Time-varying torsional stiffness identification on a vertical beam using Chebyshev polynomials

• Chebyshev polynomials were used to identify the time-varying stiffness.
• Beam flexural modes had significant impact on torsional stiffness identification.
• Data was low-pass filtered to separate torsional and flexural modes of the beam.

This paper investigates the performance of the Chebyshev polynomial basis to identify the time-varying mechanical impedance of a vertical beam in torsion. The projection, derivation and product properties of Chebyshev polynomials were used to linearize the differential equation of 1-DOF mechanical systems having multiple time-varying parameters. This allowed the identification of a reduced set of projection coefficients without prior knowledge of initial system states conditions. The method was then applied to experimental data obtained from an equilateral beam excited in torsion while one beam support location was changed over time. Results showed 6.62×10−2% error in stiffness predictions compared to theoretical estimates. Signal filtering was critical to avoid contamination by bending modes of the beam and prior knowledge of inertia led to better results.