Modal expansion of structural intensity for flexural vibration on beams

This paper derives the modal descriptions of structural intensity for flexural vibration on beams. The modal expansion of the intensity is superposistioned by modal terms expressed by the product of weight function and the product of two modes with or without spatial derivative, which is called cross-modal function" in this paper. The modal formulation has no limitation to express the exact intensity. The formulation can be simplified by the modal terms regarding the resonant mode in case of the beam with small loss factor when the beam is exciting around the resonance. Numerical simulations are carried out to verify these modal expansions and to discuss the characteristics of the weight coefficients and the cross-modal functions."