Formulation of total complex power and energy flows into a discrete system

By considering total inputs into a discrete system, this letter analytically formulates and summarizes the relationships in the complex-form power and energy flows and the dissipated power and Lagrangian energy of the system. The matrix inverse method to obtain the force/moment necessary for the power/energy flow is shown as an indirect yet analytically exact method. A 2 degree-of-freedom system is employed to analytically validate the derived formulas, followed by a computational confirmation. A finite element plate-beam model is further utilized to computationally confirm the relationships in the complex power and energy flows.

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