The compact Green’s function for a semi‐infinite elastic plate, with application to trailing edge noise and blade–vortex interaction noise

The present work focuses on the alleviation of Blade Vortex Interaction (BVI) noise annoyance through a control methodology generating high-frequency aerodynamic BVI counter-actions. The low-power requirements make the Micro-Trailing Edge Effectors (MiTEs) particularly suited for this kind of application. The controller layout is set by observing the BVI scenario while the actuation law is efficiently synthesized through a process based on an analytical unsteady sectional aerodynamic formulation. The validation of the proposed control methodology is carried out through numerical investigations of a realistic helicopter main rotor in flight descent, obtained using computational tools for potential-flow aerodynamic and aeroacoustic analyses based on boundary element method solutions. In order to capture the aerodynamic influence of MiTEs through potential-flow simulations, the MiTEs are replaced by trailing edge plain flaps which provide equivalent aerodynamic responses. Results concerning the proposed controller capability to alleviate high-frequency blade loads and subsequent emitted noise from BVI events are presented and discussed.

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An approximate Green’s function for a locally excited fluid-loaded thin elastic plate

The Journal of the Acoustical Society of America ◽

10.1121/1.1577549 ◽

2003 ◽

Vol 114 (1) ◽

pp. 194-199 ◽

Cited By ~ 5

Author(s):

Daniel T. DiPerna ◽

David Feit

Keyword(s):

Green’S Function ◽

Green's Function ◽

Elastic Plate ◽

Thin Elastic Plate ◽

Locally Excited

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The Green's function of an elastic plate

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100028413 ◽

1953 ◽

Vol 49 (2) ◽

pp. 319-326 ◽

Cited By ~ 6

Author(s):

W. R. Dean

Keyword(s):

Differential Equation ◽

Green’S Function ◽

Green's Function ◽

Elastic Plate ◽

Arbitrary Point ◽

Normal Derivative ◽

Simple Expression ◽

Transverse Force ◽

Transverse Displacement ◽

Straight Lines

In this paper a simple expression in finite terms is found for the small transverse displacement of a thin plane elastic plate due to a transverse force applied at an arbitrary point of the plate. The plate is clamped along the semi-infinite straight lines represented by AB, CD in Fig. 1, these lines being the only boundaries of the plate. The transverse displacement w at any point (x, y) of the plate is a biharmonic function of the variables (x, y) which vanishes together with its normal derivative at all points of the boundary. Clearly w is also a function of the coordinates (x0, y0) of the point of application of the force, and it is known ((5), p. 173) that it is a symmetrical function of the coordinate pairs (z, y) and (x0, y0); it is the Green's function associated with the differential equation and the boundary conditions.

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