Analytical modeling of viscoelastic dampers for structural and vibration control

Abstract

Different approaches to the mathematical modeling of viscoelastic dampers are addressed and their theoretical basis and performance are compared. The standard mechanical model (SMM) comprising linear springs and dashpots is shown to accurately describe the broad-band rheological behavior of common viscoelastic dampers and be more efficient than other models such as the fractional derivative model and the modified power law. The SMM renders a Prony series expression for the modulus and compliance functions in the time domain, and the remarkable mathematical efficiency associated with the exponential basis functions of a Prony series greatly facilitates model calibration and interconversion. While cumbersome, nonlinear regression is usually required for other models, a simple collocation or least-squares method can be used to fit the SMM to available experimental data. The model allows viscoelastic material functions to be readily determined either directly from the experimental data or through interconversion from a function established in another domain. Numerical examples on two common viscoelastic dampers demonstrate the advantages of the SMM over fractional derivative and power-law models. Detailed computational procedures for fitting and interconversion are discussed and illustrated. Published experimental data from a viscoelastic liquid damper and a viscoelastic solid damper are used in the examples.