Wavenumber-adaptive control of sound radiation from structures using a `virtual` microphone array method

A method for reducing acoustic radiation from a structure and acoustic noise transmission through the structure, the structure having generally opposed first and second exterior surfaces and an interior portion bounded by the two surfaces, the structure vibrating in a multiplicity of flexural modes of vibration, comprising the steps of:

• measuring a vibration field on the vibrating structure;
• computing, using the vibration field measurements, a far-field acoustic radiation pressure field in an ambient medium, generated by the vibrating structure;
• computing a wavenumber-space representation of the acoustic radiation pressure field in a first plane generally parallel and contiguous to a surface of the vibrating structure;
• computing a projection of the wavenumber-space representation of the acoustic radiation pressure field onto a second plane in the far-field, the second plane parallel to the first plane;
• computing a spatial representation of the acoustic radiation pressure field in the second plane, for flexural wavenumbers smaller than the acoustic wavenumber of the ambient medium, which is the set of acoustic outputs of a planar array of virtual microphones in the second plane, each output corresponding to a virtual microphone at one of a plurality of preselected positions in the second plane;
• providing said spatial representation as error signals for implementing a plurality of adaptive least mean squares algorithms generating a plurality of control signals;
• using the control signals to generate a plurality of forces that when applied to the vibrating structure suppress flexural modes of vibration characterized by flexural wavenumbers smaller than the acoustic wavenumber of the ambient medium;
• and
• applying the forces to the vibrating structure.

An apparatus for reducing acoustic radiation from a structure and acoustic noise transmission through the structure, the structure having generally opposed first and second exterior surfaces and an interior portion bounded by the two surfaces, the structure vibrating in a multiplicity of flexural modes of vibration, comprising:

• means for measuring a vibration field on the vibrating structure;
• means for computing, using the vibration field measurements, a far-field acoustic radiation pressure field in an ambient medium, generated by the vibrating structure;
• means for computing a plurality of error signals which are acoustic outputs of an array of virtual microphones, each output corresponding to a virtual microphone at one of a plurality of preselected positions in the far-field;
• means for using the error signals to generate a plurality of control signals;
• means for using the control signals to generate a plurality of forces that when applied to the vibrating structure suppress flexural modes of vibration characterized by wavenumbers smaller than a predetermined value;
• and
• means for applying the forces to the vibrating structure.

An apparatus for reducing acoustic radiation from a structure and acoustic noise transmission through the structure, the structure having generally opposed first and second exterior surfaces and an interior portion bounded by the two surfaces, the structure vibrating in a multiplicity of flexural modes of vibration, comprising:

• a plurality of accelerometers disposed on the first exterior surface of the structure;
• a plurality of piezoceramic actuators disposed on the second exterior surface of the structure;
• and
• an adaptive controller operating in a frequency domain, the controller determining control signals for the actuators from error signals derived from accelerometer measurements of the structure vibration, the error signals being acoustic outputs of an array of virtual microphones, each output corresponding to a virtual microphone at one of a plurality of preselected positions in the far-field, the control signals controlling flexural modes of vibration characterized by wavenumbers smaller than the acoustic wavenumber of the ambient medium.