## 1 Introduction
For example, if the input excitation increases and the frequency response of the system indicates an increase in resonant frequency, then the system is displaying nonlinear hardening. If the frequency response indicates a decrease in resonant frequency, then nonlinear softening is displayed in the system. Damping refers to the changing amplitude of a system's motion due to an external force that is a function of velocity [7]. Traditionally, damping is the main root of nonlinearity within a system and is seen to increase as the excitation level increases [8]. Ground vibration testing allows for the determination of these types of nonlinearities present in the system. As aforementioned, the rigidity of the BARC system changed when the central cut was introduced [4]. This allowed for a more flexible system that can better replicate a real-world environment. Previous component testing was conducted on rigid fixtures that did not recreate the service environment of the component being tested [9]. What can be seen in the industry is that most components are fixed to flexible fixtures, such as a CubeSat docking on a larger space system [10]. Therefore, by making the BARC less rigid, the removable component's dynamics can be analyzed through laboratory testing and mimic the service environments of other complex systems [11; 12; 13]. Testing complex systems may be difficult due to the different components affecting the overall system's behavior. A substructuring approach allows experimenters to break down the system into individual components and dynamically characterize their behavior. In doing so, each component can be analyzed, and the behavior of the whole system can be derived from the information found from testing the individual components [14; 15]. Our research focused on the fully assembled BARC system, utilizing two main forms of substructuring, namely, frequency-based substructuring and dynamic substructuring. Frequency-based substructuring (FBS) allows a complex structure to be broken down into subcomponents and have them analyzed through the frequency domain and characterize their dynamical properties [16; 17; 18; 19]. This type of substructuring approach can be seen all throughout industry, especially in the automotive world, as discussed in [20]. FBS is used to compare data from the automobile drivetrain and those obtained from finite element models. FBS is implemented in various applications because it allows local behavior to be analyzed faster than if the system were whole. Therefore, if there is a component present that has no effect on the dynamic behavior of the system, it can be dealt with. [PERSON] et al. [21] stated that the origin of dynamic substructuring came from domain decomposition or the separation of the problem into its components to find a concurrent solution. A complex system can be analyzed in three distinct ways in dynamic substructuring, namely, the modal, frequency, and physical domains. There is another popular substructuring method, which is known as Lagrange Multiplier Frequency-Based Substructuring (LM FBS). [PERSON] et al. [22] claim that this method, which is an extension of FBS, yields a more straightforward formulation while still being based on measured frequency-dependent transfer functions. FBS is the most common when experimenting because of the ability to define dynamic properties based on frequency response functions (FRFs) [23]. Our work applied both substructuring methods due to their explained benefits. There have been previous studies conducted on the BARC system using the same substructuring approach, but no work, to the knowledge of the authors, has been conducted on a BARC system with varying central-cut widths. Contemporary work focused on either a no-cut BARC system or a standard 0.5\({}^{\prime\prime}\) cut width system [1; 4; 24; 25]. Here, this study explored the effects on the BARC system caused by varying central-cut widths. This was accomplished by conducting three types of experimental vibration testing.