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Vehicle structure crashworthiness design is one of the most challenging problems in product development and it has been studied for decades. Challenges still remain, which include developing a reliable and systematic approach for general crashworthiness design problems, which can be used to design an optimum vehicle structure in terms of topology, shape, and size, and for both structural layout and material layout. In this paper, an advanced and systematic approach is presented, which is called Magic Cube (MQ) approach for crashworthiness design. The proposed MQ approach consists of three major dimensions: Decomposition, Design Methodology, and General Considerations. The Decomposition dimension is related to the major approaches developed for the crashworthiness design problem, which has three layers: Time (Process) Decomposition, Space Decomposition, and Scale Decomposition.

In this work, we discuss statistical energy methods for predicting mid-frequency vibration transmission between two spring-coupled substructures with parameter uncertainties. We adopt a parameter-based approach, which allows us to relax certain assumptions associated with a classical Statistical Energy Analysis (SEA) approximation. We consider both a numerical method and an analytical method. The latter is called a Parameter-based Statistical Energy Method (PSEM). An example of two elastic bars coupled by a single spring or multiple springs is examined. The power transmitted from the excited substructure to the other substructure is calculated and compared for the various methods.