System and methods for sensing the vibrations of even cross-sectional modes in a circular cylinder using a pair of piezoelectric wires

A method for non-destructive testing of soundness of a cylindrical structure with a dual piezoelectric wire sensor system, comprising:

• attaching a first H-shaped caliper to the cylindrical structure at a first radial position;
• attaching a second H-shaped caliper to the cylindrical structure at a second radial position located ninety degrees from the first radial position;
• wherein each H-shaped caliper comprises:
• a first arm, a second arm and a crossbar connected to and perpendicular to the first arm and the second arm;
• a first caliper connector located near a first end of the first arm;
• a second caliper connector located near a first end of the second arm;
• a first wire connector located near a second end of the first arm;
• a second wire connector located near a second end of the second arm;
• a piezoelectric wire connected to the first wire connector and the second wire connector, wherein the piezoelectric wire is stretched between the first wire connector and the second wire connector;
• an electrical terminal connected to the piezoelectric wire at the second wire connector of each H-shaped caliper;
• inducing vibrations within the cylindrical structure by applying an impulse force to the cylindrical structure in a radial direction at one of a position located at in a range of about 10 cm to about 16 cm above the first and second radial positions and a position located at in a range of about 10 cm to about 16 cm below the first and second radial positions;
• receiving, by the electrical terminal, an electrical signal generated by the piezoelectric wire in response to expansion and contraction of a distance between the second end of the first arm and the second end of the second arm as a result of the vibrations;
• receiving, by a two-port signal subtractor having a first port connected to the electrical terminal of the first H-shaped caliper and a second port connected to the electrical terminal of the second H-shaped caliper, the electrical signals at the first port and the second port;
• subtracting, by the two-port signal subtractor, the electrical signals;
• generating, by the two-port signal subtractor, a difference signal;
• receiving, by a measurement unit connected to the two-port signal subtractor, the difference signal;
• performing, by the measurement unit, a frequency analysis of the difference signal;
• identifying by the measurement unit, a resonant frequency of an ovalling mode of the difference signal;
• and
• identifying by the measurement unit, a stiffness value of the cylindrical structure based on the resonant frequency of the ovalling mode.