Methods and systems for non-destructive estimation of a length of a member

A system for non-destructive estimation of a length of a member, comprising:

• an impact hammer;
• a plurality of sensors attached to the member;
• and
• a computing device operably connected to the sensors, the computing device comprising a processor and a memory operably connected to the processor, wherein the memory has computer-executable instructions stored thereon that, when executed by the processor, cause the processor to:
• receive a respective signal recorded at each of the sensors, the respective signals comprising dispersive waves generated by impact between the impact hammer and the member;
• transform the respective signals into a frequency domain;
• determine an effective wavenumber of dispersive wave propagation based on the respective frequency-domain signals;
• using a dispersion relation for the member, determine a theoretical wavenumber of dispersive wave propagation;
• and
• estimate the length of the member based on the relationship between the effective wavenumber of dispersive wave propagation and the theoretical wavenumber of dispersive wave propagation.

A non-transitory computer-readable recording medium having computer-executable instructions stored thereon for estimation of a length of a member that, when executed by a computer, cause the computer to:

• receive a respective signal recorded at each of a plurality of sensors attached to the member, the respective signals comprising dispersive waves;
• transform the respective signals into a frequency domain;
• determine an effective wavenumber of dispersive wave propagation based on the respective frequency-domain signals;
• using a dispersion relation for the member, determine a theoretical wavenumber of dispersive wave propagation;
• and
• estimate the length of the member based on the relationship between the effective wavenumber of dispersive wave propagation and the theoretical wavenumber of dispersive wave propagation.