Minima of Radiated Acoustic Power are Different from Structural Vibration

Significance 

Various structures respond differently to induced vibrations, where the material structure and the foundation material play vital roles. Therefore, in structural dynamics analysis, peaks and valleys of frequency response play vital roles. Such dynamic characteristics are usually expressed in the form of natural frequencies, antiresonances or minimum response frequencies. Apparently, vibrating structures also generate acoustic radiations, that possess both peak and valleys, which pose great impedance to numerous engineering applications. Presently, sensing methods are the most widely employed techniques of obtaining radiated acoustic power at an angular frequency. Unfortunately, recent studies have unearthed that by employing the normal techniques, where the eigenvalue is proportional to the radiation efficiency of corresponding radiation mode, and is different from the eigenvalue of vibration system in that it may represent a pole or zero of the responses, the poles and minima of the radiated acoustic power still cannot be obtained with the radiation modes. Overall, disappointing results in terms of radiated acoustic power are obtained.

Professor Sheng Li and his PhD student Maolong Xia from the State Key Laboratory of Structural Analysis for Industrial Equipment at Dalian University of Technology in China addressed the aforementioned poles and minima of the radiated acoustic power. To achieve this goal, they purposed to formulate a novel technique whereby the poles and the minima would be obtained through solutions of polynomial equations. Their work is currently published in the research journal, Applied Acoustics.

They commenced their research by determining the relationship of peaks and valleys between radiated acoustic power and vibration response. Next, they conducted numerical simulations where the calculation model for the poles and minima of radiated acoustic power were developed and employed. Lastly, the two researchers applied the numerical models to a simply supported plate so as to demonstrate the effectiveness of developed technique.

The authors observed that the poles of radiated acoustic power were coincident with the poles of vibration response. Additionally, they noted that the minima of radiated acoustic power could be obtained with knowledge of the location of exciting force, modal radiation efficiencies, poles and modal shapes of structure. Furthermore, from the numerical example undertaken, a comparison of the minima of radiated acoustic power and the corresponding antiresonances showed that the adjacent modal radiation efficiencies affected their relative values.

Sheng Li-Maolong Xia study has successfully demonstrated the development of a new formulation for the poles and minima through the solution of a polynomial equation. It was mainly observed that the obtained poles and minima using the novel technique could be utilized to describe the shape of the radiated acoustic power in the frequency range of interest. Altogether, the novel technique may be a feasible approach for the control of acoustic radiation with the assignment of poles and minima of radiated acoustic power.

About the author

Sheng Li received his Ph.D. degree in Naval Architecture and Ocean Engineering from Dalian University of Technology in 2001. He currently is a Professor at School of Naval Architecture, Dalian University of Technology, China. His research interests are Vibro-acoustic analysis of complex systems, structural acoustic modeling, active and passive control in acoustics and vibration.

About the author

Maolong Xia received his B.S. degree in naval architecture and ocean engineering from Ocean University of China, in 2012. Currently, he is a Ph.D candidate in the School of Naval Architecture, Dalian University of Technology, China. His current research interests include modal analysis, eigenstructure assignment, active control of vibration and sound radiation.

Reference

Maolong Xia, Sheng Li. The poles and minima of radiated acoustic power from plate vibration. Applied Acoustics, volume 131 (2018) page 45–50

Go To Applied Acoustics

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