Volume displacement sensors for vibrating beams: Numerical approach
Sai Prassad Jangiti, Marcellin B. Zahui · The Journal of the Acoustical Society of America · 2004
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 and experimentally verified for a simply supported beam. The results show for low-frequency application, relatively simpler sensor shapes can be utilized, whereas for higher frequencies the sensor shape converges to quadratic function. Finally, sensor accuracy and the range of the application frequency are discussed and some sample shapes presented.