A Poynting vector formulation for thin shells and plates, and its application to structural intensity analysis and source localization. Part I: Theory

This paper deals with a formulation of the Poynting vector (structural intensity) for thin shells and plates, and its application to structural intensity analysis and source localization. The procedure begins with the insertion of a Taylor series expansion of the displacement components (about the middle surface of the shell) directly into the three-dimensional representation of the Poynting vector. From this representation, an average power flow per unit length, or equivalently an intensity resultant, is derived, whose form permits expressibility in terms of force and moment resultants. The corresponding equations of continuity for energy are derived for both body and surface forces, and the time integral of the net outflow is developed, yielding a technique for source localization. This technique offers a method for the determination of the structural intensity of thin, elastic shells and plates, and is successful for source localization.