-world scenarios,researchers carefully define boundary conditions and establish experimental setups to study the structure. Prior research on the system has demonstrated the importance that bolted connections and boundary conditions have on the dynamic response of the system, including nonlinear behaviors observed during modal testing and finite element analysis (FEA) [24]. Extensive research on various boundary conditions, including different hole configurations for bolted-joint connections, has provided insights into the system's behavior under various environmental tests, such as varying boundary conditions of the BARC itself [25; 26]. Prior to the introduction of the BARC, components were subjected to dynamical testing on rigid structures. This method typically fails to replicate real-world service environments, where components are subject to various degrees of flexibility. Some common examples include a missile attached to a jet wing or a CubeSat docking on a larger satellite [27]. The BARC allows for a structure that can simply replicate a service environment for specific components. Efforts have been and are currently being made to have a valuable understanding of the complexities of the BARC system, where researchers are continuously striving to enhance their grasp of its behavior under various testing conditions. Some of this research includes varying the size of the BARC and conducting multi-axis testing on the system [28; 29]. Research studies on the BARC have been conducted previously, but, to the authors' knowledge, no deep investigation on the changing of the size of the central cut has been conducted. Studies have shown two distinct iterations of the cut size, being an investigation with a no-cut case [22; 30] and studies with a common 0.5\" cut case [31; 32]. Prior work studying a BARC with a different cut width has not been shown. In this work, a configuration with a 0.25\" cut is selected due to it being the intermediate point between the no-cut and traditional 0.5\" cut system. The smallest cut that could be made on the Box Assembly (BA) is the 0.1\" thin cut. This is performed to compare the influence of just a thin cut as opposed to bigger cuts. It is not uncommon to see the removal or addition of mass to a system to influence its dynamical characteristics. The same purpose is investigated with the introduction of these two new cut systems. A recent conference paper by the authors has shown some preliminary results on the influence of the cut width on the dominant frequencies of the full BARC system [33]. This current study aims to comprehensively explore the effects of the cut width on the dynamical characteristics of the box assembly system.