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In recent years, the electrification of transport has emerged as a trend to support energy efficiency and CO2 emissions reduction targets. The true success, however, of this trend depends on the successful integration of electric vehicles on the infrastructure systems that support them. Left unmanaged electric vehicles may suffer from delays due to charging or cause destabilizing charging loads on the electrical grid. While many works have sought to mitigate these effects with advanced functionality such as coordinated charging, vehicle-togrid stabilization, and charging queue management, few works have assessed these impacts as a holistic transportation-electricity nexus. Furthermore, rigorous dynamic system mathematical models that couple the kinematic and electrical states have yet to be developed holistically. This paper develops such a model in the hopes of its application by EV fleet operators to not just assess but also improve their operations & control. The hybrid dynamic system model is composed of a marked petri-net model superimposed on the continuous time kinematic and electrical state evolution. The application of the model is demonstrated on an illustrative example of modest size and sufficient functional heterogeneity.

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A novel and continuously parameterized form of multi-step transversal linearization (MTrL) method is developed and numerically explored for solving nonlinear ordinary differential equations governing a class of boundary value problems (BVPs) of relevance in structural mechanics. A similar family of multi-step tangential linearization (MTnL) methods is also developed and applied to such BVP-s. Within the framework of MTrL and MTnL, a BVP is treated as a constrained dynamical system, i.e. a constrained initial value problem (IVP). While the MTrL requires the linearized solution manifold to transversally intersect the nonlinear solution manifold at a chosen set of points across the axis of the independent variable, the essential difference of the present MTrL method from its previous version [Roy, D., Kumar, R., 2005. A multistep transversal linearization (MTL) method in nonlinear structural dynamics. J. Sound Vib. 17, 829-852.] is that it has the flexibility of treating nonlinear damping and stiffness terms as time-variant damping and stiffness terms in the linearized system. The resulting time-variant linearized system is then solved using Magnus' characterization [Magnus, W., 1954. On the exponential solution of differential equations for a linear operator. Commun. Pure Appl. Math., 7, 649-673.]. Towards numerical illustrations, response of a tip loaded cantilever beam (Elastica) is first obtained. Next, the response of a simply supported nonlinear Timoshenko beam is obtained using a variationally correct (VC) model for the beam [Marur, S., Prathap, G., 2005. Nonlinear beam vibration problems and simplification in finite element model. Comput. Mech. 35(5), 352-360.]. The new model does not involve any simplifications commonly employed in the finite element formulations in order to ease the computation of nonlinear stiffness terms from nonlinear strain energy terms. A comparison of results through MTrL and MTnL techniques consistently indicate a superior quality of approximations via the transversal linearization technique. While the usage of tangential system matrices is common in nonlinear finite element practices, it is demonstrated that the transversal version of linearization offers an easier and more general implementation, requires no computations of directional derivatives and leads to a consistently higher level of numerical accuracy. It is also observed that higher order versions of MTrL/MTnL with Lagrangian interpolations may not work satisfactorily and hence spline interpolations are suggested to overcome this problem.

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