Modal Sensor for Axial Propagating Waves in an Infinite In-Vacuo Pipe

ABSTRACT: In an infinite in-vacuo pipe, the radial vibration can be decomposed into an infinite number of circumferential modes. For each mode, there is a right-going and a left-going propagating axial wave. In this paper, a sensor to detect either one of these waves is described. The wave chosen belongs to the first circumferential (n 2) mode of vibration, and the sensor consists of two PVDF (polyvinylidene fluoride) elements shaped in the form of sine and cosine functions. Two elements are required because the orientation of the wave at some arbitrary point on the pipe is generally unknown. The relationship between the charge generated on the element to the combination of axial and circumferential bending strains, is established for the case of in-extensional deformation. It is found that a practical sensor is sensitive to higher order modes as well as the n 2 mode, and this cross-sensitivity is dependent upon the width of the modal sensor. It is shown that the cross-sensitivity is small provided that the width of the modal sensor is less than one third of the wavelength of the propagating wave at the ring frequency. Experimental results are presented to validate the sensor sensitivity equation