# Effects of Central Cut Width on the Dynamical Characteristics of Box Assembly Structure
## 1 Introduction  
Modal testing enables the understanding of the dynamics within complex systems by subjecting these systems to a laboratory environment, closely replicating a service environment [1, 2, 3]. In doing so, modal testing grants a cost-effective alternative to field-testing, allowing for a minimization of uncertainties and greater control of the test subject. During laboratory testing, efforts are made to replicate a system's service environment as much as possible for the best results. It can prove challenging to mimic vibration testing environments as they may occur only during large scale events, such as earthquakes and mining activities [4, 5]. While doing so, one factor within the test changes at a time, giving an insight into how the dynamics of the system react to these changes. Transitioning from the laboratory to the field does pose challenges and verify knowledge of the system, as discussed by [PERSON] in [6]. Typically, dynamical testing is a very complex process. There are multiple points of interest within one system, giving researchers a difficult time trying to understand each point within a singular assembly. Running experiments on entire assemblies is often very difficult and expensive. Because of this, it is common to see researchers implement a substructuring approach that assists in the testing of various systems. Dynamic substructuring allows for the break-up of the system into individual components and characterizes the dynamical behaviors of these components by themselves, thus eventually understanding the behaviors of each component [7; 8]. Once the behaviors of each component are understood, researchers can rebuild the assembly back into the complete system with a better understanding of the complete dynamics due to substructuring. A common method of substructuring is a frequency-based substructuring approach with the goal of predicting the dynamical behavior of a system using its components through frequency response functions [9; 10; 11]. Another method commonly used in structural dynamics is component mode synthesis. This method has played a significant role in identifying dynamical behaviors of systems that are too difficult to analyze in their entirety [12]. When utilizing this substructuring method, local dynamical behavior is identified more easily than when testing the entire system since the smaller component is monitored more closely at an individual scale. A final substructuring approach to be considered for this study is the Craig-Bampton method. This method is based on creating reduced-order models of subparts for the assembly [13; 14]. This is relevant for creating reduced-order systems, but does not incorporate contact interferences, which will be seen and discussed in the experimentation section of this study. Other types of analysis include hybrid system analysis [15; 16], but the primary focus of the work carried out was on dynamic substructuring and frequency-based substructuring. This current work is conducted by investigating the linear and nonlinear characteristics within each system under consideration. A system can be determined to be linear or nonlinear by investigating the relationship between the input and output of the system. If a system has an output that corresponds to a specific input of the system, then that system is considered linear. If this relationship does not exist and there is no correspondence, the system becomes more complicated and is considered nonlinear [17; 18]. Various forms of nonlinearities can occur in a system including nonlinear damping, nonlinear hardening, and/or nonlinear softening. Nonlinear damping is considered a primary source of nonlinearity in numerous systems, which can be caused by many properties intrinsic to a system. Some of these can include geometry, material properties, and bolted-joint connections. Typically, as excitation increases in a system, the nonlinear damping force may also increase or decrease [19].