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A frame structure such as vehicle frames is usually the primary load-carrying member and typically plays a dominant role in transmitting vibratory and acoustic energies from excitation sources to a receiver that may be a human body or any other subject sensitive or vulnerable to vibration and noise. Determination of vibratory power flows between beam-like structures has been the subjects of many investigations. However, most of these studies have been confined to some simplified or specific boundary and/or junction conditions. In this investigation, a general analytical method is developed for predicting the vibratory power flows between two beams that are rigidly or non-rigidly coupled together at an arbitrary angle. The cross coupling between the flexural and longitudinal waves at the junction has been taken into account, which becomes necessary when two beams are joined together at an angle.