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This research explores the inherent vulnerability of nonlinear vehicle platoons characterized by the oscillatory behavior triggered by external perturbations. The perturbation exerted on the vehicle platoon is regarded as an external force on an object. Following the mechanical vibration analysis in mechanics, this research proposes a vibration-theoretic approach that advances our understanding of platoon vulnerability from two aspects. First, the proposed approach introduces damping intensity to characterize vehicular platoon vulnerability, which divides platoon oscillations into two types, i.e., underdamped and overdamped. The damping intensity measures the platoon’s recovery strength in responding to perturbations. Second, the proposed approach can obtain the resonance frequency of a nonlinear vehicle platoon, where resonance amplifies platoon oscillation magnitude when the external perturbation frequency equals the platoon’s damping oscillation frequency. The main contribution of this research lies in the analytical derivation of the closed-form formulas of damping intensity and resonance frequency. In particular, the proposed approach formulates platoon dynamics under perturbation as a second-order non-homogeneous ordinary differential equation, enabling rigorous derivations and analyses for platoons with complicated nonlinear car-following behaviors. Through simulations built on real-world data, this paper demonstrates that an overdamped vehicle platoon is more robust against perturbations, and an underdamped platoon can be destabilized easily by exerting a perturbation at the platoon’s resonance frequency. The theoretical derivations and simulation results shed light on the design of reliable platooning control, either for human-driven or automated vehicles, to suppress the adverse effects of oscillations. 

Connected automated vehicles (CAVs), built upon advanced vehicle control and communication technology, can improve traffic throughput, safety, and energy efficiency. Previous studies on CAVs control focus on instability and stability properties of CAV platoons; however, these analyses cannot reveal the damping platoon oscillation characteristics, which are important for enhancing CAV platoon reliability against variant continuous perturbations. To this end, this research seeks to characterize the damping oscillations of CAVs through exploiting the platoon's unforced oscillatory, i.e., damping behavior. Inspired by the mechanical vibration theory, the proposed approach is applied to a CAV platoon with linear car-following control formulated as Helly's model and the predecessor-following communication topology. The proposed approach is applied to a CAV platoon with the linear car-following control formulated as Helly's model and the predecessor-following communication topology. Numerical analysis results show that a periodic perturbation with the resonance frequency of the CAV platoon will amplify the oscillation and lead to the severest oscillatory traffic. Our analysis highlights the importance of preventing platoon oscillations from resonance in ensuring CAV platooning reliability. 

The performance of connected and automated vehicle (CAV) platoons, aimed at improving traffic efficiency and safety, depends on vehicle dynamics and communication reliability. However, CAVs are vulnerable to perturbations in vehicular communication. Such endogenous vulnerability can induce oscillatory dynamics to CAVs, leading to the failure of platooning. Differing from previous work on CA V platoon stability, this research exploits CAV platooning vulnerability under periodic perturbation by formulating the oscillatory dynamics as vibrations in a mechanical system. Akin to other mechanical systems, a CAV platoon has its inherent oscillation frequency, exhibiting unique characteristics in a perturbed travel environment. To this end, this paper proposes an approach to characterize the CAV platooning vulnerability using the mechanical vibration theory. The employed theory reveals that CAV platooning vulnerability mainly associates with its resonance frequency, through which a small periodic perturbation can amplify the platoon oscillation. The analytical formulation and simulation results show that preventing periodic perturbations from a platoon's resonance frequency is crucial to enhance the CAV platooning reliability and suppress large amplitude oscillations, helping to secure the expected benefits of CAV platoons.