Chapter 14 - Evolutionary Energy Method (EEM): An Aerothermoservoelectroelastic Application

Abstract

This chapter focuses on a novel theoretical foundation Evolutionary Energy Method (EEM) with its root in the natural law of energy conservation, precisely the first Law of Thermodynamics. The Law of Evolutionary Energy (LEE) is the encompassing foundational evolutionary equation, where the evolutionary operator Đ is a directional change operation via parameter alterations on the energy-quantities, satisfying the energy-conservation law along the actual dynamic path. It acts on the total evolving energy, which is defined as the time integral of the total actual energy interactions in a dynamic system. The EEM is an algebraic (direct) energy method; it uses and needs no knowledge of differential equations of the system for response and/or control studies of dynamic systems. Introduction of the concept of Assumed-Time Modes (ATM) for the generalized response variables and generalized control inputs of a dynamic system in conjunction with the LEE culminates in elimination of time from the system dynamics. It then completely, yields the Algebraic Evolutionary Energy description of the system dynamics for response and control studies. As an application of the EEM, an aero-thermoservoelectroelastic system is described algebraically and illustrated for studying the feasibility of structural skin temperature control in Mach 10 hypersonic flight. This is done by using optimal distributed control actuation. The structural temperature and the structural deformation are controlled simultaneously by using only temperature-feedback optimal control laws via elastothermoelectric actuation.