Random Sound Radiation of Thin Plates Under Turbulent Boundary Layer Excitations With a Symplectic Method

PAN Chenge; LI Yuyin; ZHANG Yahui

doi:10.21656/1000-0887.380151

Volume 39 Issue 1

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PAN Chenge, LI Yuyin, ZHANG Yahui. Random Sound Radiation of Thin Plates Under Turbulent Boundary Layer Excitations With a Symplectic Method[J]. Applied Mathematics and Mechanics, 2018, 39(1): 50-63. doi: 10.21656/1000-0887.380151

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Random Sound Radiation of Thin Plates Under Turbulent Boundary Layer Excitations With a Symplectic Method

doi: 10.21656/1000-0887.380151

State Key Laboratory of Structural Analysis for Industrial Equipment(Dalian University of Technology), Dalian, Liaoning 116024, P.R.China

Funds: The National Natural Science Foundation of China（11672060）

Received Date: 2017-05-23
Rev Recd Date: 2017-11-16
Publish Date: 2018-01-15

Abstract

Abstract

The random sound radiation of thin plates subjected to turbulent boundary layer (TBL) excitations was studied in the symplectic duality system. Firstly, the cross power spectral density of the TBL was represented by a Fourier series, and the problem of the random sound radiation of structures excited by a random field was reduced to solve the deterministic response function, i.e. the structural response to a spatial and temporal harmonic pressure of unit magnitude. Secondly, the free vibration analysis of thin plates was introduced to the symplectic duality system, then a symplectic eigenproblem was formed with the method of separation of variables. Finally, the decoupled governing equations were derived through expansion of the response and excitation vectors in the symplectic space, to reduce the difficulty of solving the equations, and the symplectic analytical solution was obtained. In contrast to the modal decomposition method (MDM), the presented method is formulated in the symplectic duality system and does not need modal truncation, hence the computations are of high precision. In the numerical examples, the harmonic response functions for the thin plate were studied, and a comparison was made with the MDM to verify the effectiveness of the presented method. Thereafter, the sound pressure levels (SPL) of the power spectral density of the sound pressure response to the TBL were obtained, the convergence induced by the Fourier series expansions was examined, and the directivity functions of the radiation sound field were extensively investigated.
- symplectic duality system,
- turbulent boundary layer,
- random vibration,
- random sound radiation

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References

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