Comprehension of Frequency Response Function from the Viewpoint of Wave Energy Propagation

Frequency Response Functions (FRFs) are known as primary indicators for vibration design. However, vibrational design based on profound comprehension of the time evolution of FRFs has not come into wide use, while steady state FRFs are popular in vibration analysis. Then we focused our efforts on the FRFs as the superposition of waves. Formation process of FRFs may be designed by the view point of wave energy propagation, after the comprehension of the excitation of vibration mode by the wave energy flow into each element. By these three major noise and vibration analysis techniques, such as wave analysis, modal analysis and energy analysis, we can obtain a cross-sectional method to devise structural modification to realize intended FRFs shaping. This paper utilizes the ray-trace method which is developed for one-dimensional structures to comprehend the FRFs as the superposition of waves. Then, the ray-trace method is combined with throw-off element, and accordingly wave energy flow is tied with time evolution of FRFs. Finally, it is shown that intended FRFs shaping is realized by controlling wave energy path by structural modifications.