Marcellin Zahui

Narrow band active control of sound radiated from a baffled beam using local volume displacement minimization

Abstract Further development of a control technique for reduction of sound radiated from vibrating structures is presented. This control technique is based on minimization of local volume displacement, velocity, or acceleration of a vibrating structure. Multiple, single-input/single-output cancellation devices are used. Each device controller employs a motion sensor and an acoustic actuator (loudspeaker). The motion sensor signal is related to the local volume displacement of the structure which is then reduced by a loudspeaker driven with an equal but opposing volume displacement. Previous work showed the successful implementation of this technique for uniformly vibrating radiators. This paper presents the development of this technique for reduction of sound radiated from a vibrating beam. A PVDF sensor was used for measurement of local volume displacement of the beam. This sensor was used in conjunction with an internal pressure sensor mounted in the loudspeaker enclosure. Sound reductions of up to 20 dB were achieved within a narrow range of vibration frequencies (centered around the first beam mode). Finally, design of a single integrated sensor is suggested for implementation of many PVDF sensors on a beam.

Theoretical development and experimental validation of local volume displacement sensors for a vibrating beam

Further development of local volume displacement sensors is presented. This development supports the implementation of noise control techniques that are based on minimization of local volume displacements, velocities, or accelerations of a vibrating structure. In this paper, we present a general methodology for the development of local volume displacement sensors for vibrating beams using PolyVinyliDene Fluoride (PVDF). This methodology was verified experimentally for a clamped beam. The local volume displacement measured using a single PVDF sensor matched the local volume displacement found using multiple accelerometer measurements. The resulting sensors span the entire length of the beam. They have a quadratic shape over that portion of the beam whose volume displacement is desired, and they have a linear shape over all other sections. Sensor design issues for different beam boundary conditions are discussed along with a presentation of some sample sensor shapes for various beam segments and boundary conditions.

Development of an acoustic cloud condensation nuclei counter

Theoretical development of an acoustic cloud condensation nuclei counter is presented. The proposed instrument will be able to count the number of aerosols present in a sample of air flowing through a growth chamber. The air condenses around aerosols and forms water droplets. The number of aerosols is determined by measuring the sound produced underwater by these droplets when the droplets strike a water surface at the bottom of the growth chamber with an impact velocity equal to either their terminal or maximum velocities. First, the terminal velocities of the droplets are calculated. Then, the maximum velocities that these droplets can sustain without breaking are calculated as a function of droplet diameter. Second, the sound due to droplet impact is estimated and experimentally verified. In this study the bubble sound is not considered because micro droplets falling with terminal velocities do not create bubbles. Also, when accelerated, the velocities are limited such that there is no bubble formation...

Multiphysics analysis of a loudspeaker

A coupled physics analysis of a loudspeaker is presented. This finite‐element analysis of a theoretical loudspeaker is performed using a commercial finite‐element package installed on a Window‐based personal computer. The objective is to use multiphysics modeling to analyze the loudspeaker coupled fields (electric, magnetic, structural, fluid, and acoustic) that are solved in a single step. All the components of the electro‐acoustic transducer, i.e., the rear plate, the magnet, the voice coil, the pole piece, the spider, the frame, the cone, and the dust cap are incorporated in a single finite‐element model. The system is then analyzed using an electrical input circuit also modeled using finite element to evaluate the acoustic radiation from the cone. Even though the solution is obtained in a single analysis, each physics field is separately validated with known and well‐established data. First the magnetic field is validated, then the resulting structural displacement of the cone, and finally the fluid f...

Volume displacement sensors for vibrating beams: Numerical approach

The development of volume displacement sensors for vibrating beams is revisited with emphasis on numerical approach. This development supports the implementation of noise control techniques that are based on minimization of volume displacements, velocities, or accelerations of a vibrating structure. This paper first reviews some of the existing general methodologies for the development of volume displacement sensors for vibrating beams using PolyVinyliDene Fluoride (PVDF). The presentation includes the quadratic and modal development of volume displacement sensors for vibrating beams. These techniques are extended to numerical analysis by discretizing the beam and assuming constant sensor shape on each beam element. The result is a system of linear equations in which the assumed constant shapes are the unknowns. The size of the system of equations, which determines the accuracy of the sensor, is directly related to the highest frequency in the signal to be processed. The resulting sensors are numerically ...

Development of beam volume displacement sensors using genetic algorithm

Further development of total (local) volume displacement sensors is presented. This development supports the implementation of noise control techniques that are based on the minimization of local volume displacement of vibrating structures. In this work, a genetic algorithm is used for the design of volume displacement sensors for vibrating beams using PolyVinyliDene Fluoride (PVDF). First the sensor is assumed to cover the entire beam surface. Then, the covered area is discretized into small patches. The algorithm selects the required patches to yield the PVDF shape necessary to measure the beam volume displacement. The sensor is numerically verified for various beam boundary conditions. The results show close agreement between the calculated beam volume displacement of the beam and the simulated output charge of the sensor. The extension of the genetic algorithm methodology to volume displacement sensors for 2‐D vibrating structures is briefly discussed.

Measurement of stress/charge coefficients of a thin polyvinylidene fluoride film

A new experimental/analytical approach is used to measure a piezoelectric coefficient of polyvinylidene fluoride (PVDF). This method is based on the volume displacement of a vibrating beam. The obtained value of the stress/charge coefficient is checked using modal coordinate measurement theory and finite element analysis. A PVDF film is cut into two sensors shape. These sensors measure, respectively, the volume displacement and modal coordinate of a simply supported beam vibrating at its first mode. An accelerometer and a force gauge are used to measure the volume displacement and the modal coordinate of the beam. Then, PVDF volume displacement sensor equation developed by Guigou et al. is used with the experimental data to find the stress/charge coefficient e31. This value of e31 is first checked using the PVDF modal sensor equation from Lee and Moon. Then, the anys finite element code is used to validate the method. Experimental value of e31 obtained at room temperature is presented and compared with ex...

Theoretical development and experimental verification of polyvinylidene flouride sensors for measurement of the local volume displacement of beams

One method of reducing the sound radiated from vibrating structures at lower frequencies is to reduce the volume displacement of the vibrating surface (via active control). At these low frequencies, the volume displacement is directly proportional to the sound power emitted from a vibrating surface. To extend the effective frequency range of the active control system, several systems that reduce the volume displacement over localized areas of structural surface were employed. Thus, means of measurement of structural surface volume displacement become important. A traditional approach is to employ multiple point sensors (accelerometers). Recently, a single sensor made of polyvinylidene fluoride (PVDF) was utilized and found to represent an attractive solution. These sensors, which were designed to measure the structural volume displacement over a segment of structural surface, spanned the entire length of the structure. Such arrangement was found to be inefficient. In the work presented here an integrated ...

Investigation of local volume displacement sensors for rectangular vibrating plates

Further development and validation of a technique for measurement of local volume displacement is presented. This development supports the implementation of noise control techniques that are based on minimization of local volume displacements, velocities, or accelerations of a vibrating structure. In this work, we present a brief description of the methodology for designing such sensors fabricated using polyvinylidene fluoride (PVDF) film followed by the experimental verification of these sensors for a vibrating clamped–clamped plate comprising one side of an otherwise rigid box. These experimental results were then compared against predicted values.